Motion Planning Method, Device, Equipment and Storage Medium of Wheeled-Legged Robot

Abstract

The present application discloses a motion planning method, device, equipment and storage medium for a wheel-legged robot, relating to the technical field of robot control. The method includes: obtaining a target motion task planned for the wheel-legged robot; obtaining a constraint equation set corresponding to the target motion task, where the constraint equation set is constructed based on the floating-base dynamics model corresponding to the wheel-legged robot; optimizing a target function corresponding to the target motion task based on the constraint equation set to obtain a planned motion data sequence corresponding to the target motion task. By determining the constraint equation set required for the target motion task based on the floating-base dynamics model corresponding to the wheel-legged robot, and then implementing the motion planning of the wheel-legged robot based on this constraint equation set, through the technical solution provided by the embodiments of the present application, the arbitrary motion (such as sliding, jumping motion, etc.) planning of the wheel-legged robot can be realized, thus enriching the motion ability of the wheel-legged robot.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of robot control, and particularly to a motion planning method, device, equipment and storage medium for a wheel-legged robot. Background Art

[0002] With the development of robot control technology, some organizations and research institutions have successively launched a number of wheel-legged robots that can achieve hybrid motion of sliding and walking, such as bipedal wheel-legged robots, quadrupedal wheel-legged robots, etc.

[0003] Taking the bipedal wheel-legged robot as an example, most of the current research on bipedal wheel-legged robots focuses on the design of the body structure, and relatively little research has been done on its motion control, resulting in the current bipedal wheel-legged robots basically only having the motion ability of sliding. Summary of the Invention

[0004] The embodiments of the present application provide a motion planning method, device, equipment and storage medium for a wheel-legged robot, which can enrich the motion ability of the wheel-legged robot. The technical solutions are as follows:

[0005] According to one aspect of the embodiments of the present application, a motion planning method for a wheel-legged robot is provided, and the method includes:

[0006] Obtain the target motion task planned for the wheel-legged robot;

[0007] Obtain the constraint equation set corresponding to the target motion task, where the constraint equation set is constructed based on the floating base dynamics model corresponding to the wheel-legged robot, and the constraint equation set includes constraint equations under at least one constraint condition, and the constraint equations are used to constrain the wheel-legged robot to execute the target motion task;

[0008] Optimize the objective function corresponding to the target motion task based on the constraint equation set to obtain the planned motion data sequence corresponding to the target motion task; wherein, the planned motion data sequence includes the planned motion data of the wheel-legged robot at multiple time points.

[0009] According to one aspect of the embodiments of the present application, a motion planning device for a wheel-legged robot is provided, and the device includes:

[0010] A motion task acquisition module, configured to obtain the target motion task planned for the wheel-legged robot;

[0011] A constraint equation acquisition module, configured to acquire a constraint equation set corresponding to the target motion task, where the constraint equation set is constructed based on a floating base dynamics model corresponding to the wheel-legged robot, the constraint equation set includes constraint equations under at least one constraint condition, and the constraint equations are used to constrain the wheel-legged robot to execute the target motion task;

[0012] A planning data acquisition module, configured to optimize an objective function corresponding to the target motion task based on the constraint equation set to obtain a planned motion data sequence corresponding to the target motion task; wherein, the planned motion data sequence includes planned motion data of the wheel-legged robot at multiple time points.

[0013] According to one aspect of the embodiments of the present application, there is provided a computer device, which includes a processor and a memory. At least one instruction, at least one program, a code set or an instruction set is stored in the memory, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by the processor to implement the above-mentioned motion planning method of the wheel-legged robot.

[0014] According to one aspect of the embodiments of the present application, there is provided a computer-readable storage medium, in which at least one instruction, at least one program, a code set or an instruction set is stored, and the at least one instruction, the at least one program, the code set or the instruction set is loaded and executed by a processor to implement the above-mentioned motion planning method of the wheel-legged robot.

[0015] According to one aspect of the embodiments of the present application, there is provided a computer program product or a computer program, which includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the above-mentioned motion planning method of the wheel-legged robot.

[0016] The technical solutions provided by the embodiments of the present application at least include the following beneficial effects:

[0017] By means of the constraint equations constructed based on the floating-base dynamics model corresponding to the wheel-legged robot, the constraint equation set that the wheel-legged robot needs to satisfy in the target motion task is determined. Furthermore, based on the constraint equation set, the planned motion data of the wheel-legged robot in the target motion task is determined, realizing the motion planning of the wheel-legged robot. By adopting the technical solution provided in the embodiment of the present application, arbitrary motion planning of the wheel-legged robot can be realized, such as motions like sliding, conventional jumping, and flipping, etc., thereby making the motion planning method of the wheel-legged robot universal. At the same time, the wheel-legged robot has motion capabilities such as flipping and jumping, enriching the motion capabilities of the wheel-legged robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 is a schematic structural diagram of a biped wheel-legged robot provided by an embodiment of the present application;

[0020] Figure 2 is a flowchart of a motion planning method for a wheel-legged robot provided by an embodiment of the present application;

[0021] Figure 3 and Figure 4 is a schematic diagram of a full-body dynamics model provided by an embodiment of the present application;

[0022] Figure 5 and Figure 6 is a schematic diagram of a variable-leg-length wheeled inverted pendulum model provided by an embodiment of the present application;

[0023] Figure 7 is a schematic diagram of a wheel-legged robot performing a flipping motion task provided by an embodiment of the present application;

[0024] Figure 8 is a block diagram of a motion planning device for a wheel-legged robot provided by an embodiment of the present application;

[0025] Figure 9 is a simplified structural block diagram of a computer device provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] To make the objectives, technical solutions, and advantages of the present application clearer, the following will further describe the embodiments of the present application in detail in conjunction with the drawings.

[0027] Artificial Intelligence (AI) is the theory, method, technology, and application system that uses digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use knowledge to obtain the best results. In other words, artificial intelligence is a comprehensive technology in computer science that attempts to understand the essence of intelligence and produce a new intelligent machine that can react in a way similar to human intelligence. Artificial intelligence also studies the design principles and implementation methods of various intelligent machines, enabling machines to have the functions of perception, reasoning, and decision-making.

[0028] Artificial intelligence technology is an interdisciplinary subject that involves a wide range of fields, including both hardware-level and software-level technologies. The basic technologies of artificial intelligence generally include technologies such as sensors, dedicated artificial intelligence chips, cloud computing, distributed storage, big data processing technology, operation / interaction systems, and mechatronics. The software technologies of artificial intelligence mainly include several major directions such as computer vision technology, speech processing technology, natural language processing technology, and machine learning / deep learning.

[0029] The technical solution of this application mainly relates to robotics in artificial intelligence technology, and mainly relates to robot intelligent control. A robot is a mechatronic device that combines mechanical transmission and modern microelectronics technology and can imitate a certain skill of a human. Robots are developed on the basis of electronics, mechanics, and information technology. A robot does not necessarily have to look like a human. As long as it can autonomously complete the tasks and commands given by humans, it belongs to the family of robots. A robot is an automated machine that has some intelligent capabilities similar to those of humans or living organisms, such as perception ability, planning ability, motion ability, and cooperation ability. It is an automated machine with high flexibility. With the development of computer technology and artificial intelligence technology, robots have been greatly improved in terms of function and technology level. Mobile robots and technologies such as the vision and touch of robots are typical representatives.

[0030] The motion planning method of the wheel-legged robot provided by the embodiment of this application is universal and can be applied to any motion planning of the wheel-legged robot. At the same time, it can enrich the motion capabilities of the wheel-legged robot. For example, based on the constraint equations corresponding to the target motion tasks (such as motion tasks like sliding, flipping, and regular jumping), the planned motion data sequence of the target motion task is determined, so that the wheel-legged robot can achieve the target motion task (such as motion tasks like sliding, flipping, and regular jumping) based on the planned motion data sequence.

[0031] In the method provided by the embodiments of the present application, the execution subject of each step may be a computer device, which refers to an electronic device with data calculation, processing, and storage capabilities. The computer device may be a PC (Personal Computer) device such as a desktop computer or a laptop computer; it may also be a server. Among them, the server may be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. Optionally, the computer device and the wheel-legged robot may be connected through physical lines, networks, etc. For example, the computer device sends the planned motion data sequence corresponding to the target motion task to the wheel-legged robot. Optionally, the computer device and the wheel-legged robot may also not be connected. For example, the computer device plans the target motion task offline, obtains the corresponding planned motion data sequence, and then transfers the planned motion data sequence to the wheel-legged robot in a storage, burning, or other manner. Optionally, the planned motion data sequence corresponding to the target motion task may be planned offline by the computer device or generated online by the wheel-legged robot, and the embodiments of the present application do not limit this here.

[0032] In one example, the wheel-legged robot may include a floating body and legs with active wheels (i.e., the feet are active wheels). The legs with active wheels enable the wheel-legged robot to walk and move in a wheeled manner. Optionally, the wheel-legged robot may further include a controllable tail, which can be used to balance the wheel-legged robot and assist the wheel-legged robot in moving. For example, the tail can assist the wheel-legged robot in moving during the airborne phase. Optionally, the wheel-legged robot may further include a controllable robotic arm, which can be used to perform operation tasks such as carrying and picking up. The wheel-legged robot may include a bipedal wheel-legged robot, a quadrupedal wheel-legged robot, etc., and the embodiments of the present application do not limit this here.

[0033] Exemplarily, as Figure 1 shown, it exemplarily shows a schematic structural diagram of a bipedal wheel-legged robot. Figure 1(a) and (b) in the figure are schematic diagrams of the structure of the bipedal legged robot 100 at different viewing angles. The bipedal legged robot 100 may include: a floating body 101, a tail 102, a leg 103 and a driving wheel 104. One end of the leg 103 is connected to the floating body 101, and the other end is connected to the driving wheel 104. The floating body 101 is equipped with a power supply device, which can be used to provide power to the driving wheel 104, the tail 102 and the driving joints of the leg 103. The leg 103 is a parallel structure leg (the two legs of the bipedal legged robot 100 are balanced), which includes 5 joints and has a total of 2 rotational degrees of freedom. The posture of the floating body 101 can be adjusted by adjusting the leg 103. Among them, compared with the serial structure leg, the parallel structure leg can have stronger rigidity and can withstand the impact of movements with a flying phase (such as somersaults, conventional jumps, etc.). The driving wheel 104 can provide the wheel-legged robot 100 with the ability to slide. The tail 102 is connected to the floating body 101. A passive wheel can be installed on the tail 102. The tail 102 includes one rotational degree of freedom, and the balance and posture of the bipedal wheel-legged robot 100 can be adjusted by adjusting the position of the tail 102.

[0034] Please refer to Figure 2 , which shows a flow chart of a motion planning method for a wheel-legged robot provided by an embodiment of the present application. The execution subject of each step of the method may be the above-mentioned computer device, such as a processor provided in the computer device. The method may include the following steps (201-203):

[0035] Step 201, obtaining a target motion task planned for a wheel-legged robot.

[0036] In the embodiment of the present application, the target motion task can be any motion task. For example, the target motion task can be a sliding motion task or a jumping motion task. Optionally, the target motion task can also include multiple motions. For example, a target motion task can include sliding motion and jumping motion, which is not limited in the embodiment of the present application. Among them, jumping motion includes conventional jumping motion and somersault motion, conventional jumping motion refers to a jumping motion of the wheel-legged robot without flipping, and somersault motion refers to a jumping motion of the wheel-legged robot with flipping.

[0037] Optionally, different target motion tasks can be divided into at least one stage. For example, a gliding motion task may only include one stage: the gliding stage; a conventional jumping motion task and a flip motion task can be divided into three stages: the takeoff stage, the airborne stage, and the landing stage. Optionally, the target motion task can also be divided into two stages, four stages, etc., which are not limited in the embodiments of the present application. Among them, the takeoff stage and the landing stage refer to the stages when the wheel-legged robot is in contact with the bearing surface, and the airborne stage refers to the stage when the wheel-legged robot is out of contact with the bearing surface.

[0038] In one example, the setting method corresponding to a conventional jumping motion or a flip motion can be as follows: when the jumping motion task is a conventional jumping motion task, set the rolling angle of the floating body of the wheel-legged robot at the starting moment of the landing stage to be greater than -180 and less than 180; or, when the jumping motion task is a flip motion task, set the rolling angle of the floating body of the wheel-legged robot at the starting moment of the landing stage to be less than -180 or greater than 180. Among them, if at the end moment of the landing stage, the rolling angle of the floating body is greater than -180 and less than 180, it indicates that the floating body has not flipped (for example, the floating base body swings normally left and right with the vertical direction as the reference), that is, the target motion is a conventional jumping motion. If at the end moment of the landing stage, the rolling angle of the floating body is less than -180 or greater than 180, it means that the floating body has flipped, that is, the jumping motion is a flip motion.

[0039] Optionally, the floating body refers to the torso of the wheel-legged robot. The rolling angle can refer to the difference between the pitch angle of the floating base at the initial moment of the landing stage and the pitch angle of the floating base at the end moment of the takeoff stage. For example, at the end moment of the takeoff stage, the pitch angle of the floating base is 0, that is, the floating body of the wheel-legged robot remains vertical. At the initial moment of the landing stage, the pitch angle of the floating base is 360, that is, the floating body of the wheel-legged robot still remains vertical, but the rolling angle is 360, which means that the wheel-legged robot has flipped one circle. Optionally, the rolling angle can be the angle corresponding to multiple flips. If the rolling angle is negative, it indicates that the floating body rotates reversely. If the rolling angle is positive, it indicates that the floating body rotates forward, which is not limited in the embodiments of the present application.

[0040] Step 202, obtain a constraint equation set corresponding to the target motion task. The constraint equation set is constructed based on the floating base dynamics model of the wheel-legged robot. The constraint equation set includes constraint equations under at least one constraint condition, and the constraint equations are used to constrain the wheel-legged robot to execute the target motion task.

[0041] In the embodiments of the present application, the constraint equations can be used to represent the relationships between the model parameters corresponding to the floating-base dynamic model, and such relationships can refer to the constraint relationships between the model parameters under the constraint conditions. The constraint conditions refer to the constraint conditions that need to be satisfied during the movement of the wheel-legged robot, and they can constrain the movement of the wheel-legged robot. Optionally, the system of constraint equations can include multiple constraint equations.

[0042] Exemplarily, taking the target motion task as a jumping motion task as an example. Since the jumping motion task can include a takeoff stage, a flight stage, and a landing stage, the system of constraint equations corresponding to the jumping motion task can include: the constraint equation corresponding to the takeoff stage, the continuity constraint equation between the takeoff stage and the flight stage, the constraint equation corresponding to the flight stage, the continuity constraint equation between the flight stage and the landing stage, and the constraint equation corresponding to the landing stage.

[0043] Optionally, the constraint equations corresponding to the floating-base dynamic model are designed by designers and stored in a database, and can be directly called when it is necessary to plan the target motion task.

[0044] The floating-base dynamic model refers to a planar model with a floating base simplified from the wheel-legged robot. This floating-base dynamic model can include the simplified legs of the wheel-legged robot, the driving wheels on the legs, and the floating body. Optionally, this floating-base dynamic model can also include simplified adjustment structures (such as tails and manipulators, etc.).

[0045] In one example, the wheel-legged robot can be simplified into a full-body dynamic model to reduce the complexity of the motion planning problem. The simplification process can be as follows: When the wheel-legged robot does not include adjustment mechanisms (such as tails, manipulators, etc.), the floating body can be simplified into a single rigid body. Since the legs of the wheel-legged robot are parallel-structured legs, they can be disassembled into two moving link chains (i.e., the first virtual leg and the second virtual leg below), each of the two moving link chains has a driving joint, and a closed chain is formed between the two moving link chains, that is, the two moving link chains constrain each other's motion. When the wheel-legged robot includes adjustment mechanisms but the adjustment structures are fixed, the adjustment mechanisms and the floating body can be simplified into a single rigid body. When the wheel-legged robot includes adjustment mechanisms and the adjustment structures are moving, the adjustment mechanisms can be regarded as controllable rigid bodies connected to the floating body.

[0046] Exemplarily, refer to Figure 3, when the wheel-legged robot does not include an adjustment mechanism or includes an adjustment structure but the adjustment structure is fixed, the wheel-legged robot is simplified to a full-body dynamics model 300. The floating-base dynamics model 300 includes a floating body 304, driving wheels 301, and a first virtual leg 302 and a second virtual leg 303 having a parallel relationship. Among them, the first ends of the upper limbs of the first virtual leg 302 and the second virtual leg 303 are respectively connected to the floating body 304; the second end of the upper limb of the first virtual leg 302 is connected to the first end of the lower limb of the first virtual leg 302, and the second end of the upper limb of the second virtual leg 303 is connected to the first end of the lower limb of the second virtual leg 303; the second ends of the lower limbs of the first virtual leg 302 and the second virtual leg 303 are respectively connected to the driving wheels 301.

[0047] The first virtual leg 302 and the second virtual leg 303 represent the legs of the wheel-legged robot. Among them, the upper and lower limbs of the first virtual leg 302 and the upper and lower limbs of the second virtual leg 303 form a closed-chain structure, that is, the first virtual leg 302 and the second virtual leg 303 are mutually constrained in motion. Figure 3 The length of the dotted line in [reference] is 0, which means that in the actual motion process, the end of the lower limb of the second virtual leg 303 coincides with the end of the lower limb of the first virtual leg 302, forming a closed-chain constraint, that is, it is necessary to adjust the position (such as height) of the floating body 304 by correlatively adjusting the second virtual leg 303 and the first virtual leg 302.

[0048] The driving wheels 301 represent the feet of the wheel-legged robot. Optionally, when the wheel-legged robot does not include an adjustment structure, the floating body 304 represents the floating body of the wheel-legged robot; when the wheel-legged robot includes an adjustment structure and the adjustment structure is fixed, the floating body 304 represents the floating body and the adjustment mechanism of the wheel-legged robot.

[0049] Exemplarily, refer to Figure 4, when the wheel-legged robot includes an adjustment structure and the adjustment structure moves, the wheel-legged robot is simplified to a full-body dynamics model 400, which includes a floating body 404, a driving wheel 401, a first virtual leg 402 and a second virtual leg 403 having a parallel relationship, and an adjustment mechanism 405 connected to the floating body 404. The adjustment structure 405 represents the adjustment mechanism of the wheel-legged robot. Among them, the first end of the upper limb of the first virtual leg 402 and the first end of the upper limb of the second virtual leg 403 are respectively connected to the floating body 404; the second end of the upper limb of the first virtual leg 402 is connected to the first end of the lower limb of the first virtual leg 402, and the second end of the upper limb of the second virtual leg 403 is connected to the first end of the lower limb of the second virtual leg 403; the second ends of the lower limbs of the first virtual leg 402 and the second virtual leg 403 are respectively connected to the driving wheel 401. The adjustment mechanism 405 can be, for example, a tail, a robotic arm, etc., which can be used to adjust the posture of the wheel-legged robot. Optionally, during the movement of the wheel-legged robot, it can also be used to adjust the balance of the wheel-legged robot.

[0050] In another example, the wheel-legged robot can be simplified to a variable-leg-length wheeled inverted pendulum model. The simplification process can be as follows: when the wheel-legged robot does not include an adjustment mechanism, the floating body can be simplified to a single rigid body. Since the legs of the wheel-legged robot are light, the legs of the wheel-legged robot can be simplified to a telescopic rod that can apply an active force. When the wheel-legged robot includes an adjustment mechanism but the adjustment structure is fixed, the adjustment mechanism and the floating body can be simplified to a single rigid body. When the wheel-legged robot includes an adjustment mechanism and the adjustment structure moves, the adjustment mechanism can be regarded as a rigid body connected to the floating body.

[0051] Exemplarily, referring to Figure 5, when the wheel-legged robot does not include an adjustment mechanism or includes an adjustment structure but the adjustment structure is fixed, the wheel-legged robot is simplified to a variable-leg-length wheeled inverted pendulum model 500. The variable-leg-length wheeled inverted pendulum model 500 includes a virtual leg 502 with variable leg length, a driving wheel 501 connected to the first end of the virtual leg 502, and a floating body 503 connected to the second end of the virtual leg 502. The virtual leg 502 is used to represent the leg of the wheel-legged robot. Considering that the position (such as height) of the floating body can be adjusted by adjusting the joints of the leg, the virtual leg 502 can be represented as a telescopic rod, that is, by adjusting the length of the rod, the position (such as height) of the floating body can be changed. The driving wheel 501 represents the foot of the wheel-legged robot. The floating body 503 represents the floating body of the wheel-legged robot. Optionally, when the wheel-legged robot does not include an adjustment structure, the floating body 503 represents the floating body of the wheel-legged robot; when the wheel-legged robot includes an adjustment structure but the adjustment structure is fixed, the floating body 503 represents the floating body and the adjustment mechanism of the wheel-legged robot.

[0052] Exemplarily, referring to Figure 6 , when the wheel-legged robot includes an adjustment structure and the adjustment structure moves, in addition to including a virtual leg 602 with variable leg length, a driving wheel 601 connected to the first end of the virtual leg 602, and a floating body 603 connected to the second end of the virtual leg 602, the variable-leg-length wheeled inverted pendulum model 600 further includes an adjustment mechanism 604 connected to the floating body 603. The adjustment structure 604 represents the adjustment mechanism of the wheel-legged robot, such as a tail, a robotic arm, etc., which can be used to adjust the posture of the wheel-legged robot. Optionally, during the movement of the wheel-legged robot, it can also be used to adjust the balance of the wheel-legged robot.

[0053] Optionally, the bearing surface can be used as the floating base of the floating-base dynamics model. The bearing surface can refer to the plane that provides support for the wheel-legged robot, such as the ground in the real scene. Optionally, a world coordinate system can also be established with the horizontal direction flush with the bearing surface and the vertical direction perpendicular to the bearing surface. The movement, position, posture, etc. of the wheel-legged robot can be described based on the world coordinate system. Optionally, the world coordinate system can be set at the starting position of the movement of the wheel-legged robot. For example, referring to Figure 3 , the world coordinate system is set at the lower left corner of the full-body dynamics model 300.

[0054] Step 203, optimize the objective function corresponding to the target motion task based on the constraint equations to obtain the planned motion data sequence corresponding to the target motion task; wherein, the planned motion data sequence includes the planned motion data of the wheel-legged robot at multiple time points.

[0055] Among them, the planned motion data sequence includes the state variables and control variables of the wheel-legged robot at each moment in the target motion task. For example, the planned motion data sequence includes the planned generalized coordinates, planned generalized velocities, and planned control variables of the wheel-legged robot at each moment in the target motion task, that is, it can include the center position of the planned driving wheel, the speed corresponding to the center position of the planned driving wheel, the rotation angle of the planned driving wheel, the rotation speed of the planned driving wheel, the leg length of the planned virtual leg, the pitch angle of the planned floating fuselage, the execution torque of the planned driving wheel, the active force of the planned virtual leg, etc. (the parameters involved in this embodiment will be introduced in detail below).

[0056] Exemplarily, taking the target motion task including multiple stages as an example, the acquisition process of the planned motion data sequence can be as follows: optimize the objective function based on the constraint equations corresponding to each stage included in the constraint equation set and the constraint equations between adjacent stages.

[0057] Optionally, the objective function can be set based on the optimization objective corresponding to the target motion task. For example, based on the objective function, a planned motion data sequence with the least energy consumption required for the target motion task can be obtained; alternatively, based on the objective function, a planned motion data sequence with the shortest motion path for the target motion task can be obtained; furthermore, based on the objective function, a planned motion data sequence corresponding to the jumping motion task with the farthest jump or the highest jump can be obtained, which is not limited in this embodiment of the present application.

[0058] Exemplarily, taking the acquisition of the planned motion data sequence with the least energy consumption required as an example. Set the objective function as the sum of the squares of the control variables of the wheel-legged robot at each moment in the target motion task, and perform minimization processing on this objective function based on the constraint equation set, and a planned motion data sequence with the least energy consumption required for the target motion task can be obtained. The objective function can be expressed as follows:

[0059]

[0060] Among them, u refers to the control variable (the control variable includes the execution force or execution torque of each driving joint of the wheel-legged robot), t i，s is the starting moment of the i-th stage of the target motion task, t i，e is the ending moment of the i-th stage of the target motion task, and N is the number of stages included in the target motion task.

[0061] Optionally, a hierarchical optimization method can also be adopted to obtain the planned motion data sequence corresponding to the target motion task. The specific content is as follows: First, the upper limit and lower limit of the control quantity are respectively relaxed to k1 times the original value, and the upper limit and lower limit of the generalized velocity corresponding to the generalized coordinates are relaxed to k2 times the original value (to improve the actuator performance of the wheel-legged robot). k1 and k2 are greater than 1. The feasible solution of the constraint equation system of the target motion task is obtained, and then the objective function is optimized based on the obtained feasible solution to obtain the planned motion data sequence in the state where the actuator performance of the wheel-legged robot is improved. Finally, based on the original upper limit and lower limit of the control quantity, and the original upper limit and lower limit of the generalized velocity corresponding to the generalized coordinates, the planned motion data sequence in the normal state of the actuator performance is optimized starting from the vicinity of the planned motion data sequence in the state where the actuator performance of the wheel-legged robot is improved. The embodiment of the present application reduces the calculation amount of the objective function by screening the feasible solution, and improves the acquisition efficiency of the planned motion data sequence.

[0062] Optionally, different objective functions can be set for different target motion tasks according to actual needs, or the objective function of the target motion task can be adaptively adjusted according to actual needs. Different objective functions can also be set for different stages of the target motion task, that is, the corresponding objective function is optimized based on the constraint equation of the target stage according to actual needs to obtain the planned motion data sequence of the target stage. The embodiment of the present application does not limit this here.

[0063] Optionally, after obtaining the planned motion data sequence corresponding to the target motion task, it can be sent to the wheel-legged robot, and the wheel-legged robot stores it in its own memory. If the wheel-legged robot receives an execution instruction for the target motion task (the execution instruction can be given manually or obtained by the wheel-legged robot through environmental detection and judgment), it reads the planned motion data sequence corresponding to the target motion task from the memory, adjusts the planned motion data sequence based on the current state quantity of the wheel-legged robot, and outputs the control torque of the wheel-legged robot based on the adjusted planned motion data sequence so that the wheel-legged robot executes the target motion task. Optionally, during the motion of the wheel-legged robot, the combined method of feedforward control and PD (Proportion-Derivative) control can be used to track the adjusted planned motion data sequence, or WBC (Whole Body Control) can be used to track the adjusted planned motion data sequence. The embodiment of the present application does not limit this here.

[0064] In summary, the technical solution provided by the embodiments of the present application determines the constraint equations that the wheel-legged robot needs to satisfy in the target motion task through the constraint equations constructed based on the floating-base dynamics model corresponding to the wheel-legged robot, and then determines the planned motion data of the wheel-legged robot in the target motion task based on the constraint equations, realizing the motion planning of the wheel-legged robot. By adopting the technical solution provided by the embodiments of the present application, arbitrary motion planning of the wheel-legged robot can be realized, such as sliding, conventional jumping, flipping and other motions, so that the motion planning method of the wheel-legged robot has universality, and at the same time, the wheel-legged robot has motion capabilities such as flipping and jumping, enriching the motion capabilities of the wheel-legged robot.

[0065] In addition, by simplifying the wheel-legged robot into a full-body dynamics model and determining the constraint equations of the wheel-legged robot in motion based on this model, and then determining the planned motion data of the wheel-legged robot in motion based on the constraint equations, the motion planning of the wheel-legged robot is realized. Since this model can truly reflect parameters such as the leg structure, leg pose, and leg driving force of the wheel-legged robot, accurate planned motion data can be obtained, and thus the accuracy of the motion planning of the wheel-legged robot can be improved.

[0066] In addition, by simplifying the wheel-legged robot into a variable-leg-length wheeled inverted pendulum model and determining the constraint equations of the wheel-legged robot in motion based on this model, and then determining the planned motion data of the wheel-legged robot in motion based on the constraint equations, the motion planning of the wheel-legged robot is realized. Since the structure and parameters of this model are not complex, the difficulty of the motion planning of the wheel-legged robot is reduced, and the efficiency of the motion planning of the wheel-legged robot is improved.

[0067] In an exemplary embodiment, when the wheel-legged robot is simplified into a full-body dynamics model, the model parameters of the floating-base dynamics model may include at least one of the following: the generalized coordinates, control quantities, bearing surface forces, and closed-loop forces of the floating-base dynamics model;

[0068] Exemplarily, when the full-body dynamics model does not include an adjustment mechanism or includes an adjustment mechanism but the adjustment mechanism is fixed, the model parameters of the full-body dynamics model may include generalized coordinates, control quantities, bearing surface forces, and closed-loop forces. Among them, the generalized coordinates are used to describe the pose of the floating-base dynamics model, and the generalized coordinates include the central position of the floating body, the pitch angle of the floating body, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, and the rotation angle of the active wheel.

[0069] The control quantities are used to control the first virtual leg, the second virtual leg, and the driving wheels. The control quantities include the execution torque of the driving joints of the first virtual leg, the execution torque of the driving joints of the second virtual leg, and the execution torque of the driving wheels.

[0070] The reaction force of the bearing surface is used to describe the force exerted by the bearing surface on the floating base dynamics model. The reaction force of the bearing surface includes the frictional force and the supporting force exerted by the bearing surface on the wheel-legged robot.

[0071] The closed-loop acting force is used to describe the binding force between the first virtual leg and the second virtual leg. The closed-loop acting force includes the binding force between the first virtual leg and the second virtual leg.

[0072] Among them, the generalized coordinates may include the position parameters of the whole-body dynamics model (such as the position of the floating body) and the rotation parameters (such as the pitch angle of the floating body), etc. Through these parameters, the pose (i.e., position and orientation) of the whole-body dynamics model can be described. The control quantities may include the execution force or execution torque of each joint in the whole-body dynamics model. For example, the execution torque of the driving wheels, the execution torque of the driving joints of the first virtual leg, etc. Through the execution force or execution torque of each joint, the movement of each joint of the wheel-legged robot can be controlled. The reaction force of the bearing surface can be decomposed into the acting force in the horizontal direction (i.e., the frictional force between the bearing surface and the wheel-legged robot) and the acting force in the vertical direction (i.e., the supporting force of the bearing surface on the wheel-legged robot). The closed-loop acting force may refer to the binding force of the second virtual leg on the first virtual leg (restricting the movement of the first virtual leg) when the first virtual leg is moving, which can also be understood as the pulling force of the first virtual leg on the second virtual leg. The closed-loop acting force may also refer to the binding force of the first virtual leg on the second virtual leg (restricting the movement of the second virtual leg) when the second virtual leg is moving. The closed-loop acting force may also refer to the acting force used to constrain the associated movement of the first virtual leg and the second virtual leg. In the embodiments of the present application, the reaction force of the bearing surface belongs to the external acting force of the wheel-legged robot, and the control quantities and the closed-loop acting force belong to the internal acting force of the wheel-legged robot.

[0073] For example, referring to Figure 3 , when the whole-body dynamics model includes a tail but the tail is fixed, (x, z) is the central position of the floating body 304, θ is the pitch angle of the floating body 304 in the world coordinate system (i.e., the angle by which the floating body 304 deviates from the z-axis), m B , I B , c B，x and c B，z are respectively the total mass, the total inertia, and the offset of the centroid position relative to the central position of the floating body 304 of the floating body 304 and the tail, m HF , I HF , c HF , l HFand q HF respectively refer to the mass, inertia, position of the center of mass relative to the driving joint, length, and rotation angle of the upper limb of the first virtual leg 302, m KF , I KF , c KF , l KF and q KF respectively refer to the mass, inertia, position of the center of mass relative to the driving joint, length, and rotation angle of the lower limb of the first virtual leg 302, m HB , I HB , c HB , l HB and q HB respectively refer to the mass, inertia, position of the center of mass relative to the driving joint, length, and rotation angle of the upper limb of the second virtual leg 303, m KB , I KB , c KB , l KB and q KB respectively refer to the mass, inertia, position of the center of mass relative to the driving joint, length, and rotation angle of the lower limb of the second virtual leg 303, m w , I w , q w and r are respectively the mass, inertia, rotation angle, and radius of the driving wheel 301.

[0074] Then the generalized coordinates can be expressed as follows:

[0075] q = (x, z, θ, q HF , q KF , q HB , q KB , q W ) T Equation (2)

[0076] where q is the generalized coordinate of the whole-body dynamics model.

[0077] The control variables can be expressed as follows:

[0078] u = (τ HF , τ HB , τ W ) T Equation (3)

[0079] where u is the control variable of the whole-body dynamics model, τ HF , τ HB and τ W are respectively the executive torques of the driving joints of the first virtual leg 302, the second virtual leg 303, and the driving wheel 301.

[0080] The reaction force of the bearing surface can be expressed as follows:

[0081] f c = (f c，x , f c，z ) T Equation (4)

[0082] where f c is the reaction force of the load-bearing surface of the whole-body dynamics model, and f c，x and f c，z represent the reaction forces of the load-bearing surface in the x and z directions (i.e., frictional force and supporting force), respectively.

[0083] The closed-loop acting force can be expressed as follows:

[0084] f L = (f L，x , f L，z ) T Equation (5)

[0085] where f L is the closed-loop reaction force of the whole-body dynamics model, and f L，x and f L，z represent the closed-loop acting forces in the x and z directions, respectively.

[0086] Exemplarily, when the whole-body dynamics model includes an adjustment mechanism and the adjustment mechanism is in motion, the model parameters of the whole-body dynamics model can include generalized coordinates, control quantities, load-bearing surface acting forces, and closed-loop acting forces. Among them, the generalized coordinates are used to describe the pose of the floating-base dynamics model, and the generalized coordinates include the central position of the floating body, the pitch angle of the floating body, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, the rotation angle of the driving wheel, and the rotation angle of the adjustment mechanism.

[0087] The control quantities are used to control the first virtual leg, the second virtual leg, and the driving wheel, and the control quantities include the execution torque of the driving joint of the first virtual leg, the execution torque of the driving joint of the second virtual leg, the execution torque of the driving wheel, and the execution torque of the adjustment mechanism.

[0088] The load-bearing surface reaction force is used to describe the acting force of the load-bearing surface on the floating-base dynamics model, and the load-bearing surface reaction force includes the frictional force and the supporting force of the load-bearing surface on the wheel-legged robot.

[0089] The closed-loop acting force is used to describe the binding force between the first virtual leg and the second virtual leg, and the closed-loop acting force includes the binding force between the first virtual leg and the second virtual leg.

[0090] For example, refer to Figure 4, (x, z) is the central position of the floating body 404, θ is the pitch angle of the floating body 404 in the world coordinate system, m B 、I B 、c B，x and c B，z are respectively the total mass, total inertia, and the offset of the center of mass position of the floating body 404 and the tail 405 relative to the central position of the floating body 404, m HF 、I HF 、c HF 、l HF and q HF are respectively the mass, inertia, the position of the center of mass relative to the drive joint, length, and rotation angle of the upper limb of the first virtual leg 402, m KF 、I KF 、c KF 、l KF and q KF are respectively the mass, inertia, the position of the center of mass relative to the drive joint, length, and rotation angle of the lower limb of the first virtual leg 402, m HB 、I HB 、c HB 、l HB and q HB are respectively the mass, inertia, the position of the center of mass relative to the drive joint, length, and rotation angle of the upper limb of the second virtual leg 403, m KB 、I KB 、c KB 、l KB and q KB are respectively the mass, inertia, the position of the center of mass relative to the drive joint, length, and rotation angle of the lower limb of the second virtual leg 403, m TU 、I TU 、c TU 、l TU and q TU are respectively the mass, inertia, the position of the center of mass relative to the drive joint, length, and rotation angle of the tail 405, m w 、I w 、q w and r are respectively the mass, inertia, rotation angle, and radius of the driving wheel 401.

[0091] Then the generalized coordinates can be expressed as follows:

[0092] q = (x, z, θ, q HF ,q KF ,q HB ,q KB ,q TU ,q W ) T Equation (6)

[0093] The control quantity can be expressed as follows:

[0094] u = (τ HF , τ HB , τ TU , T W ) T Equation (7)

[0095] where u is the control quantity of the whole-body dynamics model, and τ HF , τ HB , τ TU and τ W are the executive torques of the driving joints of the first virtual leg 402, the executive torques of the driving joints of the second virtual leg 403, the executive torque of the tail 405, and the executive torque of the driving wheel 401, respectively.

[0096] The reaction force of the bearing surface can be expressed as follows:

[0097] f c = (f c，x , f c，z ) T Equation (8)

[0098] The closed-loop acting force can be expressed as follows:

[0099] f L = (f L，x , f L，z ) T Equation (9)

[0100] In an exemplary embodiment, when the wheel-legged robot is simplified to a variable-leg-length wheeled inverted pendulum model, the construction process of the model parameters of the floating-base dynamics model can be as follows:

[0101] Optionally, when the variable-leg-length wheeled inverted pendulum model does not include an adjustment mechanism or includes an adjustment mechanism but the adjustment mechanism is fixed, the variable-leg-length wheeled inverted pendulum model can at least include generalized coordinates, a control quantity, and a reaction force of the bearing surface. The construction processes of the generalized coordinates, the control quantity, and the reaction force of the bearing surface can be as follows: Based on the central position of the driving wheel, the rotation angle of the driving wheel, the leg length of the virtual leg, and the pitch angle of the floating body, construct the generalized coordinates of the variable-leg-length wheeled inverted pendulum model; Based on the executive torque of the driving wheel and the active force of the virtual leg, construct the control quantity of the variable-leg-length wheeled inverted pendulum model; Based on the friction force and the supporting force of the bearing surface on the wheel-legged robot, construct the reaction force of the bearing surface of the variable-leg-length wheeled inverted pendulum model.

[0102] For example, referring to Figure 5When the variable-leg-length wheeled inverted pendulum model includes a tail but the tail is fixed, (x, z) is the center position of the driving wheel 501, φ is the rotation angle of the driving wheel 501 in the world coordinate system, m w and I w are the mass and inertia of the driving wheel 501 respectively, r is the radius of the driving wheel 501, m b and I b are the total mass and total inertia of the floating body 503 and the tail respectively, θ is the pitch angle of the floating body 503 (a single rigid body formed by the floating body and the tail) in the world coordinate, and l is the leg length of the virtual leg 502. Then the generalized coordinates can be expressed as follows:

[0103] q = (x, z, φ, l, θ) T Equation (10)

[0104] where q is the generalized coordinate of the variable-leg-length wheeled inverted pendulum model.

[0105] The control quantity can be expressed as follows:

[0106] u = (τ w , f l ) T Equation (11)

[0107] where u is the control quantity of the variable-leg-length wheeled inverted pendulum model, τ w is the execution torque of the driving wheel 501, and f l is the active force of the virtual leg 502.

[0108] The reaction force of the bearing surface can be expressed as follows:

[0109] f c = (f c，x , f c，z ) T Equation (12)

[0110] where f c is the reaction force of the bearing surface of the variable-leg-length wheeled inverted pendulum model, and f c，x and f c，z represent the reaction forces of the bearing surface in the x and z directions (i.e., frictional force and supporting force) respectively.

[0111] Optionally, when the variable-leg-length wheeled inverted pendulum model includes an adjustment mechanism and the adjustment mechanism is in motion, the construction processes of the generalized coordinates, control quantities, and bearing surface reaction forces of the variable-leg-length wheeled inverted pendulum model are as follows: Based on the central position of the driving wheel, the rotation angle of the driving wheel, the leg length of the virtual leg, the pitch angle of the floating body, and the rotation angle of the adjustment mechanism, the generalized coordinates of the variable-leg-length wheeled inverted pendulum model are constructed; Based on the executive torque of the driving wheel, the active force of the virtual leg, and the executive torque of the adjustment mechanism, the control quantities of the variable-leg-length wheeled inverted pendulum model are constructed; Based on the frictional force and support force of the bearing surface on the wheel-legged robot, the bearing surface reaction forces of the variable-leg-length wheeled inverted pendulum model are constructed.

[0112] For example, referring to Figure 6 , when the variable-leg-length wheeled inverted pendulum model includes an adjustment mechanism and the adjustment mechanism is in motion, (x, z) is the central position of the driving wheel 601, φ is the rotation angle of the driving wheel 601 in the world coordinate system, m w and I w are the mass and inertia of the driving wheel 601 respectively, r is the radius of the driving wheel 601, m b and I b are the total mass and total inertia of the floating body 603 and the tail 604 respectively, θ is the pitch angle of the floating body 603 in the world coordinate, l is the leg length of the virtual leg 602, h x and h z are the relative positions of the tail 604 and the center of the floating body 603, m t , I t , c t , l t and q t are the mass, inertia, distance from the center of mass to the driving joint of the tail 604, length, and rotation angle of the tail 604 respectively. Then the generalized coordinates can be expressed as follows:

[0113] q = (x, z, φ, l, θ, q t ) T Equation (13)

[0114] The control quantities can be expressed as follows:

[0115] u = (τ w , f l , τ t ) T Equation (14)

[0116] where, τ w is the executive torque of the driving wheel 601, f l is the active force of the virtual leg 602, τ t is the executive torque of the driving joint of the tail 604.

[0117] The reaction force of the bearing surface can be expressed as follows:

[0118] f c =(f c，x , f c，z ) T Equation (15)

[0119] By constructing the model parameters of the floating-base dynamics model in the embodiments of the present application, a basis is provided for the construction of the constraint equation (or system of constraint equations).

[0120] In an exemplary embodiment, the process of constructing the system of constraint equations can be as follows:

[0121] Optionally, in the case where the wheel-legged robot is simplified to a full-body dynamics model, the system of constraint equations is constructed based on the generalized coordinates, control quantities, bearing surface acting forces, and closed-loop acting forces of the floating-base dynamics model. The process of constructing the system of constraint equations can be as follows:

[0122] In the case where the target motion task includes only one stage, according to the generalized coordinates, control quantities, bearing surface reaction forces, and closed-loop acting forces of the floating-base dynamics model, the constraint equation corresponding to this one stage is determined, and the constraint equation corresponding to this one stage is the system of constraint equations of the target motion task.

[0123] In the case where the target motion task includes multiple stages, according to the generalized coordinates, control quantities, bearing surface reaction forces, and closed-loop acting forces of the floating-base dynamics model, the constraint equations corresponding to each of the multiple stages are determined; according to the generalized coordinates of the floating-base dynamics model, the continuity constraint equations between adjacent stages among the multiple stages are determined; based on the constraint equations corresponding to each of the multiple stages and the continuity constraint equations between adjacent stages, the system of constraint equations corresponding to the target motion task is constructed.

[0124] Optionally, in the case where the wheel-legged robot is simplified to a variable-leg-length wheeled inverted pendulum model, the system of constraint equations is constructed based on the generalized coordinates, control quantities, and bearing surface acting forces of the floating-base dynamics model. The process of constructing the system of constraint equations can be as follows:

[0125] In the case where the target motion task includes only one stage, according to the generalized coordinates, control quantities, and bearing surface reaction forces, the constraint equation corresponding to this one stage is determined, and the constraint equation corresponding to this one stage is the system of constraint equations of the target motion task.

[0126] In the case where the target motion task includes multiple stages, constraint equations corresponding to each of the multiple stages are determined according to the generalized coordinates, control quantities, and reaction forces of the bearing surface; constraint equations between adjacent stages among the multiple stages are determined according to the generalized coordinates; based on the constraint equations corresponding to each of the multiple stages and the constraint equations between adjacent stages, a constraint equation set for implementing the target motion task is determined.

[0127] Based on the model parameters of the floating-base dynamics model, the embodiments of the present application implement the construction of constraint equations or a constraint equation set.

[0128] In an exemplary embodiment, when a wheel-legged robot is simplified to a full-body dynamics model and the full-body dynamics model does not include an adjustment mechanism or includes an adjustment structure but the adjustment mechanism is fixed, the planning method for the jumping motion task of the wheel-legged robot may be as follows:

[0129] Construct a full-body dynamics model of the wheel-legged robot. The full-body dynamics model includes a floating body, driving wheels, and a first virtual leg and a second virtual leg having a parallel relationship; wherein, the first ends of the upper limbs of the first virtual leg and the second virtual leg are respectively connected to the floating body; the second end of the upper limb of the first virtual leg is connected to the first end of the lower limb of the first virtual leg, and the second end of the upper limb of the second virtual leg is connected to the first end of the lower limb of the second virtual leg; the second ends of the lower limbs of the first virtual leg and the second virtual leg are respectively connected to the driving wheels.

[0130] Based on the central position of the floating body, the pitch angle of the floating body, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, and the rotation angle of the driving wheel, generalized coordinates of the full-body dynamics model are constructed; based on the execution torque of the driving joint of the first virtual leg, the execution torque of the driving joint of the second virtual leg, and the execution torque of the driving wheel, control quantities of the full-body dynamics model are constructed; based on the friction force and support force of the bearing surface on the wheel-legged robot, reaction forces of the bearing surface of the full-body dynamics model are constructed; based on the binding force between the first virtual leg and the second virtual leg, closed-loop acting forces of the full-body dynamics model are constructed.

[0131] Exemplarily, the generalized coordinates can be expressed as the above formula (2), the control quantities can be expressed as the above formula (3), the reaction forces of the bearing surface can be expressed as the above formula (4), and the closed-loop acting forces can be expressed as the above formula (5).

[0132] Taking the jumping motion task as an example, the jumping motion task can be divided into three stages: the take-off stage, the airborne stage, and the landing stage. The constraint equations corresponding to the take-off stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the take-off stage, the friction constraint equation corresponding to the take-off stage, the anti-collision constraint equation corresponding to the take-off stage, the boundary constraint equation corresponding to the take-off stage, and the continuity constraint equation between the take-off stage and the airborne stage; the constraint equations corresponding to the airborne stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the airborne stage, the anti-collision constraint equation corresponding to the airborne stage, the boundary constraint equation corresponding to the airborne stage, and the continuity constraint equation between the airborne stage and the landing stage; the constraint equations corresponding to the landing stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the landing stage, the friction constraint equation corresponding to the landing stage, the anti-collision constraint equation corresponding to the landing stage, and the boundary constraint equation corresponding to the landing stage.

[0133] Optionally, the process of obtaining the constraint equations corresponding to the take-off stage can be as follows:

[0134] 1. Dynamic constraint equation.

[0135] In the embodiments of the present application, the dynamic constraint equation is obtained based on the dynamic equation of the wheel-legged robot. The dynamic constraint equation can be used to describe the constraint relationship between the generalized coordinates and generalized forces of the wheel-legged robot. Based on the dynamic constraint equation, the state variables of the wheel-legged robot can be constrained. Among them, the generalized force refers to the equivalent comprehensive force corresponding to the wheel-legged robot, that is, the equivalent force corresponding to the external force and the internal force. The state variables of the wheel-legged robot are used to describe the motion state of the wheel-legged robot, which can include generalized coordinates and the generalized velocities corresponding to the generalized coordinates. Optionally, the dynamic constraint equation can be represented based on the generalized velocity and the generalized acceleration corresponding to the generalized coordinates.

[0136] In one example, at least one of the above-mentioned constraint conditions may include a first constraint condition and a second constraint condition. The first constraint condition is used to limit the motion between the floating-base dynamics model and the bearing surface to pure rolling, and the second constraint condition is used to limit the closed-loop constraint to be satisfied between the first virtual leg and the second virtual leg of the floating-base dynamics model; the dynamic constraint equation corresponding to the takeoff stage is used to constrain the floating-base dynamics model to satisfy the first constraint condition, the second constraint condition, and the dynamic equation corresponding to the takeoff stage; wherein, the dynamic equation corresponding to the takeoff stage is constructed based on the generalized coordinates, control quantities, bearing surface reaction forces, and closed-loop acting forces of the floating-base dynamics model; the dynamic constraint equation corresponding to the airborne stage is used to constrain the floating-base dynamics model to satisfy the second constraint condition and the dynamic equation corresponding to the airborne stage; wherein, the dynamic equation corresponding to the airborne stage is constructed based on the generalized coordinates, control quantities, and closed-loop acting forces of the floating-base dynamics model; the dynamic constraint equation corresponding to the landing stage is used to constrain the floating-base dynamics model to satisfy the first constraint condition, the second constraint condition, and the dynamic equation corresponding to the landing stage; wherein, the dynamic equation corresponding to the landing stage is constructed based on the generalized coordinates, control quantities, bearing surface reaction forces, and closed-loop acting forces of the floating-base dynamics model.

[0137] Optionally, the determination process of the dynamic constraint equation may be as follows: Obtain the first constraint condition and the second constraint condition; Determine a first intermediate constraint equation based on the first constraint condition, and determine a second intermediate constraint equation based on the second constraint condition; wherein, the first intermediate constraint equation is used to represent that the acceleration of the contact point between the floating-base dynamics model and the bearing surface is 0, and the second intermediate constraint equation is used to represent that the acceleration difference of the closing point between the first virtual leg and the second virtual leg is 0; Based on the first intermediate constraint equation, the second intermediate constraint equation, and the dynamic equation corresponding to the takeoff stage, determine the dynamic constraint equation corresponding to the takeoff stage, and based on the first intermediate constraint equation, the second intermediate constraint equation, and the dynamic equation corresponding to the landing stage, determine the dynamic constraint equation corresponding to the landing stage; Based on the dynamic constraint equation corresponding to the airborne stage and the second intermediate constraint equation, determine the dynamic constraint equation corresponding to the airborne stage.

[0138] Exemplarily, the derivation process of the dynamic constraint equation may be as follows:

[0139] Based on the generalized coordinates and generalized velocities, calculate the total kinetic energy E and the total potential energy V corresponding to the whole-body dynamics model, then the Lagrangian of the system can be expressed as L = E - V. In the takeoff stage, the wheel-legged robot includes internal acting forces (i.e., the equivalent forces corresponding to the control quantities and the closed-loop acting forces) and external acting forces (i.e., the bearing surface reaction forces). According to the Lagrange equation, the dynamic equation corresponding to the takeoff stage can be obtained as follows:

[0140]

[0141] where q refers to the generalized coordinate, refers to the generalized velocity corresponding to the generalized coordinate, refers to the generalized acceleration corresponding to the generalized coordinate, u refers to the control quantity of the whole-body dynamics model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, S is the selection matrix, J C is the Jacobian matrix of the contact point between the active wheel and the bearing surface of the whole-body dynamics model, J L is the difference between the Jacobian matrices of the ends of the first virtual leg and the second virtual leg of the whole-body dynamics model.

[0142] During the takeoff phase, assuming pure rolling between the active wheel and the bearing surface, the acceleration of the contact point between the active wheel and the bearing surface in the world coordinate system is:

[0143]

[0144] Since the closed-chain constraint is satisfied between the first virtual leg and the second virtual leg, the acceleration difference of the closing point between the first virtual leg and the second virtual leg is 0, and the following expression can be obtained:

[0145]

[0146] Combining equations (16), (17) and (18) gives:

[0147]

[0148] Since D(q) is a square matrix and full rank, J C and J L are row full rank, so it can be judged that the first term on the left side of equation (19) is full rank, and the generalized acceleration, closed-loop force and bearing surface reaction force can be obtained as:

[0149]

[0150] Take the state quantity of the wheel-legged robot as Express the dynamic constraint equation in terms of the generalized velocity and generalized acceleration of the whole-body dynamics model, then there is:

[0151]

[0152] where Ab refers to the representation matrix of the generalized acceleration corresponding to the generalized coordinate, refers to the derivative of the state quantity of the floating-base dynamics model, q refers to the generalized coordinate, refers to the generalized velocity corresponding to the generalized coordinate, refers to the generalized acceleration corresponding to the generalized coordinate.

[0153] The dynamic constraint equations during the takeoff phase can be expressed as follows:

[0154]

[0155] where the matrix matrix A 1，up b1 refers to the product of the first n rows of matrix A1 and matrix b1, where n is the number of parameters in the generalized coordinates of the floating-base dynamic model, refers to the derivative of the state variables of the floating-base dynamic model, q refers to the generalized coordinates, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control variable of the floating-base dynamic model, D is the inertia matrix, C is the centrifugal and Coriolis force vector, G is the gravity vector, S represents the selection matrix, J C represents the Jacobian matrix of the contact point between the active wheel and the bearing surface of the floating-base dynamic model, J L is the difference between the Jacobian matrices of the ends of the first virtual leg and the second virtual leg of the floating-base dynamic model.

[0156] Furthermore, at any time t during the takeoff phase, the dynamic constraint equations can be expressed as follows:

[0157]

[0158] 2. Friction constraint equations.

[0159] In one example, the above at least one constraint condition may further include a third constraint condition, and the third constraint condition is used to constrain the bearing surface reaction force of the floating-base dynamic model to satisfy the friction cone; the friction constraint equations corresponding to the takeoff phase and the friction constraint equations corresponding to the landing phase are used to constrain the floating-base dynamic model to satisfy the third constraint condition.

[0160] where the friction constraint equation is constructed based on the friction cone constraint between the bearing surface and the wheel-legged robot, and the constraint on the generalized coordinates can be obtained by constraining the bearing surface reaction force. Optionally, the determination process of the friction constraint equation can be as follows: obtain the third constraint condition; based on the third constraint condition, linearize the bearing surface reaction force of the floating-base dynamic model to determine the friction constraint equation.

[0161] Exemplarily, the derivation process of the friction constraint equation can be as follows:

[0162] During the takeoff phase, based on the assumption of pure rolling, the bearing surface reaction force should satisfy the friction cone constraint. By linearizing the Coulomb friction of the bearing surface reaction force, the friction constraint equation can be obtained, and the friction constraint equation can be expressed as follows:

[0163]

[0164] Among them, the matrix matrix refers to the friction constraint matrix corresponding to the i-th driving wheel of the floating-base dynamic model, N C is the number of driving wheels, A 1，down b1 refers to the product of the last 2N C rows of matrix A1 and matrix b1, μ i is the friction coefficient corresponding to the i-th driving wheel, n c，i is the unit outer normal vector of the contact point between the i-th driving wheel and the bearing surface, o c，i is the unit tangent vector of the contact point between the i-th driving wheel and the bearing surface, q refers to the generalized coordinates of the floating-base dynamic model, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control quantity of the floating-base dynamic model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, S represents the selection matrix, J C represents the Jacobian matrix of the contact point between the driving wheel and the bearing surface, J L is the difference between the Jacobian matrices of the ends of the first virtual leg and the second virtual leg of the floating-base dynamic model.

[0165] Furthermore, at any moment t during the takeoff phase, the friction constraint equation can be expressed as follows:

[0166]

[0167] 3. Anti-collision constraint equation.

[0168] In one example, the above at least one constraint condition may further include a fourth constraint condition, and the fourth constraint condition is used to constrain that the mechanism of the floating-base dynamic model other than the driving wheel does not collide with the bearing surface; the anti-collision constraint equation corresponding to the takeoff phase, the anti-collision constraint equation corresponding to the airborne phase, and the anti-collision constraint equation corresponding to the landing phase are used to constrain the floating-base dynamic model to satisfy the fourth constraint condition.

[0169] Among them, the anti-collision constraint equation can be used to limit each parameter in the generalized coordinates, thereby forming a constraint on the generalized coordinates. Optionally, the determination process of the anti-collision constraint equation can be as follows; obtain the fourth constraint condition; based on the fourth constraint condition, perform constraint processing on the parameters in the generalized coordinates of the floating-base dynamic model to determine the anti-collision constraint equation.

[0170] Exemplarily, the derivation process of the anti-collision constraint equation can be as follows:

[0171] During the takeoff phase, the floating fuselage, the first virtual leg, the second virtual leg, the driving wheel, and the adjusting mechanism of the full-body dynamics model cannot be embedded below the ground. Therefore, the anti-collision constraint equations can be obtained as follows:

[0172]

[0173] where d is the number of connecting rods included in the floating base dynamics model, k and j are the numbers of adjacent connecting rods of the floating base dynamics model, (p j，x , p j，z ) and (p k，x , p k，z ) are the positions of two adjacent connecting rods in the world coordinate system respectively, z w refers to the coordinate of the driving wheel of the floating base dynamics model in the z-axis direction of the world coordinate system, x w refers to the coordinate of the driving wheel in the x-axis direction of the world coordinate system, r is the radius of the driving wheel, h m refers to the height function of any point in the world coordinate system, and α and β are range parameters.

[0174] Furthermore, when the full-body dynamics model does not include the adjustment structure or the adjusting mechanism is fixed, d = 6. Then, at any moment t during the takeoff phase, the anti-collision constraint equations can be expressed as follows:

[0175] p j，z (t)+α(p k，z (t)-p j，z (t))≥h m (p k，x (t)+α(p j，x (t)-p k，x (t))), α ∈ [0, 1], j, k ∈ [1, 6] Equation (26)

[0176] z w (t)+rcos(β)≥h m (x w (t)+rsin(β)), β ∈ [0, 2π]

[0177] 4. Boundary constraint equations.

[0178] In one example, the above at least one constraint condition may further include a fifth constraint condition, which is used to constrain the upper and lower limit values of the state variables of the floating base dynamics model, and the upper and lower limit values of the control variables of the floating base dynamics model; the boundary constraint equations corresponding to the takeoff phase, the boundary constraint equations corresponding to the airborne phase, and the boundary constraint equations corresponding to the landing phase are used to constrain the floating base dynamics model to satisfy the fifth constraint condition and the state variable constraints corresponding to the jumping motion task, and the state variable constraints are used to constrain the state variables of the floating base dynamics model.

[0179] Among them, the boundary constraint equation can be constructed based on the self-limitation of the wheel-legged robot, the physical characteristics of the motor, and the task settings corresponding to the target motion task (such as the state quantity constraint below), and it can be used to limit the state quantity and control quantity of the wheel-legged robot. The physical characteristics of the motor can be determined according to the measured motor torque and speed curves. Optionally, the determination process of the boundary constraint equation can be as follows: Obtain the fifth constraint condition and the state quantity constraint corresponding to the jumping motion task; Based on the fifth constraint condition and the state quantity constraint corresponding to the jumping motion task, determine the boundary constraint equation.

[0180] Exemplarily, the larger value between the lower limit value of the state quantity and the lower limit value corresponding to the state quantity constraint can be used as the lower limit value of the state quantity in the jumping motion task, and the smaller value between the upper limit value of the state quantity and the upper limit value corresponding to the state quantity constraint can be used as the upper limit value of the state quantity in the jumping motion task. When the state quantity constraint limits the state quantity at the target moment, the state quantity of the wheel-legged robot at that moment can be constrained based on the state quantity constraint at that moment, which is not limited in the embodiments of the present application.

[0181] The boundary constraint equation can be expressed as follows;

[0182] X(t) = X t

[0183] X min ≤ X(t) ≤ X max Equation (27)

[0184] u min ≤ u(t) ≤ u max

[0185] Among them, X max and X min respectively refer to the upper limit value and the lower limit value of the state quantity corresponding to the jumping motion task, u max and u min respectively refer to the upper limit value and the lower limit value of the control quantity corresponding to the jumping motion task, X t refers to the state quantity constraint at time t.

[0186] Exemplarily, assuming that the state quantity constraint limits the initial state quantity corresponding to the jumping motion task to be X 1，s , then at the initial moment of the takeoff stage, the state quantity of the wheel-legged robot satisfies the following constraints:

[0187] X(t) = X 1，s , t = t 1，s

[0188] Among them, t 1，s refers to the initial moment of the takeoff stage, and the state quantity and control quantity of the wheel-legged robot also need to satisfy:

[0189] Optionally, in the jumping motion task, the state variables corresponding to the initial moment of the takeoff phase and the end moment of the landing phase can be set, and based on this setting, the state variables at the remaining moments of the jumping motion task can be planned to implement the jumping motion task. The state variables at different moments in the jumping motion task can also be limited in combination with the actual application situation, which is not limited in this embodiment of the present application.

[0190] 5. Continuity constraint equation.

[0191] In an example, the continuity constraint equation between the takeoff phase and the airborne phase is used to constrain that the state variables of the floating base dynamics model at the end moment of the takeoff phase are the same as the state variables of the floating base dynamics model at the start moment of the airborne phase.

[0192] Among them, the continuity constraint equation is used to constrain the motion continuity between adjacent phases. Optionally, the determination process of the continuity constraint equation between the takeoff phase and the airborne phase can be as follows: obtain the state variables of the floating base dynamics model at the end moment of the takeoff phase and the state variables of the floating base dynamics model at the start moment of the airborne phase; based on the state variables of the floating base dynamics model at the end moment of the takeoff phase and the state variables of the floating base dynamics model at the start moment of the airborne phase, determine the continuity constraint equation between the takeoff phase and the airborne phase.

[0193] Exemplarily, the continuity constraint equation between the takeoff phase and the airborne phase can be expressed as follows:

[0194] X(t 1，e )=X(t 2，s ) Equation (28)

[0195] Among them, t 1，e and t 2，s respectively refer to the end moment of the takeoff phase and the start moment of the airborne phase.

[0196] Optionally, the acquisition process of the constraint equation corresponding to the airborne phase can be as follows:

[0197] 1. Dynamic constraint equation.

[0198] In the airborne phase, the wheel-legged robot includes internal acting forces, does not include external acting forces (i.e., bearing surface reaction forces), and still needs to ensure the closed-chain constraint between the first virtual leg and the second virtual leg. Then, according to the Lagrange equation, the dynamic equation corresponding to the airborne phase can be obtained:

[0199]

[0200] Combined with Equation (29), the dynamic constraint equation corresponding to the take-off phase is expressed as follows:

[0201]

[0202] where the matrix matrix A 2，up b2 refers to the product of the first n rows of matrix A2 and matrix b2, where n is the number of parameters in the generalized coordinates of the floating-base dynamic model, refers to the derivative of the state quantity of the floating-base dynamic model, q refers to the generalized coordinates of the floating-base dynamic model, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control quantity of the floating-base dynamic model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, S represents the selection matrix, and J L is the difference between the Jacobian matrices at the ends of the first virtual leg and the second virtual leg of the floating-base dynamic model.

[0203] Furthermore, at any time t during the take-off phase, the dynamic constraint equation can be expressed as follows:

[0204]

[0205] 2. Friction constraint equation.

[0206] During the take-off phase, since the whole-body dynamic model is disengaged from the bearing surface, the take-off phase does not involve the friction constraint equation.

[0207] 3. Anti-collision constraint equation.

[0208] During the take-off phase, since the floating body, the first virtual leg, the second virtual leg, the driving wheels, and the adjusting mechanism of the whole-body dynamic model cannot be embedded below the ground, the anti-collision constraint equation identical to the above Equation (25) can be obtained. Then, at any time t during the take-off phase, the anti-collision constraint equation can be expressed as the above Equation (26).

[0209] 4. Boundary constraint equation.

[0210] During the take-off phase, it is necessary to ensure that the state quantity of the whole-body dynamic model conforms to the state quantity constraint, the state quantity does not exceed the upper and lower limit values of the state quantity, and the control quantity of the whole-body dynamic model does not exceed the upper and lower limit values of the control quantity. Then, the boundary constraint equation during the take-off phase has the same form as the above Equation (27).

[0211] 5. Continuity constraint equation.

[0212] In one example, the above at least one constraint condition further includes a sixth constraint condition and a seventh constraint condition. The sixth constraint condition is used to restrict the inelastic collision between the floating-base dynamics model and the bearing surface during the landing phase, and the seventh constraint condition is used to represent the constraint relationship between the state quantities of the floating-base dynamics model before and after the landing collision; the continuity constraint equation between the airborne phase and the landing phase is used to constrain the floating-base dynamics model to satisfy the sixth constraint condition, the second constraint condition, the law of conservation of momentum, and the seventh constraint condition.

[0213] Optionally, the process of obtaining the continuity constraint equation between the airborne phase and the landing phase is as follows: Obtain the state quantity of the floating-base dynamics model at the end moment of the airborne phase, and obtain the state quantity of the floating-base dynamics model at the starting moment of the landing phase; Obtain the sixth constraint condition and the seventh constraint condition; Based on the sixth constraint condition, the second constraint condition, and the law of conservation of momentum, determine the generalized velocity of the floating-base dynamics model at the starting moment of the landing phase; Based on the state quantity of the floating-base dynamics model at the end moment of the airborne phase, the state quantity of the floating-base dynamics model at the starting moment of the landing phase, the generalized velocity of the floating-base dynamics model at the starting moment of the landing phase, and the seventh constraint condition, determine the continuity constraint equation between the airborne phase and the landing phase.

[0214] Exemplarily, the derivation process of the continuity constraint equation between the airborne phase and the landing phase can be as follows:

[0215] In the landing phase, assume that the full-body dynamics model and the bearing surface are in an inelastic collision, that is, the collision is completed instantaneously. According to the law of conservation of momentum, the following relationship is satisfied between the state quantity after the collision and the state quantity before the collision:

[0216]

[0217] Where, refers to the generalized velocity at the end moment of the airborne phase, q 2，e refers to the generalized coordinate at the end moment of the airborne phase, q 3，s refers to the generalized coordinate at the starting moment of the landing phase, refers to the generalized velocity at the starting moment of the landing phase, and q 2，e = q 3，s ,

[0218] At the starting moment of the landing phase, the velocity of the contact point between the driving wheel and the receiving surface is 0, and the closed-chain constraint is satisfied between the first virtual leg and the second virtual leg. Then there is:

[0219]

[0220] Combining Equation (32) and Equation (33) gives:

[0221]

[0222] Since D(q 2，e ) is a square matrix and full rank, and J C (q 2，e ) and J L (q 2，e ) are row full rank, it can be determined that the first term on the left side of Equation (34) is full rank. Then, the expressions for the generalized velocity, closed acting force, and bearing surface reaction force at the starting moment of the landing phase can be obtained as follows:

[0223]

[0224] Then, the continuity constraint equations between the airborne phase and the landing phase can be expressed as follows:

[0225]

[0226] Among them, the matrix matrix Q up p refers to the product of the first n rows of matrix Q and matrix p, where n is the number of parameters in the generalized coordinates of the floating base dynamics model. q 3，s refers to the generalized coordinates of the floating base dynamics model at the starting moment of the landing phase, refers to the generalized velocity of the floating base dynamics model at the starting moment of the landing phase. q 2，e refers to the generalized coordinates of the floating base dynamics model at the ending moment of the airborne phase, refers to the generalized velocity of the floating base dynamics model at the ending moment of the airborne phase. D is the inertia matrix, and J C represents the Jacobian matrix of the contact point between the active wheel of the floating base dynamics model and the bearing surface. J L is the difference between the Jacobian matrices of the ends of the first virtual leg and the second virtual leg of the floating base dynamics model.

[0227] Optionally, the process of obtaining the constraint equations corresponding to the landing phase can be as follows:

[0228] 1. Dynamic constraint equations.

[0229] During the landing phase, the wheeled-leg robot includes internal acting forces (i.e., the equivalent forces corresponding to the control quantity and the closed-loop acting force) and external acting forces (i.e., the bearing surface reaction force). Then, the dynamic equations in the landing phase are the same as those in the takeoff phase. Additionally, the same assumptions as in the takeoff phase are established: pure rolling between the active wheel and the bearing surface, and a closed-chain constraint is satisfied between the first virtual leg and the second virtual leg. Then, at any moment t during the landing phase, the dynamic constraint equations have the same form as Equation (22) above.

[0230] 2. Friction constraint equation.

[0231] During the landing phase, based on the assumption of pure rolling between the driving wheels and the bearing surface, the reaction force of the bearing surface should satisfy the friction cone constraint. Then, at any moment t during the landing phase, the friction constraint equation can be expressed as the above formula (24).

[0232] 3. Anti-collision constraint equation.

[0233] During the landing phase, the floating fuselage, the first virtual leg, the second virtual leg, the driving wheels and the adjusting mechanism of the whole-body dynamics model cannot be embedded below the ground. When the whole-body dynamics model does not include the adjusting structure or the adjusting mechanism is fixed, at any moment t during the landing phase, the anti-collision constraint equation has the same form as the above formula (26).

[0234] 4. Boundary constraint equation.

[0235] During the landing phase, it is necessary to ensure that the state variables of the whole-body dynamics model conform to the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the whole-body dynamics model do not exceed the upper and lower limit values of the control variables. Then, at any moment t during the landing phase, the boundary constraint equation has the same form as the above formula (27).

[0236] In summary, in the case of simplifying the wheel-legged robot into a whole-body dynamics model, if the whole-body dynamics model does not include the adjusting mechanism or includes the adjusting mechanism but the adjusting mechanism is fixed, the constraint equation set of the jumping motion task includes:

[0237] 1. Formulas (22), (24), (26), (27) and (28) corresponding to the take-off phase.

[0238] 2. Formulas (31), (26), (27) and (36) corresponding to the airborne phase.

[0239] 3. Formulas (22), (24), (26) and (27) corresponding to the landing phase.

[0240] Based on the constraint equations corresponding to the three phases of the jumping motion task, the objective function is optimized to obtain the planned motion data sequence corresponding to the jumping motion task.

[0241] Exemplarily, taking the example of obtaining the planned motion data sequence with the least required energy consumption. Based on equations (22), (24), (26), (27), and (28) corresponding to the take-off phase, equations (31), (26), (27), and (36) corresponding to the airborne phase, and equations (22), (24), (26), and (27) corresponding to the landing phase, equation (1) is minimized to obtain the planned motion data at each time point in the jumping motion task.

[0242] By adopting the technical solution provided by the embodiment of the present application, it is realized to plan the jumping motion tasks (such as conventional jumping motion tasks and flip motion tasks) of the wheel-legged robot based on the whole-body dynamics model when there is no adjustment mechanism or the adjustment mechanism is fixed (i.e., regarding the adjustment structure and the floating fuselage as a rigid body).

[0243] In an exemplary embodiment, when the wheel-legged robot is simplified to a whole-body dynamics model and the adjustment mechanism is included in the whole-body dynamics model and the adjustment mechanism moves, the jumping motion planning method of the wheel-legged robot can be as follows:

[0244] Construct a whole-body dynamics model of the wheel-legged robot. The floating-base dynamics model includes a floating fuselage, driving wheels, a first virtual leg and a second virtual leg with a parallel relationship, and an adjustment mechanism connected to the floating fuselage, and the adjustment mechanism is used to adjust the posture of the wheel-legged robot; wherein, the first ends of the upper limbs of the first virtual leg and the first ends of the upper limbs of the second virtual leg are respectively connected to the floating fuselage; the second end of the upper limb of the first virtual leg is connected to the first end of the lower limb of the first virtual leg, and the second end of the upper limb of the second virtual leg is connected to the first end of the lower limb of the second virtual leg; the second ends of the lower limbs of the first virtual leg and the second ends of the lower limbs of the second virtual leg are respectively connected to the driving wheels.

[0245] Based on the central position of the floating fuselage, the pitch angle of the floating fuselage, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, the rotation angle of the driving wheel, and the rotation angle of the adjustment mechanism, construct the generalized coordinates of the whole-body dynamics model; based on the execution torque of the driving joint of the first virtual leg, the execution torque of the driving joint of the second virtual leg, the execution torque of the driving wheel, and the execution torque of the adjustment mechanism, construct the control quantities of the whole-body dynamics model; based on the friction force and the supporting force of the bearing surface on the wheel-legged robot, construct the bearing surface reaction force of the whole-body dynamics model; based on the binding force between the first virtual leg and the second virtual leg, construct the closed-loop acting force of the whole-body dynamics model.

[0246] Exemplarily, the generalized coordinates can be expressed as in Equation (6) above, the control quantity can be expressed as in Equation (7) above, the reaction force of the bearing surface can be expressed as in Equation (8) above, and the closed-loop acting force can be expressed as in Equation (9) above.

[0247] Taking the jumping motion task as an example, the jumping motion task can be divided into three stages: the takeoff stage, the airborne stage, and the landing stage. The constraint equations corresponding to the takeoff stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the takeoff stage, the friction constraint equation corresponding to the takeoff stage, the anti-collision constraint equation corresponding to the takeoff stage, the boundary constraint equation corresponding to the takeoff stage, and the continuity constraint equation between the takeoff stage and the airborne stage; the constraint equations corresponding to the airborne stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the airborne stage, the anti-collision constraint equation corresponding to the airborne stage, the boundary constraint equation corresponding to the airborne stage, and the continuity constraint equation between the airborne stage and the landing stage; the constraint equations corresponding to the landing stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the landing stage, the friction constraint equation corresponding to the landing stage, the anti-collision constraint equation corresponding to the landing stage, and the boundary constraint equation corresponding to the landing stage.

[0248] Optionally, the process of obtaining the constraint equations corresponding to the takeoff stage can be as follows:

[0249] 1. Dynamic constraint equation.

[0250] Based on the generalized coordinates and generalized velocities, the total kinetic energy E and total potential energy V corresponding to the whole-body dynamic model are calculated. Then the Lagrangian of the system can be expressed as L = E - V. In the takeoff stage, the wheel-legged robot includes internal acting forces (i.e., the equivalent forces corresponding to the control quantity and the closed-loop acting force) and external acting forces (i.e., the reaction force of the bearing surface). According to the Lagrange equation, a dynamic equation with the same representation as Equation (16) above can be obtained. However, since the model constructed in this embodiment is different from the model corresponding to Equation (16), the specific expressions of the various parameters in this dynamic equation are different from those in Equation (16).

[0251] Assuming pure rolling between the driving wheel and the bearing surface, an equation with the same representation as Equation (17) above can be obtained. Additionally, since the first virtual leg and the second virtual leg satisfy the closed-chain constraint, an equation with the same representation as Equation (18) above can be obtained. Combining Equation (16) and Equation (17) above gives Equation (18). Then, at any moment t in the takeoff stage, the representation of the dynamic constraint equation is the same as Equation (22) above.

[0252] 2. Friction constraint equation.

[0253] During the landing phase, based on the assumption that pure rolling occurs between the driving wheels and the bearing surface, the reaction force of the bearing surface should satisfy the friction cone constraint. Therefore, at any moment t during the landing phase, the friction constraint equation has the same form as the above equation (24).

[0254] 3. Anti-collision constraint equation.

[0255] During the takeoff phase, the floating fuselage, the first virtual leg, the second virtual leg, the driving wheels, and the adjustment mechanism of the whole-body dynamics model cannot be embedded below the ground. When the adjustment mechanism is in motion, d = 7. At any moment t during the takeoff phase, the anti-collision constraint equation can be expressed as follows:

[0256] p j，z (t)+α(p k，z (t)-p j，z (t))≥h m (p k，x (t)+α(p j，x (t)-p k，x (t))), α ∈ [0, 1], j, k ∈ [1, 7] Equation (37)

[0257] z w (t)+rcos(β)≥h m (x w (t)+rsin(β)), β ∈ [0, 2π]

[0258] 4. Boundary constraint equation.

[0259] During the takeoff phase, it is necessary to ensure that the state variables of the whole-body dynamics model comply with the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the whole-body dynamics model do not exceed the upper and lower limit values of the control variables. Therefore, at any moment t during the landing phase, the boundary constraint equation has the same form as the above equation (27).

[0260] 5. Continuity constraint equation.

[0261] During the takeoff phase, it is necessary to ensure that the state variables of the whole-body dynamics model at the end moment of the takeoff phase are the same as the state variables of the whole-body dynamics model at the starting moment of the airborne phase. The continuity constraint equation between the takeoff phase and the airborne phase has the same form as the above equation (28).

[0262] Optionally, the process of obtaining the constraint equation corresponding to the airborne phase can be as follows:

[0263] 1. Dynamics constraint equation.

[0264] During the airborne phase, the wheel-leg robot includes internal forces and excludes external forces (i.e., the reaction force of the bearing surface), and still needs to ensure the closed-chain constraint between the first virtual leg and the second virtual leg. Then, according to the Lagrange equation, the dynamic equation with the same representation form as the above equation (29) can be obtained.

[0265] Based on equation (29), at any time t during the airborne phase, the dynamic constraint equation has the same representation form as the above equation (31).

[0266] 2. Friction constraint equation.

[0267] During the airborne phase, since the full-body dynamic model is disengaged from the bearing surface, the friction constraint equation is not involved in the airborne phase.

[0268] 3. Anti-collision constraint equation.

[0269] During the takeoff phase, the floating body, the first virtual leg, the second virtual leg, the driving wheel, and the adjustment mechanism of the full-body dynamic model cannot be embedded below the ground. When the adjustment mechanism is moving, d = 7. At any time t during the airborne phase, the anti-collision constraint equation can be expressed as the above equation (37).

[0270] 4. Boundary constraint equation.

[0271] During the airborne phase, it is necessary to ensure that the state variables of the full-body dynamic model conform to the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the variable-leg-length wheeled inverted pendulum model do not exceed the upper and lower limit values of the control variables. Then, the boundary constraint equation in the airborne phase has the same representation form as the above equation (27).

[0272] 5. Continuity constraint equation.

[0273] During the landing phase, assuming that the full-body dynamic model and the bearing surface are inelastic collisions, that is, the collision is completed instantaneously. According to the law of conservation of momentum, the relationship between the state variables after the collision and the state variables before the collision satisfies the above equation (32). Among them, the generalized coordinates at the end moment of the airborne phase are the same as the generalized coordinates at the start moment of the landing phase, and the generalized velocities at the end moment of the airborne phase are different from the generalized velocities at the start moment of the landing phase. At the start moment of the landing phase, the velocity of the contact point between the driving wheel and the receiving surface is 0, and the closed-chain constraint is satisfied between the first virtual leg and the second virtual leg. Then, the above equation (33) can be obtained. Combining the above equation (32) and the above equation (33) can obtain the same relational expression as the above equation (34). Furthermore, based on the above equation (34), the continuity constraint equation between the airborne phase and the landing phase has the same representation form as the above equation (36).

[0274] Optionally, the process of obtaining the constraint equation corresponding to the landing phase can be as follows:

[0275] 1. Kinetic constraint equation.

[0276] During the landing phase, the wheel-legged robot includes internal forces (i.e., the equivalent forces corresponding to the control quantities and the closed-loop forces) and external forces (i.e., the reaction forces of the bearing surface). Then, the kinetic equation in the landing phase is the same as that in the takeoff phase. Additionally, the same assumptions as in the takeoff phase are established: pure rolling exists between the driving wheel and the bearing surface, and a closed-chain constraint is satisfied between the first virtual leg and the second virtual leg. Then, at any moment t during the landing phase, the kinetic constraint equation has the same representation form as Equation (22) above.

[0277] 2. Friction constraint equation.

[0278] During the landing phase, based on the assumption of pure rolling between the driving wheel and the bearing surface, the reaction force of the bearing surface should satisfy the friction cone constraint. Then, at any moment t during the landing phase, the friction constraint equation can be expressed as Equation (24) above.

[0279] 3. Anti-collision constraint equation.

[0280] During the landing phase, the floating body, the first virtual leg, the second virtual leg, the driving wheel, and the adjustment mechanism of the whole-body kinetic model cannot be embedded below the ground. In the case where the whole-body kinetic model does not include the adjustment structure or the adjustment mechanism is fixed, at any moment t during the landing phase, the anti-collision constraint equation has the same representation form as Equation (37) above.

[0281] 4. Boundary constraint equation.

[0282] During the landing phase, it is necessary to ensure that the state quantities of the whole-body kinetic model conform to the state quantity constraints, the state quantities do not exceed the upper and lower limit values of the state quantities, and the control quantities of the whole-body kinetic model do not exceed the upper and lower limit values of the control quantities. Then, at any moment t during the landing phase, the boundary constraint equation has the same representation form as Equation (27) above.

[0283] In summary, in the case of simplifying the wheel-legged robot into a whole-body kinetic model, if the whole-body kinetic model includes an adjustment mechanism and the adjustment mechanism moves, the constraint equation set of the jumping motion task includes:

[0284] 1. Equations (22), (24), (37), (27), and (28) corresponding to the takeoff phase.

[0285] 2. Equations (31), (37), (27), and (36) corresponding to the airborne phase.

[0286] 3. Equations (22), (24), (37), and (27) corresponding to the landing phase.

[0287] Based on the constraint equations corresponding to the three stages of the jumping motion task, the objective function is optimized to obtain the planned motion data sequence corresponding to the jumping motion task.

[0288] Exemplarily, taking the example of obtaining the planned motion data sequence with the least required energy consumption. Based on equations (22), (24), (37), (27), and (28) corresponding to the takeoff stage, equations (31), (37), (27), and (36) corresponding to the airborne stage, and equations (22), (24), (37), and (27) corresponding to the landing stage, equation (1) is minimized to obtain the planned motion data at each time point in the jumping motion task.

[0289] By adopting the technical solution provided in the embodiment of the present application, it is realized to plan the jumping motion tasks (such as conventional jumping motion tasks and somersault motion tasks) of the wheel-legged robot based on the whole-body dynamics model in the case where the adjustment mechanism is included and the adjustment mechanism is moving.

[0290] In an exemplary embodiment, when the wheel-legged robot is simplified to a variable-leg-length wheeled inverted pendulum model, and the variable-leg-length wheeled inverted pendulum model does not include an adjustment mechanism or includes an adjustment mechanism but the adjustment mechanism is fixed, the jumping motion planning method of the wheel-legged robot can be as follows:

[0291] Construct a variable-leg-length wheeled inverted pendulum model of the wheel-legged robot. The variable-leg-length wheeled inverted pendulum model includes a virtual leg with variable leg length, a driving wheel connected to the first end of the virtual leg, and a floating body connected to the second end of the virtual leg.

[0292] Based on the central position of the driving wheel, the rotation angle of the driving wheel, the leg length of the virtual leg, and the pitch angle of the floating body, construct the generalized coordinates of the variable-leg-length wheeled inverted pendulum model; based on the execution torque of the driving wheel and the active force of the virtual leg, construct the control quantity of the variable-leg-length wheeled inverted pendulum model; based on the friction force and the supporting force of the bearing surface on the wheel-legged robot, construct the bearing surface reaction force of the variable-leg-length wheeled inverted pendulum model.

[0293] Exemplarily, the generalized coordinates can be expressed as equation (10) above, the control quantity can be expressed as equation (11) above, and the bearing surface reaction force can be expressed as equation (12) above.

[0294] Taking the jumping motion task as an example, the jumping motion task can be divided into three stages: the take-off stage, the airborne stage, and the landing stage. The constraint equations corresponding to the take-off stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the take-off stage, the friction constraint equation corresponding to the take-off stage, the anti-collision constraint equation corresponding to the take-off stage, the boundary constraint equation corresponding to the take-off stage, the continuity constraint equation between the take-off stage and the airborne stage; the constraint equations corresponding to the airborne stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the airborne stage, the anti-collision constraint equation corresponding to the airborne stage, the boundary constraint equation corresponding to the airborne stage, the continuity constraint equation between the airborne stage and the landing stage; the constraint equations corresponding to the landing stage of the wheel-legged robot can include: the dynamic constraint equation corresponding to the landing stage, the friction constraint equation corresponding to the landing stage, the anti-collision constraint equation corresponding to the landing stage, the boundary constraint equation corresponding to the landing stage.

[0295] Optionally, the process of obtaining the constraint equations corresponding to the take-off stage can be as follows:

[0296] 1. Dynamic constraint equation.

[0297] Based on the generalized coordinates and generalized velocities, the total kinetic energy E and total potential energy V corresponding to the variable leg-length wheeled inverted pendulum model are calculated. Then, the Lagrangian of the system can be expressed as L = E - V. In the take-off stage, the variable leg-length wheeled inverted pendulum model includes internal forces (i.e., the equivalent forces corresponding to the control quantities) and external forces (i.e., the bearing surface reaction forces). According to the Lagrangian equation, the dynamic equation corresponding to the take-off stage can be obtained as follows:

[0298]

[0299] where q refers to the generalized coordinates, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control quantity of the variable leg-length wheeled inverted pendulum model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, S represents the selection matrix, and J C represents the Jacobian matrix of the contact point between the active wheel of the variable leg-length wheeled inverted pendulum model and the bearing surface.

[0300] In the take-off stage, assuming pure rolling between the active wheel and the bearing surface, the acceleration of the contact point between the active wheel and the bearing surface in the world coordinate system is:

[0301]

[0302] Combining Equation (38) and Equation (39) gives:

[0303]

[0304] Since D(q) is a square matrix and full rank, J C is row full rank. Therefore, it can be determined that the first term on the left side in Equation (40) is full rank, and the expressions for the generalized acceleration and the bearing surface reaction force can be obtained as follows:

[0305]

[0306] Take the state variables of the wheel-leg robot as Then the dynamic constraint equations during the takeoff phase can be expressed as follows:

[0307]

[0308] Among them, the matrix The matrix A up b refers to the product of the first n rows of matrix A and matrix b, where n is the number of parameters in the generalized coordinates of the variable-leg-length wheeled inverted pendulum model, refers to the derivative of the state variables of the variable-leg-length wheeled inverted pendulum model, q refers to the generalized coordinates, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control quantity of the variable-leg-length wheeled inverted pendulum model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, S represents the selection matrix, J C represents the Jacobian matrix of the contact point between the driving wheel of the variable-leg-length wheeled inverted pendulum model and the bearing surface.

[0309] Furthermore, at any moment t during the takeoff phase, the dynamic constraint equations can be expressed as follows:

[0310]

[0311] 2. Friction constraint equations.

[0312] During the takeoff phase, based on the assumption of pure rolling, the bearing surface reaction force should satisfy the friction cone constraint. By linearizing the Coulomb friction of the bearing surface reaction force, the friction constraint equations can be obtained, and the friction constraint equations can be expressed as follows:

[0313]

[0314] Among them, the matrix The matrix refers to the friction constraint matrix corresponding to the i-th driving wheel of the variable-leg-length wheeled inverted pendulum model, N C is the number of driving wheels, A down b refers to the product of the last 2N C rows of matrix A and matrix b, μ iis the friction coefficient corresponding to the i-th driving wheel, n c，i is the unit outer normal vector of the contact point between the i-th driving wheel and the bearing surface, o c，i is the unit tangent vector of the contact point between the i-th driving wheel and the bearing surface, q refers to the generalized coordinates of the variable-leg-length wheeled inverted pendulum model, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control quantity of the variable-leg-length wheeled inverted pendulum model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, S represents the selection matrix, J C represents the Jacobian matrix of the contact point between the driving wheel and the bearing surface.

[0315] Furthermore, at any moment t during the takeoff phase, the friction constraint equation can be expressed as follows:

[0316]

[0317] 3. Anti-collision constraint equation.

[0318] During the takeoff phase, the floating fuselage, virtual legs and driving wheels of the variable-leg-length wheeled inverted pendulum model cannot be embedded below the ground, so the anti-collision constraint equation can be obtained as follows:

[0319]

[0320] where z refers to the coordinate of the driving wheel of the variable-leg-length wheeled inverted pendulum model in the z-axis direction of the world coordinate system, x refers to the coordinate of the driving wheel in the x-axis direction of the world coordinate system, l is the length of the virtual leg of the variable-leg-length wheeled inverted pendulum model, θ is the pitch angle of the floating fuselage of the variable-leg-length wheeled inverted pendulum model in the world coordinate system, r is the radius of the driving wheel, h m is the height function of any point in the world coordinate system, and α and β are range parameters.

[0321] Furthermore, at any moment t during the takeoff phase, the anti-collision constraint equation can be expressed as follows:

[0322]

[0323] 4. Boundary constraint equation.

[0324] During the takeoff phase, it is necessary to ensure that the state variables of the variable-leg-length wheeled inverted pendulum model comply with the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control quantity of the variable-leg-length wheeled inverted pendulum model does not exceed the upper and lower limit values of the control quantity. Then the boundary constraint equation can be expressed as follows:

[0325] X(t) = X t

[0326] X min ≤X(t)≤X max Formula (48)

[0327] u min ≤u(t)≤u max

[0328] Among them, X max and X min They refer to the upper and lower limits of the state quantity corresponding to the jumping motion task, u max and u min They refer to the upper and lower limits of the control amount corresponding to the jumping motion task, X t It refers to the state quantity constraint at time t.

[0329] 5. Continuity constraint equation.

[0330] In the take-off phase, it is necessary to ensure that the state quantity of the variable-leg long-wheel inverted pendulum model at the end of the take-off phase is the same as the state quantity of the variable-leg long-wheel inverted pendulum model at the start of the take-off phase. The continuity constraint equation between the take-off phase and the take-off phase can be expressed as follows:

[0331] X(t 1，e )=X(t 2，s ) Formula (49)

[0332] Among them, t 1，e and t 2，s They refer to the end time of the take-off phase and the start time of the flight phase respectively.

[0333] Optionally, the process of obtaining the constraint equation corresponding to the flight phase may be as follows:

[0334] 1. Dynamic constraint equations.

[0335] In the air phase, since the variable-leg long-wheel inverted pendulum model includes internal forces but not external forces (i.e., the reaction force of the bearing surface), the dynamic equation corresponding to the air phase can be obtained according to the Lagrange equation:

[0336]

[0337] Combined with equation (50), the dynamic constraint equation corresponding to the take-off stage can be expressed as follows:

[0338]

[0339] in, refers to the derivative of the state quantity of the variable-leg long-wheel inverted pendulum model, q refers to the generalized coordinates of the variable-leg long-wheel inverted pendulum model, refers to the generalized velocity corresponding to the generalized coordinates, It refers to the generalized acceleration corresponding to the generalized coordinates, u refers to the control quantity of the variable-leg long-wheel inverted pendulum model, D is the inertia matrix, C is the centrifugal force and Coriolis force vector, G is the gravity vector, and S represents the selection matrix.

[0340] Furthermore, at any time t in the flight phase, the dynamic constraint equation can be expressed as follows:

[0341]

[0342] 2. Friction constraint equation.

[0343] In the air stage, since the variable-leg long-wheel inverted pendulum model is out of contact with the bearing surface, the friction constraint equation is not involved in the air stage.

[0344] 3. Anti-collision constraint equation.

[0345] Since the floating body, virtual legs and driving wheels of the variable-leg long-wheel inverted pendulum model cannot be embedded under the ground, the anti-collision constraint equation that is the same as the above equation (46) can be obtained. Then, at any time t in the take-off stage, the anti-collision constraint equation can be expressed as the above equation (47).

[0346] 4. Boundary constraint equations.

[0347] During the take-off phase, it is necessary to ensure that the state quantity of the variable-leg long-wheel inverted pendulum model meets the state quantity constraint, the state quantity does not exceed the upper and lower limits of the state quantity, and the control quantity of the variable-leg long-wheel inverted pendulum model does not exceed the upper and lower limits of the control quantity. The boundary constraint equation of the take-off phase is the same as the expression of the above formula (48).

[0348] 5. Continuity constraint equation.

[0349] In the landing stage, it is assumed that the variable-leg long-wheel inverted pendulum model collides inelasticly with the bearing surface, that is, the collision is completed in an instant. According to the law of conservation of momentum, the state quantity after the collision and the state quantity before the collision satisfy the following relationship:

[0350]

[0351] in, refers to the generalized speed at the end of the flight phase, q 2，e refers to the generalized coordinates of the end time of the flight phase, q 3，s refers to the generalized coordinates of the starting moment of the landing phase, refers to the generalized speed at the beginning of the landing phase, and q 2，e =q 3，s ,

[0352] At the initial moment of the landing phase, the velocity of the contact point between the driving wheel and the bearing surface is 0, so we have:

[0353]

[0354] Combining Equation (53) and Equation (54), we can obtain:

[0355]

[0356] Since D(q 2，e ) is a square matrix and full rank, and J C (q 2，e ) is row full rank, it can be judged that the first term on the left side of Equation (55) is full rank. Then, the expressions for the generalized velocity and the bearing surface reaction force at the initial moment of the landing phase can be obtained as:

[0357]

[0358] Then, the continuity constraint equation between the airborne phase and the landing phase can be expressed as follows:

[0359]

[0360] Among them, the matrix The matrix Q up p refers to the product of the first n rows of the matrix Q and the matrix p. n is the number of parameters in the generalized coordinates of the variable leg length wheeled inverted pendulum model. q 3，s refers to the generalized coordinates of the variable leg length wheeled inverted pendulum model at the initial moment of the landing phase. refers to the generalized velocity of the variable leg length wheeled inverted pendulum model at the initial moment of the landing phase. q 2，e refers to the generalized coordinates of the variable leg length wheeled inverted pendulum model at the end moment of the airborne phase. refers to the generalized velocity of the variable leg length wheeled inverted pendulum model at the end moment of the airborne phase. D is the inertia matrix, and J C represents the Jacobian matrix of the contact point between the driving wheel and the bearing surface of the variable leg length wheeled inverted pendulum model.

[0361] Optionally, the process of obtaining the constraint equation corresponding to the landing phase can be as follows:

[0362] 1. Dynamic constraint equation.

[0363] In the landing phase, the same assumptions as in the takeoff phase are established: pure rolling between the driving wheel and the bearing surface, and the dynamic equation in the landing phase is the same as that in the takeoff phase. Then, at any moment t in the landing phase, the dynamic constraint equation has the same expression form as Equation (43) above.

[0364] 2. Friction constraint equation.

[0365] During the landing phase, based on the assumption of pure rolling between the driving wheel and the bearing surface, the reaction force of the bearing surface should satisfy the friction cone constraint. Therefore, at any time t during the landing phase, the friction constraint equation has the same form as the above equation (45).

[0366] 3. Anti-collision constraint equation.

[0367] During the landing phase, the floating body, virtual leg, and driving wheel of the variable-leg-length wheeled inverted pendulum model cannot be embedded below the ground. Therefore, at any time t during the landing phase, the anti-collision constraint equation has the same form as the above equation (47).

[0368] 4. Boundary constraint equation.

[0369] During the landing phase, it is necessary to ensure that the state variables of the variable-leg-length wheeled inverted pendulum model conform to the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the variable-leg-length wheeled inverted pendulum model do not exceed the upper and lower limit values of the control variables. Therefore, at any time t during the landing phase, the boundary constraint equation has the same form as the above equation (48).

[0370] In summary, when the wheel-legged robot is simplified to a variable-leg-length wheeled inverted pendulum model, if the variable-leg-length wheeled inverted pendulum model does not include an adjustment mechanism or includes an adjustment mechanism but the adjustment mechanism is fixed, the constraint equation set of the jumping motion task includes:

[0371] 1. Equations (43), (45), (47), (48), and (49) corresponding to the takeoff phase.

[0372] 2. Equations (52), (47), (48), and (57) corresponding to the airborne phase.

[0373] 3. Equations (43), (45), (47), and (48) corresponding to the landing phase.

[0374] Based on the constraint equations corresponding to the three phases of the jumping motion task, the objective function is optimized to obtain the planned motion data sequence corresponding to the jumping motion task.

[0375] Exemplarily, taking the example of obtaining the planned motion data sequence with the least required energy consumption. Based on equations (43), (45), (47), (48), and (49) corresponding to the takeoff phase, equations (52), (47), (48), and (57) corresponding to the airborne phase, and equations (43), (45), (47), and (48) corresponding to the landing phase, equation (1) is minimized to obtain the planned motion data at each time point in the jumping motion task.

[0376] By adopting the technical solution provided by the embodiment of the present application, the jumping motion tasks (such as conventional jumping motion tasks and somersault motion tasks) of the wheel-legged robot are planned based on the variable-leg-length wheeled inverted pendulum model without including an adjustment mechanism or including an adjustment mechanism but with the adjustment mechanism fixed.

[0377] In an exemplary embodiment, when the wheel-legged robot is simplified to a variable-leg-length wheeled inverted pendulum model and the adjustment mechanism in the variable-leg-length wheeled inverted pendulum model is in motion, the jumping motion planning method of the wheel-legged robot can be as follows:

[0378] Construct a variable-leg-length wheeled inverted pendulum model of the wheel-legged robot. The variable-leg-length wheeled inverted pendulum model includes a virtual leg with variable leg length, a driving wheel connected to the first end of the virtual leg, a floating body connected to the second end of the virtual leg, and an adjustment mechanism connected to the floating body. The adjustment mechanism can be a tail, a robotic arm, etc.

[0379] Based on the central position of the driving wheel, the rotation angle of the driving wheel, the leg length of the virtual leg, the pitch angle of the floating body, and the rotation angle of the adjustment mechanism, construct the generalized coordinates of the variable-leg-length wheeled inverted pendulum model; based on the execution torque of the driving wheel, the active force of the virtual leg, and the execution torque of the adjustment mechanism, construct the control quantities of the variable-leg-length wheeled inverted pendulum model; based on the friction force and support force of the bearing surface on the wheel-legged robot, construct the bearing surface reaction force of the variable-leg-length wheeled inverted pendulum model.

[0380] Exemplarily, the generalized coordinates can be expressed as the above formula (13), the control quantities can be expressed as the above formula (14), and the bearing surface reaction force can be expressed as the above formula (15).

[0381] Taking the jumping motion task as an example, the jumping motion task can be divided into three stages: the takeoff stage, the airborne stage, and the landing stage. The constraint equations corresponding to the wheel-legged robot in the takeoff stage can include: the dynamic constraint equation corresponding to the takeoff stage, the friction constraint equation corresponding to the takeoff stage, the anti-collision constraint equation corresponding to the takeoff stage, the boundary constraint equation corresponding to the takeoff stage, the continuity constraint equation between the takeoff stage and the airborne stage; the constraint equations corresponding to the wheel-legged robot in the airborne stage can include: the dynamic constraint equation corresponding to the airborne stage, the anti-collision constraint equation corresponding to the airborne stage, the boundary constraint equation corresponding to the airborne stage, the continuity constraint equation between the airborne stage and the landing stage; the constraint equations corresponding to the wheel-legged robot in the landing stage can include: the dynamic constraint equation corresponding to the landing stage, the friction constraint equation corresponding to the landing stage, the anti-collision constraint equation corresponding to the landing stage, the boundary constraint equation corresponding to the landing stage.

[0382] Optionally, the process of obtaining the constraint equations corresponding to the takeoff stage can be as follows:

[0383] 1. Kinetic constraint equation.

[0384] Based on the generalized coordinates and the generalized velocities corresponding to the generalized coordinates, the total kinetic energy E and the total potential energy V of the variable-leg-length wheeled inverted pendulum model are calculated. Then, the Lagrangian of the system can be expressed as L = E - V. During the takeoff phase, the wheel-legged robot includes internal forces (i.e., the equivalent forces corresponding to the control quantities) and external forces (i.e., the reaction forces of the bearing surface). According to the Lagrangian equation, the dynamic equation with the same representation form as the above formula (38) can be obtained. However, due to the different constructed models, the specific expressions of the various parameters in this dynamic equation are different from those in formula (38).

[0385] Assume that the contact between the driving wheel and the bearing surface is pure rolling. Then, the acceleration of the contact point between the driving wheel and the bearing surface in the world coordinate system has the same representation form as the above formula (39). Combining the above formula (38) and the above formula (39) gives the above formula (40). Then, at any moment t during the takeoff phase, the representation form of the kinetic constraint equation is the same as the above formula (43).

[0386] 2. Friction constraint equation.

[0387] Based on the assumption that the contact between the driving wheel and the bearing surface is pure rolling, the reaction force of the bearing surface should satisfy the friction cone constraint. By linearizing the Coulomb friction of the reaction force of the bearing surface, the friction constraint equation with the same representation form as the above formula (44) can be obtained. Then, at any moment t during the takeoff phase, the friction constraint equation can be expressed as the above formula (45).

[0388] 3. Anti-collision constraint equation.

[0389] In the variable-leg-length wheeled inverted pendulum model, there is an adjustment mechanism connected to the floating body. When the adjustment mechanism is in motion, during the takeoff phase, the floating body, the virtual leg, the driving wheel, and the adjustment mechanism of the variable-leg-length wheeled inverted pendulum model cannot be embedded below the ground. Therefore, the anti-collision constraint equation can be obtained as follows:

[0390] z + αlcos(θ) ≥ h m (x + lsin(θ)), α ∈ [0, 1]

[0391] z + rcos(β) ≥ h m (x + rsim(β)), β ∈ [0, 2π] Formula (58)

[0392] p t，z + α(P t，e，z - p t，z ) ≥ h m (P t，x + α(P t，e，x - p t，x), α ∈ [0, 1]

[0393] Where z refers to the coordinate of the active wheel of the variable-leg-length wheeled inverted pendulum model in the z-axis direction of the world coordinate system, x refers to the coordinate of the active wheel in the x-axis direction of the world coordinate system, l is the length of the virtual leg of the variable-leg-length wheeled inverted pendulum model, θ is the pitch angle of the floating body of the variable-leg-length wheeled inverted pendulum model in the world coordinate system, r is the radius of the active wheel, h m is the height function of any point in the world coordinate system, α and β are range parameters, p t，z is the coordinate of the driving joint of the adjustment mechanism of the variable-leg-length wheeled inverted pendulum model in the z-axis direction of the world coordinate system, p t，x is the coordinate of the driving joint of the adjustment mechanism in the x-axis direction of the world coordinate system, p t，e，z is the coordinate of the end of the adjustment mechanism in the z-axis direction of the world coordinate system, p t，e，x is the coordinate of the end of the adjustment mechanism in the x-axis direction of the world coordinate system.

[0394] Furthermore, at any moment t during the takeoff phase, the anti-collision constraint equation can be expressed as follows:

[0395]

[0396] 4. Boundary constraint equation.

[0397] During the takeoff phase, it is necessary to ensure that the state variables of the variable-leg-length wheeled inverted pendulum model conform to the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the variable-leg-length wheeled inverted pendulum model do not exceed the upper and lower limit values of the control variables. Then, at any moment t during the takeoff phase, the boundary constraint equation has the same form as the above formula (48). However, compared with the above embodiments, the state variable constraints in this embodiment also include restrictions on the rotation angle, rotation speed, etc. of the adjustment mechanism, and the control variables also include restrictions on the execution torque of the adjustment mechanism.

[0398] 5. Continuity constraint equation.

[0399] During the takeoff phase, it is necessary to ensure that the state variables of the variable-leg-length wheeled inverted pendulum model at the end of the takeoff phase are the same as the state variables of the variable-leg-length wheeled inverted pendulum model at the start of the airborne phase. Then, the continuity constraint equation between the takeoff phase and the airborne phase has the same form as the above formula (49).

[0400] The process of obtaining the constraint equation corresponding to the airborne phase can be as follows:

[0401] 1. Dynamic constraint equation.

[0402] During the airborne phase, since the variable-leg-length wheeled inverted pendulum model includes internal forces and does not include external forces (i.e., the reaction force of the bearing surface), at any moment t during the airborne phase, the dynamic constraint equation has the same form as the above equation (52).

[0403] 2. Friction constraint equation.

[0404] During the airborne phase, since the variable-leg-length wheeled inverted pendulum model is disengaged from the bearing surface, the friction constraint equation is not involved during the airborne phase.

[0405] 3. Anti-collision constraint equation.

[0406] When the variable-leg-length wheeled inverted pendulum model includes an adjustment mechanism connected to the floating fuselage and the adjustment mechanism is in motion, during the airborne phase, the floating fuselage, virtual leg, driving wheel, and adjustment mechanism of the variable-leg-length wheeled inverted pendulum model cannot be embedded below the ground. Therefore, at any moment t during the airborne phase, the anti-collision constraint equation has the same form as the above equation (59).

[0407] 4. Boundary constraint equation.

[0408] During the airborne phase, it is necessary to ensure that the state variables of the variable-leg-length wheeled inverted pendulum model conform to the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the variable-leg-length wheeled inverted pendulum model do not exceed the upper and lower limit values of the control variables. Then, at any moment t during the airborne phase, the boundary constraint equation has the same form as the above equation (48).

[0409] 5. Continuity constraint equation.

[0410] During the landing phase, assuming that the variable-leg-length wheeled inverted pendulum model has an inelastic collision with the bearing surface, that is, the collision is completed instantaneously. According to the law of conservation of momentum, the relationship between the state variables after the collision and the state variables before the collision satisfies the above equation (53). Among them, the generalized coordinates at the end moment of the airborne phase are the same as the generalized coordinates at the start moment of the landing phase, and the generalized velocities at the end moment of the airborne phase are different from the generalized velocities at the start moment of the landing phase. At the start moment of the landing phase, the velocity of the contact point between the driving wheel and the receiving surface is 0, which can be expressed by the above equation (54). Combining the above equation (53) and the above equation (54) gives the same relational expression as the above equation (55). Furthermore, based on the above equation (55), the continuity constraint equation between the airborne phase and the landing phase has the same form as the above equation (57).

[0411] The process of obtaining the constraint equation corresponding to the landing phase can be as follows:

[0412] 1. Dynamic constraint equation.

[0413] During the landing phase, the same assumptions as in the takeoff phase are established: pure rolling between the driving wheel and the bearing surface, and the dynamic equations in the landing phase are the same as those in the takeoff phase. Then, at any moment t during the landing phase, the dynamic constraint equations have the same form as those in Equation (43) above.

[0414] 2. Friction constraint equation.

[0415] During the landing phase, based on the assumption of pure rolling between the driving wheel and the bearing surface, the reaction force of the bearing surface should satisfy the friction cone constraint. Then, at any moment t during the landing phase, the friction constraint equation has the same form as that in Equation (45) above.

[0416] 3. Anti-collision constraint equation.

[0417] In the variable-leg-length wheeled inverted pendulum model including an adjustment mechanism connected to the floating body, and when the adjustment mechanism is in motion, during the landing phase, the floating body, virtual leg, driving wheel, and adjustment mechanism of the variable-leg-length wheeled inverted pendulum model cannot be embedded below the ground. Therefore, at any moment t during the landing phase, the anti-collision constraint equation has the same form as that in Equation (59) above.

[0418] 4. Boundary constraint equation.

[0419] During the landing phase, it is necessary to ensure that the state variables of the variable-leg-length wheeled inverted pendulum model conform to the state variable constraints, the state variables do not exceed the upper and lower limit values of the state variables, and the control variables of the variable-leg-length wheeled inverted pendulum model do not exceed the upper and lower limit values of the control variables. Then, at any moment t during the landing phase, the boundary constraint equation can be expressed as Equation (48) above.

[0420] In summary, in the case of simplifying the wheel-legged robot into a variable-leg-length wheeled inverted pendulum model, if the variable-leg-length wheeled inverted pendulum model includes an adjustment mechanism and the adjustment mechanism is in motion, the constraint equation set for the jumping motion task includes:

[0421] 1. Equations (43), (45), (59), (48), and (49) corresponding to the takeoff phase.

[0422] 2. Equations (52), (59), (48), and (57) corresponding to the airborne phase.

[0423] 3. Equations (43), (45), (59), and (48) corresponding to the landing phase.

[0424] Based on the constraint equations corresponding to the three phases of the jumping motion task respectively, the objective function is optimized to obtain the planned motion data sequence corresponding to the jumping motion task.

[0425] Exemplarily, taking the example of obtaining the planned motion data sequence with the least required energy consumption. Based on equations (43), (45), (59), (48), and (49) corresponding to the takeoff phase, equations (52), (59), (48), and (57) corresponding to the airborne phase, and equations (43), (45), (59), and (48) corresponding to the landing phase, equation (1) is minimized to obtain the planned motion data at each time point in the jumping motion task.

[0426] By adopting the technical solution provided by the embodiment of the present application, it is realized to plan the jumping motion tasks (such as conventional jumping motion tasks and somersault motion tasks) of the wheel-leg robot based on the variable leg length wheeled inverted pendulum model in the case where the adjustment mechanism is included and the adjustment mechanism moves.

[0427] In an exemplary embodiment, taking the somersault motion task as the target motion task, since the somersault motion task includes a takeoff phase, an airborne phase, and a landing phase, the planned motion data sequence may include the following contents:

[0428] 1. The planned motion data sequence corresponding to the initial stage of the takeoff phase, which is used to control the driving wheels of the wheel-leg robot to reverse backward and control the floating body of the wheel-leg robot to tilt forward to prepare for accelerating the driving wheels.

[0429] 2. The planned motion data sequence corresponding to the middle stage of the takeoff phase, which is used to control the driving wheels to accelerate to obtain the horizontal speed required for the airborne phase.

[0430] 3. The planned motion data sequence corresponding to the final stage of the takeoff phase, which is used to control the driving wheels to decelerate, the legs of the wheel-leg robot to output active force to the bearing surface, and the tail of the wheel-leg robot to swing backward to obtain the vertical speed required for the airborne phase.

[0431] 4. The planned motion data sequence corresponding to the initial stage of the airborne phase, which is used to contract the tail and legs of the wheel-leg robot to reduce the moment of inertia.

[0432] 5. The planned motion data sequence corresponding to the middle stage of the airborne phase, which is used to keep the tail and legs of the wheel-leg robot contracted.

[0433] 6. The planned motion data sequence corresponding to the final stage of the airborne phase, which is used to extend the legs of the wheel-leg robot to prepare for the wheel-leg robot to land.

[0434] 7. The planned motion data sequence corresponding to the initial stage of the landing phase, which is used to contract the legs of the wheel-leg robot to prepare for the wheel-leg robot to land and buffer.

[0435] 8. The planned motion data sequence corresponding to the end stage of the landing phase is used to adjust the driving wheel to control the wheel-legged robot to reach the final state of the flip motion task.

[0436] Exemplarily, referring to Figure 7 , the wheel-legged robot is simplified into a model 700, and the model 700 includes a driving wheel 701, virtual legs 702 (including a first virtual leg and a second virtual leg), a floating body 703, and a tail 704.

[0437] The initial state of the model 700 is upright, that is, the pitch angle of the floating body 703 is 0.

[0438] In the initial stage of the takeoff phase, the model 700 controls the driving wheel 701 to reverse backward and controls the floating body 703 to tilt forward based on the planned motion data sequence corresponding to the initial stage of the takeoff phase.

[0439] In the middle stage of the takeoff phase, the model 700 controls the driving wheel 701 to move forward with positive acceleration based on the planned motion data sequence corresponding to the middle stage of the takeoff phase.

[0440] In the end stage of the takeoff phase, the model 700 controls the driving wheel 701 to decelerate, controls the virtual legs 702 to output active force to the bearing surface, and controls the tail 704 to swing backward based on the planned motion data sequence corresponding to the end stage of the takeoff phase.

[0441] In the initial stage of the airborne phase, the model 700 contracts the tail 704 and the virtual legs 702 based on the planned motion data sequence corresponding to the initial stage of the airborne phase.

[0442] In the middle stage of the airborne phase, the model 700 continues to contract the tail 704 and the virtual legs 702 based on the planned motion data sequence corresponding to the middle stage of the airborne phase.

[0443] In the end stage of the airborne phase, the model 700 extends the virtual legs 702 based on the planned motion data sequence corresponding to the end stage of the airborne phase to prepare for the landing of the model 700.

[0444] In the initial stage of the landing phase, the model 700 contracts the virtual legs 702 based on the planned motion data sequence corresponding to the initial stage of the landing phase to prepare for the landing buffer of the model 700.

[0445] In the end stage of the landing phase, the model 700 adjusts the driving wheel 701 based on the planned motion data sequence corresponding to the end stage of the landing phase to control the model 700 to reach the target state after landing of the flip motion task.

[0446] Based on the planned motion data sequence obtained from the technical solution provided in the embodiments of the present application, the flip motion task of the wheel-legged robot is realized.

[0447] The following is an embodiment of the device of the present application, which can be used to execute the method embodiment of the present application. For details not disclosed in the device embodiment of the present application, please refer to the method embodiment of the present application.

[0448] Please refer to Figure 8 , which shows a block diagram of a motion planning device for a wheel-legged robot provided by an embodiment of the present application. The device has the function of implementing the motion planning method of the above-mentioned wheel-legged robot, and the function can be implemented by hardware or by hardware executing corresponding software. The device can be a computer device or can be set in a computer device. The device 800 may include: a motion task acquisition module 801, a constraint equation acquisition module 802, and a planning data acquisition module 803.

[0449] The motion task acquisition module 801 is configured to acquire a target motion task planned for the wheel-legged robot.

[0450] The constraint equation acquisition module 802 is configured to acquire a constraint equation set corresponding to the target motion task, where the constraint equation set is constructed based on a floating-base dynamics model corresponding to the wheel-legged robot, the constraint equation set includes constraint equations under at least one constraint condition, and the constraint equations are used to constrain the wheel-legged robot to execute the target motion task.

[0451] The planning data acquisition module 803 is configured to optimize an objective function corresponding to the target motion task based on the constraint equation set to obtain a planned motion data sequence corresponding to the target motion task; wherein, the planned motion data sequence includes planned motion data of the wheel-legged robot at multiple time points.

[0452] In an exemplary embodiment, the floating-base dynamics model includes a floating body, a driving wheel, and a first virtual leg and a second virtual leg having a parallel relationship; wherein,

[0453] A first end of an upper limb of the first virtual leg and a first end of an upper limb of the second virtual leg are respectively connected to the floating body;

[0454] A second end of the upper limb of the first virtual leg is connected to a first end of a lower limb of the first virtual leg, and a second end of the upper limb of the second virtual leg is connected to a first end of a lower limb of the second virtual leg;

[0455] A second end of the lower limb of the first virtual leg and a second end of the lower limb of the second virtual leg are respectively connected to the driving wheel.

[0456] In an exemplary embodiment, the generalized coordinates, control quantities, bearing surface acting forces, and closed-loop acting forces of the floating-base dynamics model; wherein,

[0457] The generalized coordinates are used to describe the pose of the floating-base dynamic model, and the generalized coordinates include the central position of the floating body, the pitch angle of the floating body, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, and the rotation angle of the driving wheel;

[0458] The control quantities are used to control the first virtual leg, the second virtual leg, and the driving wheel, and the control quantities include the execution torque of the driving joint of the first virtual leg, the execution torque of the driving joint of the second virtual leg, and the execution torque of the driving wheel;

[0459] The bearing surface reaction force is used to describe the force exerted by the bearing surface on the floating-base dynamic model, and the bearing surface reaction force includes the frictional force and the supporting force of the bearing surface on the wheel-legged robot;

[0460] The closed-loop acting force is used to describe the binding force between the first virtual leg and the second virtual leg, and the closed-loop acting force includes the binding force between the first virtual leg and the second virtual leg.

[0461] In an exemplary embodiment, the floating-base dynamic model includes a floating body, a driving wheel, a first virtual leg and a second virtual leg having a parallel relationship, and an adjusting mechanism connected to the floating body, and the adjusting mechanism is used to adjust the pose of the wheel-legged robot; wherein,

[0462] The first ends of the upper limbs of the first virtual leg and the second virtual leg are respectively connected to the floating body;

[0463] The second end of the upper limb of the first virtual leg is connected to the first end of the lower limb of the first virtual leg, and the second end of the upper limb of the second virtual leg is connected to the first end of the lower limb of the second virtual leg;

[0464] The second ends of the lower limbs of the first virtual leg and the second virtual leg are respectively connected to the driving wheel.

[0465] In an exemplary embodiment, the model parameters of the floating-base dynamic model include at least one of the following: the generalized coordinates, control quantities, bearing surface acting forces, and closed-loop acting forces of the floating-base dynamic model; wherein,

[0466] The generalized coordinates are used to describe the pose of the floating-base dynamic model, and the generalized coordinates include the central position of the floating body, the pitch angle of the floating body, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, the rotation angle of the driving wheel, and the rotation angle of the adjusting mechanism;

[0467] The control quantities are used to control the first virtual leg, the second virtual leg, and the driving wheel, and the control quantities include the execution torque of the driving joint of the first virtual leg, the execution torque of the driving joint of the second virtual leg, the execution torque of the driving wheel, and the execution torque of the adjusting mechanism;

[0468] The bearing surface reaction force is used to describe the force exerted by the bearing surface on the floating-base dynamic model, and the bearing surface reaction force includes the friction force and the supporting force of the bearing surface on the wheel-legged robot;

[0469] The closed-loop acting force is used to describe the binding force between the first virtual leg and the second virtual leg, and the closed-loop acting force includes the binding force between the first virtual leg and the second virtual leg.

[0470] In an exemplary embodiment, the target motion task is divided into multiple stages;

[0471] The construction process of the constraint equation set corresponding to the target motion task is as follows:

[0472] According to the generalized coordinates, control quantities, bearing surface reaction force, and closed-loop acting force of the floating-base dynamic model, determine the constraint equations corresponding to each of the multiple stages;

[0473] According to the generalized coordinates of the floating-base dynamic model, determine the continuity constraint equations between adjacent stages among the multiple stages;

[0474] Based on the constraint equations corresponding to each of the multiple stages and the continuity constraint equations between adjacent stages, construct the constraint equation set corresponding to the target motion task.

[0475] In an exemplary embodiment, the target motion task is a jumping motion task, and the jumping motion task includes a takeoff stage, a flight stage, and a landing stage;

[0476] The constraint equation set corresponding to the jumping motion task includes: the constraint equation corresponding to the takeoff stage, the continuity constraint equation between the takeoff stage and the flight stage, the constraint equation corresponding to the flight stage, the continuity constraint equation between the flight stage and the landing stage, and the constraint equation corresponding to the landing stage.

[0477] In an exemplary embodiment, when the jumping motion task is a conventional jumping motion task, the rolling angle of the floating body of the wheel-legged robot at the start of the landing phase is set to be greater than -180 and less than 180;

[0478] Alternatively, when the jumping motion task is a somersault motion task, the rolling angle of the floating body of the wheel-legged robot at the start of the landing phase is set to be less than -180 or greater than 180.

[0479] In an exemplary embodiment, the constraint equations corresponding to the take-off stage of the wheel-legged robot include at least one of the following: a dynamic constraint equation corresponding to the take-off stage, a friction constraint equation corresponding to the take-off stage, an anti-collision constraint equation corresponding to the take-off stage, a boundary constraint equation corresponding to the take-off stage, and a continuity constraint equation between the take-off stage and the flight stage;

[0480] The constraint equations corresponding to the wheel-legged robot in the soaring stage include at least one of the following: a dynamic constraint equation corresponding to the soaring stage, an anti-collision constraint equation corresponding to the soaring stage, a boundary constraint equation corresponding to the soaring stage, and a continuity constraint equation between the soaring stage and the landing stage;

[0481] The constraint equations corresponding to the wheel-legged robot during the landing phase include at least one of the following: a dynamic constraint equation corresponding to the landing phase, a friction constraint equation corresponding to the landing phase, an anti-collision constraint equation corresponding to the landing phase, and a boundary constraint equation corresponding to the landing phase.

[0482] In an exemplary embodiment, the at least one constraint condition includes a first constraint condition and a second constraint condition, wherein the first constraint condition is used to limit the movement between the floating base dynamics model and the bearing surface to pure rolling, and the second constraint condition is used to limit the movement between the first virtual leg and the second virtual leg of the floating base dynamics model to satisfy a closed chain constraint;

[0483] The dynamic constraint equation corresponding to the take-off stage is used to constrain the floating base dynamic model to satisfy the first constraint condition, the second constraint condition and the dynamic equation corresponding to the take-off stage; wherein the dynamic equation corresponding to the take-off stage is constructed based on the generalized coordinates, control quantity, bearing surface reaction force and closed-loop force of the floating base dynamic model;

[0484] The dynamic constraint equations corresponding to the take-off phase are used to constrain the floating-base dynamic model to satisfy the second constraint condition and the dynamic equations corresponding to the take-off phase; wherein, the dynamic equations corresponding to the take-off phase are constructed based on the generalized coordinates, control quantities, and closed-loop acting forces of the floating-base dynamic model;

[0485] The dynamic constraint equations corresponding to the landing phase are used to constrain the floating-base dynamic model to satisfy the first constraint condition, the second constraint condition, and the dynamic equations corresponding to the landing phase; wherein, the dynamic equations corresponding to the landing phase are constructed based on the generalized coordinates, control quantities, bearing surface reaction forces, and closed-loop acting forces of the floating-base dynamic model.

[0486] In an exemplary embodiment, the dynamic constraint equations are expressed as follows:

[0487]

[0488] wherein, Ab refers to the representation matrix of the generalized acceleration corresponding to the generalized coordinates, refers to the derivative of the state quantity of the floating-base dynamic model, q refers to the generalized coordinates, refers to the generalized velocity corresponding to the generalized coordinates, refers to the generalized acceleration corresponding to the generalized coordinates.

[0489] In an exemplary embodiment, the at least one constraint condition further includes a third constraint condition, and the third constraint condition is used to constrain the bearing surface reaction force of the floating-base dynamic model to satisfy the friction cone;

[0490] The friction constraint equations corresponding to the take-off phase and the friction constraint equations corresponding to the landing phase are used to constrain the floating-base dynamic model to satisfy the third constraint condition.

[0491] In an exemplary embodiment, the at least one constraint condition further includes a fourth constraint condition, and the fourth constraint condition is used to constrain the mechanisms other than the driving wheels of the floating-base dynamic model not to collide with the bearing surface;

[0492] The anti-collision constraint equations corresponding to the take-off phase, the anti-collision constraint equations corresponding to the take-off phase, and the anti-collision constraint equations corresponding to the landing phase are used to constrain the floating-base dynamic model to satisfy the fourth constraint condition.

[0493] In an exemplary embodiment, the at least one constraint condition further includes a fifth constraint condition, and the fifth constraint condition is used to constrain the upper and lower limit values of the state quantity of the floating-base dynamic model, as well as the upper and lower limit values of the control quantity of the floating-base dynamic model;

[0494] The boundary constraint equations corresponding to the takeoff stage, the boundary constraint equations corresponding to the airborne stage, and the boundary constraint equations corresponding to the landing stage are used to constrain the floating base dynamics model to satisfy the fifth constraint condition and the state quantity constraints corresponding to the jumping motion task; wherein, the state quantity constraints are used to constrain the state quantities of the floating base dynamics model.

[0495] In an exemplary embodiment, the continuity constraint equation between the takeoff stage and the airborne stage is used to constrain the state quantities of the floating base dynamics model at the end moment of the takeoff stage to be the same as the state quantities of the floating base dynamics model at the start moment of the airborne stage.

[0496] In an exemplary embodiment, the at least one constraint condition further includes a sixth constraint condition and a seventh constraint condition. The sixth constraint condition is used to restrict the floating base dynamics model to have an inelastic collision with the bearing surface during the landing stage, and the seventh constraint condition is used to represent the constraint relationship between the state quantities of the floating base dynamics model before and after the landing collision;

[0497] The continuity constraint equation between the airborne stage and the landing stage is used to constrain the floating base dynamics model to satisfy the sixth constraint condition, the second constraint condition, the law of conservation of momentum, and the seventh constraint condition.

[0498] In summary, the technical solution provided by the embodiments of the present application determines the constraint equation set that the wheel-legged robot needs to satisfy in the target motion task through the constraint equations constructed based on the floating base dynamics model corresponding to the wheel-legged robot, and then determines the planned motion data of the wheel-legged robot in the target motion task based on the constraint equation set, realizing the motion planning of the wheel-legged robot. By adopting the technical solution provided by the embodiments of the present application, arbitrary motion planning of the wheel-legged robot can be realized, such as sliding, conventional jumping, flipping and other motions, so that the motion planning method of the wheel-legged robot has universality, and at the same time, the wheel-legged robot has motion capabilities such as flipping and jumping, enriching the motion capabilities of the wheel-legged robot.

[0499] It should be noted that when the device provided in the above embodiment realizes its functions, only the above-mentioned division of each functional module is used for illustration. In actual application, the above functions can be allocated to different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the device provided in the above embodiment and the method embodiment belong to the same concept, and the specific implementation process is detailed in the method embodiment, which will not be repeated here.

[0500] Please refer to Figure 9, which shows a simplified structural block diagram of a computer device provided in an embodiment of the present application. This computer device can be used to implement the motion planning method of the wheel-legged robot provided in the above embodiment. Specifically:

[0501] Optionally, the computer device includes a processor 901 and a memory 902. The processor 901 includes, but is not limited to, any one of the following: CPU (Central Processing Unit, central processor), GPU (Graphics Processing Unit, graphics processor), and FPGA (Field Programmable Gate Array, field programmable logic gate array), etc. The memory 902 may include storage devices such as RAM (Random-Access Memory, random access memory) and ROM (Read-Only Memory, read-only memory). The processor 901 and the memory 902 can be connected through a system bus.

[0502] In an exemplary embodiment, at least one instruction, at least one program, a code set, or an instruction set is stored in the memory 902, and the at least one instruction, the at least one program, the code set, or the instruction set is loaded and executed by the processor 901 to implement the motion planning method of the above wheel-legged robot.

[0503] In an exemplary embodiment, a computer-readable storage medium is further provided. At least one instruction, at least one program, a code set, or an instruction set is stored in the storage medium, and the at least one instruction, the at least one program, the code set, or the instruction set implements the motion planning method of the above wheel-legged robot when executed by a processor of a computer device.

[0504] Optionally, the computer-readable storage medium may include: ROM (Read-Only Memory, read-only memory), RAM (Random-Access Memory, random access memory), SSD (Solid State Drives, solid state drive), or optical disc, etc. Among them, the random access memory may include ReRAM (Resistance Random Access Memory, resistive random access memory) and DRAM (Dynamic Random Access Memory, dynamic random access memory).

[0505] In an exemplary embodiment, a computer program product or a computer program is further provided. The computer program product or the computer program includes computer instructions stored in a computer-readable storage medium. A processor of the wheel-legged robot reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions to cause the computer device to execute the above-mentioned motion planning method of the wheel-legged robot.

[0506] It should be understood that "a plurality of" mentioned herein refers to two or more. "And / or" describes the association relationship of associated objects and indicates that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after. In addition, the step numbers described herein only exemplarily show a possible execution sequence between steps. In some other embodiments, the above steps may not be executed in the order of the numbers. For example, two steps with different numbers are executed simultaneously, or two steps with different numbers are executed in the reverse order of the illustration. The embodiments of the present application do not limit this.

[0507] The above are only exemplary embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A motion planning method for a wheel-legged robot, characterized in that, The method includes: Obtaining a target motion task planned for the wheel-legged robot; Obtaining a constraint equation set corresponding to the target motion task, where the constraint equation set is constructed based on the floating-base dynamics model corresponding to the wheel-legged robot. The constraint equation set includes constraint equations under at least one constraint condition. The constraint equations are used to constrain the wheel-legged robot to execute the target motion task. The target motion task is divided into multiple stages. The constraint equation set includes constraint equations corresponding to each of the multiple stages and continuity constraint equations between adjacent stages among the multiple stages. The constraint equations corresponding to each of the multiple stages are determined according to the generalized coordinates, control quantities, support surface reaction forces, and closed-loop acting forces of the floating-base dynamics model, or are determined according to the generalized coordinates, control quantities, and support surface reaction forces of the floating-base dynamics model. The continuity constraint equations between adjacent stages are determined according to the generalized coordinates of the floating-base dynamics model; Optimizing an objective function corresponding to the target motion task based on the constraint equation set to obtain a planned motion data sequence corresponding to the target motion task; wherein, the planned motion data sequence includes planned motion data of the wheel-legged robot at multiple time points.

2. The method according to claim 1, characterized in that, The floating-base dynamics model includes a floating body, driving wheels, and a first virtual leg and a second virtual leg having a parallel relationship; wherein, The first ends of the upper limbs of the first virtual leg and the second virtual leg are respectively connected to the floating body; The second end of the upper limb of the first virtual leg is connected to the first end of the lower limb of the first virtual leg, and the second end of the upper limb of the second virtual leg is connected to the first end of the lower limb of the second virtual leg; The second ends of the lower limbs of the first virtual leg and the second virtual leg are respectively connected to the driving wheels.

3. The method according to claim 2, wherein The model parameters of the floating-base dynamics model include at least one of the following: the generalized coordinates, control quantities, support surface acting forces, and closed-loop acting forces of the floating-base dynamics model; wherein, The generalized coordinates are used to describe the pose of the floating-base dynamics model. The generalized coordinates include the central position of the floating body, the pitch angle of the floating body, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, and the rotation angle of the driving wheels; The control quantities are used to control the first virtual leg, the second virtual leg, and the driving wheels. The control quantities include the execution torque of the driving joints of the first virtual leg, the execution torque of the driving joints of the second virtual leg, and the execution torque of the driving wheels; The support surface reaction forces are used to describe the acting forces of the support surface on the floating-base dynamics model. The support surface reaction forces include the friction force and the support force of the support surface on the wheel-legged robot; The closed-loop acting force is used to describe the binding force between the first virtual leg and the second virtual leg, and the closed-loop acting force includes the binding force between the first virtual leg and the second virtual leg.

4. The method according to claim 1, characterized in that The floating-base dynamic model includes a floating fuselage, a driving wheel, a first virtual leg and a second virtual leg having a parallel relationship, and an adjusting mechanism connected to the floating fuselage, where the adjusting mechanism is used to adjust the posture of the wheel-legged robot; where The first ends of the upper limbs of the first virtual leg and the first virtual leg of the second virtual leg are respectively connected to the floating fuselage; The second end of the upper limb of the first virtual leg is connected to the first end of the lower limb of the first virtual leg, and the second end of the upper limb of the second virtual leg is connected to the first end of the lower limb of the second virtual leg; The second ends of the lower limbs of the first virtual leg and the second virtual leg are respectively connected to the driving wheel.

5. The method according to claim 4, wherein The model parameters of the floating-base dynamic model include at least one of the following: the generalized coordinates of the floating-base dynamic model, the control quantity, the bearing surface acting force, and the closed-loop acting force; where The generalized coordinates are used to describe the pose of the floating-base dynamic model, and the generalized coordinates include the central position of the floating fuselage, the pitch angle of the floating fuselage, the rotation angle of the upper limb of the first virtual leg, the rotation angle of the lower limb of the first virtual leg, the rotation angle of the upper limb of the second virtual leg, the rotation angle of the lower limb of the second virtual leg, the rotation angle of the driving wheel, and the rotation angle of the adjusting mechanism; The control quantity is used to control the first virtual leg, the second virtual leg, and the driving wheel, and the control quantity includes the execution torque of the driving joint of the first virtual leg, the execution torque of the driving joint of the second virtual leg, the execution torque of the driving wheel, and the execution torque of the adjusting mechanism; The bearing surface reaction force is used to describe the acting force of the bearing surface on the floating-base dynamic model, and the bearing surface reaction force includes the friction force and the supporting force of the bearing surface on the wheel-legged robot; The closed-loop acting force is used to describe the binding force between the first virtual leg and the second virtual leg, and the closed-loop acting force includes the binding force between the first virtual leg and the second virtual leg.

6. The method according to claim 1, wherein The target motion task is a jumping motion task, and the jumping motion task includes a takeoff stage, a flight stage, and a landing stage; The constraint equations corresponding to the jumping motion task include: the constraint equation corresponding to the takeoff stage, the continuity constraint equation between the takeoff stage and the flight stage, the constraint equation corresponding to the flight stage, the continuity constraint equation between the flight stage and the landing stage, and the constraint equation corresponding to the landing stage.

7. The method according to claim 6, wherein When the jumping motion task is a conventional jumping motion task, the roll angle of the floating fuselage of the wheel-legged robot at the start time of the landing stage is set to be greater than -180 and less than 180; Or, In the case where the jumping motion task is a somersault motion task, the rolling angle of the floating body of the wheel-legged robot at the start of the landing phase is set to be less than -180 or greater than 180.

8. The method according to claim 6, characterized in that The constraint equations corresponding to the wheel-legged robot in the take-off stage include at least one of the following: a dynamic constraint equation corresponding to the take-off stage, a friction constraint equation corresponding to the take-off stage, an anti-collision constraint equation corresponding to the take-off stage, a boundary constraint equation corresponding to the take-off stage, and a continuity constraint equation between the take-off stage and the flying stage; The constraint equations corresponding to the wheel-legged robot in the soaring stage include at least one of the following: a dynamic constraint equation corresponding to the soaring stage, an anti-collision constraint equation corresponding to the soaring stage, a boundary constraint equation corresponding to the soaring stage, and a continuity constraint equation between the soaring stage and the landing stage; The constraint equations corresponding to the wheel-legged robot during the landing phase include at least one of the following: a dynamic constraint equation corresponding to the landing phase, a friction constraint equation corresponding to the landing phase, an anti-collision constraint equation corresponding to the landing phase, and a boundary constraint equation corresponding to the landing phase.

9. The method according to claim 8, wherein The at least one constraint condition includes a first constraint condition and a second constraint condition, wherein the first constraint condition is used to limit the movement between the floating base dynamics model and the bearing surface to pure rolling, and the second constraint condition is used to limit the movement between the first virtual leg and the second virtual leg of the floating base dynamics model to satisfy a closed chain constraint; The dynamic constraint equation corresponding to the take-off stage is used to constrain the floating base dynamic model to satisfy the first constraint condition, the second constraint condition and the dynamic equation corresponding to the take-off stage; wherein the dynamic equation corresponding to the take-off stage is constructed based on the generalized coordinates, control quantity, bearing surface reaction force and closed-loop force of the floating base dynamic model; The dynamic constraint equation corresponding to the take-off stage is used to constrain the floating base dynamic model to satisfy the second constraint condition and the dynamic equation corresponding to the take-off stage; wherein the dynamic equation corresponding to the take-off stage is constructed based on the generalized coordinates, control quantity and closed-loop force of the floating base dynamic model; The dynamic constraint equation corresponding to the landing stage is used to constrain the floating base dynamic model to satisfy the first constraint condition, the second constraint condition and the dynamic equation corresponding to the landing stage; wherein the dynamic equation corresponding to the landing stage is constructed based on the generalized coordinates, control quantity, bearing surface reaction force and closed-loop force of the floating base dynamic model.

10. The method according to claim 8, wherein The dynamic constraint equation is expressed as follows: where Ab represents the matrix of the generalized accelerations corresponding to the generalized coordinates, represents the derivative of the state variables of the floating-base dynamic model, q represents the generalized coordinates, represents the generalized velocities corresponding to the generalized coordinates, represents the generalized accelerations corresponding to the generalized coordinates.

11. The method according to claim 8, characterized in that, The at least one constraint condition further includes a third constraint condition, and the third constraint condition is used to constrain the reaction force of the bearing surface of the floating base dynamics model to satisfy a friction cone; The friction constraint equation corresponding to the take-off phase and the friction constraint equation corresponding to the landing phase are used to constrain the floating base dynamics model to satisfy the third constraint condition.

12. The method according to claim 8, characterized in that, The at least one constraint condition further includes a fourth constraint condition for constraining that the mechanism of the floating-base dynamic model other than the driving wheels does not collide with the bearing surface; The anti-collision constraint equations corresponding to the takeoff stage, the anti-collision constraint equations corresponding to the airborne stage, and the anti-collision constraint equations corresponding to the landing stage are used to constrain the floating-base dynamic model to satisfy the fourth constraint condition.

13. The method according to claim 8, wherein The at least one constraint condition further includes a fifth constraint condition for constraining the upper and lower limit values of the state variables of the floating-base dynamic model, and the upper and lower limit values of the control variables of the floating-base dynamic model; The boundary constraint equations corresponding to the takeoff stage, the boundary constraint equations corresponding to the airborne stage, and the boundary constraint equations corresponding to the landing stage are used to constrain the floating-base dynamic model to satisfy the fifth constraint condition and the state variable constraints corresponding to the jumping motion task; wherein, the state variable constraints are used to constrain the state variables of the floating-base dynamic model.

14. The method according to claim 8, wherein The continuity constraint equation between the takeoff stage and the airborne stage is used to constrain that the state variables of the floating-base dynamic model at the end moment of the takeoff stage are the same as the state variables of the floating-base dynamic model at the start moment of the airborne stage.

15. The method according to claim 8, wherein The at least one constraint condition further includes a sixth constraint condition and a seventh constraint condition. The sixth constraint condition is used to limit that the collision between the floating-base dynamic model and the bearing surface in the landing stage is inelastic, and the seventh constraint condition is used to represent the constraint relationship between the state variables of the floating-base dynamic model before and after the landing collision; The continuity constraint equation between the airborne stage and the landing stage is used to constrain the floating-base dynamic model to satisfy the sixth constraint condition, the second constraint condition, the law of conservation of momentum, and the seventh constraint condition.

16. A motion planning device for a wheel-leg robot, characterized in that, The device includes: A motion task acquisition module for acquiring a target motion task planned for the wheel-legged robot; A constraint equation acquisition module for acquiring a constraint equation set corresponding to the target motion task. The constraint equation set is constructed based on the floating-base dynamic model corresponding to the wheel-legged robot. The constraint equation set includes constraint equations under at least one constraint condition. The constraint equations are used to constrain the wheel-legged robot to execute the target motion task. The target motion task is divided into multiple stages. The constraint equation set includes the constraint equations corresponding to each of the multiple stages and the continuity constraint equations between adjacent stages among the multiple stages. The constraint equations corresponding to each of the multiple stages are determined according to the generalized coordinates, control variables, bearing surface reaction forces, and closed-loop acting forces of the floating-base dynamic model, or are determined according to the generalized coordinates, control variables, and bearing surface reaction forces of the floating-base dynamic model. The continuity constraint equations between adjacent stages are determined according to the generalized coordinates of the floating-base dynamic model; A planning data acquisition module, configured to optimize an objective function corresponding to the target motion task based on the constraint equations to obtain a planned motion data sequence corresponding to the target motion task; wherein, the planned motion data sequence includes planned motion data of the wheel-legged robot at multiple time points.

17. A computer device, characterized in that, The computer device includes a processor and a memory, and at least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to implement the motion planning method of the wheel-legged robot according to any one of claims 1 to 15.

18. A computer-readable storage medium, characterized in that, At least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the motion planning method of the wheel-legged robot according to any one of claims 1 to 15.

19. A computer program product, characterized in that, The computer program product includes computer instructions, the computer instructions are stored in a computer-readable storage medium, and the processor reads and executes the computer instructions from the computer-readable storage medium to implement the motion planning method of the wheel-legged robot according to any one of claims 1 to 15.

Images