Wheel-legged hybrid robot rolling and jumping motion control method and system based on maximum torque minimization

Abstract

The invention belongs to the field of autonomous movement of wheel-legged robots, and particularly discloses a wheel-legged hybrid robot rolling and jumping motion control method and system based on maximum torque minimization. According to the position relation between the robot and the obstacle and the height of the obstacle, the expected motion track of the robot in the jumping process is determined, the motion track comprises a take-off track, a flight track and a landing track, and the take-off track is optimized with the maximum torque minimization as the optimization target; in the jumping control aspect, the expected angle, angular velocity and angular acceleration of each joint of the robot are determined according to the expected motion track in the jumping process of the robot, then the joint torque of robot motion is obtained by combining the external force distribution of the foot end of the robot, and the whole jumping process of the robot is controlled. According to the method, the jumping movement track of the wheel-leg hybrid robot can be optimized, and safe and efficient movement of the wheel-leg hybrid robot in a complex scene is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of autonomous movement of wheel-legged robots, and more specifically, relates to a rolling and jumping motion control method and system for a wheel-legged hybrid robot based on minimization of maximum torque. Background Art

[0002] The motion control of wheel-leg hybrid robots has always been a hot topic in the field of robotics research. When a robot faces extreme terrain, such as steep slopes, tall obstacles, or drastic changes in terrain, the traditional single mode of movement limits the robot's obstacle-crossing performance due to its lack of flexibility and adaptability. To solve this problem, jumping technology is seen as an innovative solution to cope with complex terrain. For wheel-leg hybrid robots, jumping technology can not only help them quickly cross obstacles, but also improve their ability to move flexibly on rugged terrain. However, the jumping control of wheel-leg hybrid robots has significant difficulties. During the jumping process, the trajectory needs to be accurately planned to ensure the stability and safety of the robot under different terrains. The complex dynamic model and highly nonlinear torque control also put forward higher requirements for the real-time control of the system.

[0003] Therefore, how to achieve efficient and precise jumping control has become a core problem in the jumping technology of wheel-leg hybrid robots. Summary of the invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a rolling jumping motion control method and system for a wheel-leg hybrid robot based on minimization of maximum torque, the purpose of which is to realize safe and efficient jumping motion of the wheel-leg hybrid robot in a complex environment.

[0005] To achieve the above object, according to one aspect of the present invention, a rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization is proposed, comprising the following steps:

[0006] The desired motion trajectory of the robot during the jumping process is determined according to the positional relationship between the robot and the obstacle and the height of the obstacle; the motion trajectory includes a take-off trajectory, a flight trajectory and a landing trajectory, wherein:

[0007] The jumping trajectory optimization model is constructed with the minimization of the maximum torque of the joint motor as the optimization goal, and the jumping trajectory of the robot is obtained by solving the jumping trajectory optimization model.

[0008] The maximum ground clearance of the robot is determined based on the detected ground clearance speed, and then the joint angles of the robot during flight are solved by inverse kinematics in combination with the obstacle height, and the flight posture of the robot is adjusted to obtain the flight trajectory.

[0009] When the robot is detected to be in the landing stage, the robot's joint angles when landing are solved by inverse kinematics according to the real-time height of the robot's body center of mass from the ground, and the robot's landing posture is adjusted to obtain the landing trajectory;

[0010] According to the expected motion trajectory of the robot's jumping process, the expected angle, angular velocity and angular acceleration of each joint of the robot are determined, and then combined with the external force distribution at the robot's foot end, the joint torque of the robot's movement is obtained to achieve control of the entire robot jumping process.

[0011] As a further preferred embodiment, the objective function J and constraint conditions of the jump trajectory optimization model are:

[0012]

[0013] in, Represents the maximum value of the joint torque τ max The upper limit function of (t), Represents the minimum value τ in the joint torque min (t) is the lower limit function; t represents the time, t0 represents the initial time of the take-off phase, t f Indicates the end time of the take-off phase.

[0014] As a further preferred embodiment, when iteratively solving the jump trajectory optimization model, for the kth iteration, the upper limit function Lower limit function Take the maximum and minimum values ​​of the joint torque in the optimization results obtained in the k-1th iteration respectively.

[0015] As a further preference, the constraints of the jumping trajectory optimization model also include: the robot foot always maintains contact with the ground during the take-off phase, the contact force between the foot and the ground satisfies the friction cone constraint and the motion space constraint of the robot foot.

[0016] As a further preference, when the robot meets the landing detection condition, the robot is considered to be in the landing stage; the landing detection condition is as follows:

[0017] (t≥t h )and(p z -0.5L)≥x obs

[0018] Among them, t represents the time, t h represents the time it takes for the robot to reach its highest point, L represents the length of the robot, and p X Indicates the position of the robot's body mass center in the X-axis direction, x obs Indicates the position of the obstacle boundary in the X-axis direction, with the robot's wheel rolling direction as the X-axis.

[0019] As a further preferred embodiment, the joint torque of the robot motion is obtained by solving the whole machine dynamics model, and the whole machine dynamics model is expressed as:

[0020]

[0021] Where τ represents the joint torque of the robot, M(q) represents the generalized mass matrix of multi-rigid body dynamics, represents the generalized Coriolis force, G(q) represents the generalized gravity vector of the multi-rigid body system, J T (q) represents the rigid body Jacobian matrix of the quadruped robot; q, They represent the robot's joint angle, angular velocity, and angular acceleration respectively; F represents the external force at the robot's foot end.

[0022] As a further preferred embodiment, the calculation method of the external force distribution at the foot end of the robot is:

[0023] According to the current posture of the robot, the motion state of the robot in the future is predicted, and the predicted state is as close as possible to the expected motion trajectory. Combined with the foot-end contact force constraint, the external force distribution of the robot's foot is obtained online.

[0024] As a further preferred embodiment, the wheel-leg hybrid robot is modeled as a single rigid body in advance to obtain a single rigid body dynamics model; when calculating the external force distribution at the foot end of the robot, the motion state of the robot in the future is predicted based on the single rigid body dynamics model, and it is assumed that within the predicted time, the position of the contact point of the foot end of the wheel-leg hybrid robot relative to the body center of mass remains unchanged.

[0025] As a further preferred embodiment, after the joint torque of the robot movement is calculated, a feedback torque is generated through proportional-differential control to compensate for the motor angle error and optimize the motor response.

[0026] According to another aspect of the present invention, a rolling and jumping motion control system of a wheel-leg hybrid robot based on maximum torque minimization is provided, comprising a processor, wherein the processor is used to execute the above-mentioned rolling and jumping motion control method of the wheel-leg hybrid robot based on maximum torque minimization.

[0027] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0028] 1. The present invention divides the jumping process into three stages: take-off, flight and landing, and generates the robot's jumping trajectory with the maximum torque minimization as the optimization goal, which can effectively improve the robot's movement efficiency and stability; and then combines the external force distribution at the robot's foot end to achieve efficient and accurate control of the entire jumping process of the wheel-leg hybrid robot; it can be applied to mobile inspection, operation and other tasks in working environments such as energy and chemical industry, electric power, fire protection, and underground pipe corridors.

[0029] 2. The present invention adopts a single rigid body dynamics model to predict the external force at the foot end of the wheel-leg hybrid robot to ensure its real-time online operation, and establishes the whole machine dynamics model of the robot through the Newton-Euler equation to realize the control of the whole process of the robot jumping; in addition, proportional-differential control is introduced to further ensure the stability and flexibility of the robot in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 1 is a flow chart of a method for controlling a rolling and jumping motion of a wheel-leg hybrid robot based on minimization of maximum torque in an embodiment of the present invention;

[0031] Figure 2 It is a schematic diagram of a specific implementation process of environmental information extraction and jumping action judgment in an embodiment of the present invention;

[0032] Figure 3 It is a schematic diagram of a specific implementation flow of the jump process analysis in an embodiment of the present invention;

[0033] Figure 4a It is a schematic diagram of a specific implementation process of the trajectory optimization model building process in the take-off phase in an embodiment of the present invention;

[0034] Figure 4b It is a schematic diagram of a specific implementation process of the trajectory optimization model solving process in the take-off phase in an embodiment of the present invention;

[0035] Figure 5a This is a schematic diagram of a specific implementation flow of the flight process analysis in an embodiment of the present invention;

[0036] Figure 5b It is a schematic diagram of a specific implementation process of flight state detection and attitude adjustment in an embodiment of the present invention;

[0037] Figure 6a It is a flowchart of a specific embodiment of the analysis of the landing process in the landing stage in an embodiment of the present invention;

[0038] Figure 6b It is a flowchart of a specific embodiment of landing state detection and landing posture adjustment in the landing stage of an embodiment of the present invention;

[0039] Figure 6cIt is a schematic diagram of a specific embodiment of the process of solving the joint angle of the robot by inverse dynamics in an embodiment of the present invention;

[0040] Figure 7 It is a schematic diagram of a specific embodiment of a single rigid body modeling process in an embodiment of the present invention;

[0041] Figure 8a is a schematic diagram of a specific embodiment of the foot end contact force modeling process in an embodiment of the present invention;

[0042] Figure 8b It is a schematic diagram of a specific embodiment flow of MPC solving the external force of the foot end in an embodiment of the present invention;

[0043] Figure 9a It is a schematic diagram of a specific embodiment of the process of establishing a dynamic model of the robot in an embodiment of the present invention;

[0044] Figure 9b It is a schematic diagram of a specific embodiment of the process of solving joint torques using a robot whole machine dynamics model in an embodiment of the present invention;

[0045] Fig.10 It is a flowchart of a specific embodiment of calculating the motor torque in combination with the PD control method in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0047] A method for controlling the rolling jumping motion of a wheel-leg hybrid robot based on minimization of maximum torque provided by an embodiment of the present invention comprises the following steps: the robot determines the minimum take-off speed and height of the robot's jump according to information such as the position and size of obstacles fed back by environmental information, designs the robot's take-off trajectory with the minimization of maximum torque as the optimization goal, adjusts the leg position in real time during flight, extends the legs after entering the landing phase to land more smoothly, optimizes and solves the robot's foot-end external force in real time during the entire jumping process, solves the robot's joint torque according to the robot's overall machine dynamics model combined with a proportional-differential controller, adjusts the robot's posture, and enables the robot to safely and efficiently perform jumping movements.

[0048] In this embodiment, the motion control method is based on an environment information module, a jump trajectory generation module, a model predictive control (MPC) module, and a motion control module based on whole machine dynamics. Figure 1 As shown, the details are as follows.

[0049] 1. Environmental Information Module

[0050] The environmental information module mainly provides real-time environmental data support for the planning and adjustment of jumping trajectories through the wheel-leg hybrid robot's perception of the environment, enabling the robot to adjust its jumping posture in real time according to obstacles and complete stable and efficient jumping movements.

[0051] like Figure 2 As shown in the figure, the wheel-leg hybrid robot obtains information through sensors such as laser radar, depth camera or ultrasonic sensor, and uses methods such as extended Kalman filtering to fuse information to obtain three-dimensional data of its own positioning and surrounding environment, and models obstacles through algorithms to estimate their geometric features and determine whether the robot should jump over the obstacles. Subsequently, based on geometric analysis, the distance between the robot and the obstacle, the height of the obstacle and other information are calculated and input into the jumping trajectory generation module. Combined with real-time feedback, the robot can adjust the jumping parameters in real time according to the information of the obstacle to complete a stable and efficient jumping action.

[0052] 2. Jump trajectory generation module

[0053] The jumping trajectory generation module determines the motion trajectory of the robot's jumping process according to the positional relationship between the robot and the obstacle in the environmental information and the height of the obstacle. It includes a take-off module, a flight module and a landing module, which are used to generate the take-off trajectory, the flight trajectory and the landing trajectory respectively. Figure 3 As shown in the figure, during the take-off process, the robot starts from the initial position and prepares for the jump. First, the robot accumulates energy by squatting or compressing the elastic structure of the legs. During this process, the robot generates sufficient vertical ground reaction force by adjusting the leg joints. When the optimized squatting posture is reached, the robot quickly extends its legs to obtain vertical speed to achieve take-off. At the same time, the wheel-leg hybrid robot provides forward horizontal speed by actively driving the wheels. After the fuselage obtains sufficient vertical and horizontal speeds, the robot retracts its legs to enter the flight phase, adjusts the center of gravity and prepares for the subsequent landing.

[0054] Specifically, the jumping process can be divided into two main cases: jumping in place and jumping forward. In jumping in place, the robot only moves in the vertical direction without producing obvious horizontal displacement. In jumping forward, the robot not only jumps vertically, but also uses the wheels to generate forward horizontal speed to obtain additional horizontal displacement.

[0055] The wheels provide the robot with horizontal speed during the jump. The robot's jump height determines the robot's flight time. The forward distance of the robot during the jump is obtained based on the environmental information. The forward speed v of the wheel-leg hybrid robot during movement is c Provided by wheel rotation:

[0056] v c =ω w r w

[0057] where ω w is the angular velocity of the wheel, r w is the wheel radius.

[0058] 1. Take-off module

[0059] The take-off module mainly uses the obstacle information fed back by the environmental information combined with the dynamic characteristics of the robot and the motion characteristics of the take-off process, and generates a robot motion trajectory that meets the take-off speed as much as possible through an optimization method, while keeping the robot's body horizontal during the take-off process to ensure the stability of the fuselage.

[0060] The robot jump trajectory generation method is as follows Figure 4a and Figure 4b As shown in the figure, during the jumping process, the robot's speed off the ground determines the robot's jumping height. Affected by the mechanical structure of the wheel-leg hybrid robot, the legs account for a certain proportion of the total weight of the robot. This results in that when the foot of the wheel-leg hybrid robot leaves the ground, the vertical speed of the robot's body center of mass will decrease due to the gravity of the calf and wheels. At this time, the calf and the wheel can be regarded as a whole, and it is assumed that the total momentum of the calf and the wheel is zero at the moment of leaving the ground. In the vertical direction, the speed of the wheel is zero when taking off, and the speed of the calf joint is also close to zero. Based on the principle of conservation of momentum, it can be deduced that the speed of the robot's body center of mass when leaving the ground is

[0061]

[0062] Where m b is the mass of the robot excluding the wheels and the shank joint, m is the mass of the robot as a whole, and are the vertical velocities of the robot’s center of mass before and after it leaves the ground. In the jumping task, the height of the robot’s jumping obstacle is h obs , according to the energy conservation theorem, the robot's speed off the ground can be obtained as

[0063]

[0064] (1) Establishment of take-off trajectory optimization model

[0065] The modeling process of the take-off trajectory optimization model is as follows: Figure 4a As shown. In terms of constraints, the robot foot always keeps in contact with the ground during the take-off phase, the contact force between the foot and the ground satisfies the friction cone constraint, and the motion space of the robot foot is also limited by the robot configuration. Specifically, according to the feedback information of the robot system, the constraints in the entire trajectory optimization process are set as follows:

[0066] Dynamic constraints:

[0067] Foot contact restraint:

[0068] Leg activity space constraint: r∈[r min , r max ]

[0069] Friction constraint:

[0070] Joint angle constraint: q∈[q min ,q max ]

[0071] Initial robot joint angle: q(t0) = q0

[0072] where τ is the joint torque of the robot, M(q) is the generalized mass matrix of multi-rigid body dynamics, is the generalized Coriolis force, G(q) represents the generalized gravity vector of the multi-rigid body system, J T (q) represents the rigid body Jacobian matrix of the quadruped robot. is the foot position of the robot's i-th leg along the Z axis in the world coordinate system, μ is the friction coefficient, and Represent the reaction force between the robot foot and the ground in the X, Y, and Z directions respectively.

[0073] During the robot's take-off phase, in order to meet the minimum take-off speed, the robot's joint angular velocity increases significantly, requiring a larger joint torque. However, joint torque overload will not only accelerate motor wear and shorten the motor's service life, but may also cause the robot to fail to complete the task. At the same time, in order to minimize the robot's energy consumption during movement, the energy integral of the joint's maximum torque is considered as the optimization indicator. Therefore, the objective function can be expressed as

[0074]

[0075] where τ i(t) is the motor torque of joint i. The optimization goal is to minimize the maximum torque of the joint motor. The purpose is to control the joint torque within a narrow range while meeting the trajectory requirements, thereby preventing the motor from being overloaded due to excessive torque, reducing the motor burden, and improving the stability and reliability of the overall robot system.

[0076] (2) Solution of the maximum moment minimization model

[0077] In the jump trajectory optimization objective function, it is difficult to find a suitable optimization method by directly using the objective function of minimizing the maximum torque for optimization.

[0078]

[0079] where τ max (t), τ min (t) are the maximum and minimum values ​​of the joint torque, respectively.

[0080] For N joint torques, the function can be constructed to get the maximum and minimum values ​​of the two joint torques:

[0081]

[0082] Then the maximum value τ of the N joint torques can be calculated by iterative method max (t) and the minimum value τ min (t).

[0083] In order to facilitate the optimization, two upper and lower limit functions are introduced to limit the maximum value of the joint torque function.

[0084] τ u (t)-τ max (t)≥0

[0085] τ min (t)-τ l (t)≥0

[0086] Where: τ u (t) is the maximum value τ max The upper limit function of (t), τ l (t) is the minimum value τ min (t) is the lower limit function. However, it is difficult to directly obtain the optimal solution by introducing the upper and lower limit functions to achieve the optimization goal of minimizing the maximum moment. Therefore, the feasible domain range is refined through the shrinkable boundary function, and the maximum moment function is gradually shrunk to make it approach the optimal upper and lower limit functions. In the initial optimization process, the objective function of the optimization model is expressed as:

[0087]

[0088] In order to refine the feasible region, the maximum value of the moment function is reduced by iterative method. In the kth iteration, the maximum value of the optimization result obtained by the (k-1)th iteration is used. and minimum value As the new boundary constraint, the optimization model of the iterative process is as follows:

[0089]

[0090] The specific process of take-off trajectory optimization is as follows Figure 4b As shown, the trajectory optimization model can be solved by a nonlinear optimization solver such as CasADi. The jump trajectory optimization model updates the upper limit function and the lower limit function of the torque during the iteration process, which satisfies the optimization purpose of minimizing the maximum torque without adding new nonlinear constraints to the original model. At the same time, due to the introduction of iterative optimization, the dependence of the optimization model on the initial value is greatly reduced.

[0091] The minimization of the maximum torque proposed in the present invention is used as the core optimization goal, which is not only suitable for the design of jumping trajectories, but also can be used in scenarios such as trajectory optimization and reinforcement learning training, thereby effectively improving the movement efficiency and stability of the robot.

[0092] 2. Flight module

[0093] The flight module mainly detects the robot's lift-off speed through the robot's IMU feedback information, and adjusts the leg posture based on the obstacle height fed back by environmental information to ensure smooth jumping.

[0094] When the robot's four legs leave the ground, it officially enters the flight phase. In this phase, the robot is no longer supported by the ground, and its feet are completely suspended in the air. The state of motion is completely determined by the kinetic energy and potential energy accumulated during the jump. Since the robot is only affected by gravity, the trajectory of motion will be parabolic.

[0095] The robot's attitude adjustment during the flight phase is as follows: Figure 5a As shown in the figure, after taking off, the robot retracts its legs and leaves the ground to enter the flight phase. The highest point h of the robot's foot off the ground is:

[0096] h=h obs +Δh

[0097] Where Δh is the retraction distance of the robot’s legs after taking off, h obs It is determined by the height of the obstacle.

[0098] The robot posture adjustment process during the flight phase is as follows: Figure 5bAs shown in the figure, the retraction distance Δh of the robot's legs needs to take into account the robot's avoidance of obstacles in the air. In the design of the robot's leg position during the flight phase, as Δh increases, the distance between the robot's foot and the obstacle increases. During the flight, the size of Δh is adjusted in combination with the obstacle, and the foot position of the robot during the flight phase is adjusted.

[0099] 3. Landing module

[0100] The landing module detects the landing of the robot by combining the robot joint information with the environment information to determine whether the robot has landed successfully. According to the detection results, the robot's posture when landing is further adjusted to ensure a smooth landing of the robot.

[0101] During the landing phase, when the robot begins to descend from the highest point of flight, it will actively stretch its legs to a certain length to reduce the impact force when landing. During the jumping process, in order to ensure that the robot lands quickly and stably, it is necessary to accurately control its motion state during the flight phase to meet the mission requirements and maintain the stability of the landing to the greatest extent possible.

[0102] (1) Landing detection module

[0103] The landing detection module detects whether the robot is in the landing stage, so as to better adjust the robot's landing posture and ensure that the robot lands smoothly.

[0104] During the jump, the robot needs to complete the flight phase and land quickly to reduce the challenges of flight time on attitude control. Prolonging the flight time may cause the pitch angle to change too much, affecting the stability of the landing posture, thereby increasing the risk of imbalance or tipping. In addition, an excessively long flight phase may cause the pre-designed reference trajectory to deviate from actual requirements, especially when landing, it is difficult to achieve stable contact with the ground.

[0105] To solve this problem, it is necessary to first detect whether the robot is in the landing stage, and then adjust the leg joint angle according to the current position of the robot. Figure 6a The flight status of the robot in the air when it enters the landing phase is given. The detection conditions of the robot landing phase are as follows:

[0106] if(t≥t h )and(p X -0.5L)≥x obs

[0107] Then adjust the robot leg joint angle

[0108] where t h is the time it takes for the robot to reach its highest point, L is the length of the robot, and p x is the position of the robot's body mass center in the X-axis direction, xobs is the position of the obstacle boundary along the X-axis. Condition 1 is to determine whether the robot is in the grounded state, and condition 2 is to ensure that the robot successfully jumps onto the obstacle and completes the jumping task.

[0109] (2) Landing posture adjustment module

[0110] The posture adjustment of the robot during the landing phase is as follows: Figure 6b As shown, the landing posture adjustment module is to detect that the robot is in the landing state, and then solve the joint angles of the robot when it lands through inverse kinematics to ensure that the robot lands smoothly.

[0111] When the detection robot is in the landing stage, the height h between the robot and the landing plane is calculated through IMU data. LA When adjusting the landing leg position, keep the joint angles of the four legs consistent, take the height from the body center of mass to the landing plane as the height from the foot end to the fuselage, adjust the wheel center to just below the robot shoulder joint and solve the robot's joint angles through inverse kinematics. The joint angles solved by inverse dynamics are as follows: Figure 6c As shown, through trigonometric functions we can get

[0112]

[0113] Where q1 and q2 represent the angles of the robot's thigh joint and calf joint, respectively, and l1 and l2 represent the lengths of the robot's thigh and calf, respectively.

[0114] 3. Model Predict Control (MPC) Module

[0115] The MPC module predicts the motion state in the future based on the current posture of the robot and solves the external force distribution at the robot foot end online.

[0116] 1. Single rigid body dynamics modeling

[0117] Single rigid body dynamics modeling is performed in advance, which simplifies the robot into a single rigid body system and retains some dynamic characteristics to meet the computational efficiency requirements of MPC for solving the external force at the foot end.

[0118] The structure of the wheel-leg hybrid robot is a multi-rigid body structure connected by movable joints. The dynamic model is complex, resulting in the calculation time being unable to meet the requirements of real-time control. A simplified dynamic model can meet the dynamic characteristics requirements of the wheel-leg hybrid robot and significantly reduce the time required for solution.

[0119] In order to establish a simplified dynamic model of the wheel-leg hybrid robot, the following assumptions are made:

[0120] (1) The angles and angular velocities of the robot’s body rotation and pitch during the take-off phase are relatively small.

[0121] (2) The off-diagonal terms of the inertia tensor at the center of mass of the robot body are very small.

[0122] (3) The robot does not generate any external torque at the point of contact with the ground.

[0123] (4) Ignore the changes in leg mass distribution caused by changes in joint position.

[0124] Based on the above assumptions, the wheel-leg hybrid robot is modeled as a single rigid body, such as Figure 7 As shown, the rotation angle ZYX of the fuselage is expressed by Euler angles as θ = [αβγ] T The rotation matrix from the body coordinate system to the world coordinate system is It can be expressed as

[0125]

[0126] Where R n (θ) represents the rotation matrix of the rotation angle θ around the n-axis.

[0127] According to Newton's second law and the angular momentum theorem, the single rigid body dynamics model of the wheel-leg hybrid robot is established as follows:

[0128]

[0129] in: is the position of the robot's body mass center in the world coordinate system; g∈r 3×1 is the acceleration due to gravity; F i ∈R 3×1 is the external force at the foot end of the robot’s i-th leg; ω∈R 3×1 is the angular velocity of the robot at its body mass center; r i ∈R 3×1 is the position of the foot end of the i-th leg of the wheel-leg hybrid robot relative to the body mass center, which is related to the rotation angle of the robot trunk and the joint angle of the i-th leg and can be solved by forward kinematics. w ∈R 3×3 is the inertia tensor of the body's center of mass in the world coordinate system, which can be obtained by the inertia tensor of the body in the fuselage coordinate system I b ∈R 2×3 Converted.

[0130] When cosβ≠0, by assumption 1, the differential mapping of the robot's angular velocity and Euler angle can be approximately expressed as

[0131]

[0132] Here R Z (γ) represents the rotation matrix of the rotation angle γ around the axis. Based on the above simplification, the formula can be combined into the continuous state equation of a single rigid body system

[0133]

[0134] in F i ∈R 3×1 is the contact force between the robot’s leg and the ground, and the values ​​of A and B are

[0135]

[0136] Among them I 3×3 is the identity matrix, e = [00-1] T ,[r i ] × is the vector r i The antisymmetric matrix of .

[0137] 2. Calculation of external force at the foot end

[0138] In order to ensure the real-time online operation of the control system, a single rigid body dynamics model is adopted. In a small prediction time interval, the position change of the foot end relative to the center of mass can be ignored. Therefore, it can be assumed that the position of the foot end contact point of each leg of the robot relative to the center of mass of the body remains unchanged to simplify the calculation process. This simplification not only reduces the computational burden, but also effectively improves the real-time performance of MPC while maintaining precise control of the robot's motion state.

[0139] The model predictive control module predicts the future period in each control cycle and establishes the optimization problem equation based on the prediction equation. The state equation of the single rigid body dynamics discretization is recursively converted to the state equation of k prediction intervals:

[0140]

[0141] The state and control quantities in the k prediction intervals are integrated as

[0142] X=[x T (1) x T (2) … x T (k)] T ∈R 13k×1

[0143] U=[u T (0) u T (1) … u T (k-1)] T ∈R 12k×1

[0144] Furthermore, the recursive process is integrated into

[0145] X=A qp x(0)+B qp U

[0146] Where: A qp ∈R 13k×13 is the coefficient state coefficient matrix; B qp ∈R 13k×12k is the control coefficient matrix; x(0) is the current state of the robot, which can be obtained through sensors and state estimators.

[0147] To ensure that the wheels do not slide relative to the ground, Figure 8a As shown in the figure, the constraint condition of the reaction force of the ground on the wheel foot end can be expressed as

[0148]

[0149] Since the friction constraint is a nonlinear constraint, it is split into linear constraints to simplify the calculation. At the same time, the magnitude of the plantar reaction force in the vertical direction is limited. In order to simplify the expression, the constraint is written in matrix form.

[0150] f i ≤d

[0151] in f max It is the maximum reaction force of the robot foot in the vertical direction.

[0152] In order to track the desired trajectory, it is necessary to find a control quantity U that satisfies the conditions so that the future system state X is as close to the desired trajectory as possible. The optimization problem can be established as follows

[0153] min J=(XX ref ) T Q(XX ref )+U T WU

[0154] F i ≤d, i=1, 2, 3, 4

[0155] Among them: Q is the feedback weight matrix, W is the control weight matrix.

[0156] The process of MPC solving the external force of the robot foot is as follows Figure 8b As shown, the optimization model can use a general quadratic programming solver library to quickly solve the optimal foot-end force of the wheel foot.

[0157] 4. Motion control module based on whole machine dynamics

[0158] 1. Torque control module for whole machine dynamics

[0159] The torque control module of the whole machine dynamics solves the robot's expected angle, angular velocity and angular acceleration based on the robot's jumping trajectory designed by the trajectory generator and the robot's feedback information. It combines the foot-end external force optimized by the MPC module and solves the robot's expected joint torque through the whole machine dynamics model.

[0160] In the process of establishing the whole machine dynamics model, 6 virtual coordinate systems are set for the fuselage, corresponding to the translation along the X, Y, and Z axes in the world coordinate system and the rotation around the X, Y, and Z axes (with the vertical direction as the Z axis and the horizontal movement direction of the wheels as the X axis). On this basis, starting from the fuselage coordinate system, coordinate systems are established for each joint of each leg of the robot one by one, and the specific number is dynamically adjusted according to the joint configuration.

[0161] In order to ensure the simplicity of the robot dynamics modeling process, the Newton-Euler recursion is used to establish a closed-form inverse dynamics model. Starting from the fuselage coordinate system, the motion spin and generalized acceleration vector of the connecting rod are recursively calculated to the end of each leg. Then, the force spin of each joint is recursively calculated starting from the wheel end of the wheel-leg hybrid robot. The contact force between the wheel and the ground is converted into the joint torque through the Jacobian matrix. Finally, the overall dynamics equation of the robot is obtained as follows:

[0162]

[0163] The joint torque of the robot is solved by the whole machine dynamics model. Figure 9b As shown in the figure, in order to achieve precise control of the wheel-leg hybrid robot, the force between the wheel-foot and the ground is calculated by the MPC module. Based on the jump trajectory generator, the change of the robot joint angle within the robot control cycle Δt is regarded as uniformly accelerated linear motion, so the expected angle q of each joint of the wheel-leg hybrid robot at the next moment is determined. d , angular velocity and angular acceleration for

[0164] q d =q ref

[0165]

[0166] Among them, q ref is the joint motion trajectory obtained from the trajectory optimization generator, is the joint angular velocity at the current moment.

[0167] 2. PD control module

[0168] The PD control module is a module unit that tracks and controls the robot based on the designed jumping trajectory generated by the trajectory and the real-time joint angle information of the robot.

[0169] In order to reduce the error caused by model simplification in the model predictive control module, after the joint torque is calculated using the dynamic model of the wheel-leg hybrid robot, the control strategy is dynamically adjusted using the current joint angle feedback from the motor. The PD control module for the expected rotation angle of the robot joint motor is introduced to compensate for the angle error and further optimize the motor response.

[0170] Fig.10 The solution process of the robot joint motor torque is given. After the joint motor command obtained by the inverse dynamics calculation of the wheel-leg hybrid robot is used, the feedback torque is estimated by the joint angle feedback from the motor and combined with the feedforward torque τ provided by the whole machine dynamics torque control module. The torque after comprehensive adjustment is:

[0171]

[0172] Where: K p and K d is the parameter of the PD controller.

[0173] The PD control module can not only eliminate the foot-end force distribution error caused by model simplification in model predictive control, but also make use of the characteristics of small calculation amount and high control frequency of PD controller to make up for the low calculation frequency caused by solving quadratic programming problems in model predictive control.

[0174] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A rolling jumping motion control method for a wheel-leg hybrid robot based on maximum torque minimization, characterized in that: The steps include: The desired motion trajectory of the robot during the jumping process is determined according to the positional relationship between the robot and the obstacle and the height of the obstacle; the motion trajectory includes a take-off trajectory, a flight trajectory and a landing trajectory, wherein: The jumping trajectory optimization model is constructed with the minimization of the maximum torque of the joint motor as the optimization goal, and the jumping trajectory of the robot is obtained by solving the jumping trajectory optimization model. The maximum ground clearance of the robot is determined based on the detected ground clearance speed, and then the joint angles of the robot during flight are solved by inverse kinematics in combination with the obstacle height, and the flight posture of the robot is adjusted to obtain the flight trajectory. When the robot is detected to be in the landing stage, the robot's joint angles when landing are solved by inverse kinematics according to the real-time height of the robot's body center of mass from the ground, and the robot's landing posture is adjusted to obtain the landing trajectory; According to the expected motion trajectory of the robot's jumping process, the expected angle, angular velocity and angular acceleration of each joint of the robot are determined, and then combined with the external force distribution at the robot's foot end, the joint torque of the robot's movement is obtained to achieve control of the entire robot jumping process.

2. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 1, characterized in that: The objective function J and constraints of the jump trajectory optimization model are: in, Represents the maximum value of the joint torque τ max The upper limit function of (t), Represents the minimum value τ in the joint torque min (t) is the lower limit function; t represents the time, t0 represents the initial time of the take-off phase, t f Indicates the end time of the take-off phase.

3. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 2, characterized in that: When iteratively solving the jump trajectory optimization model, for the kth iteration, the upper limit function Lower limit function Take the maximum and minimum values ​​of the joint torque in the optimization results obtained in the k-1th iteration respectively.

4. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 3 is characterized in that: The constraints of the jumping trajectory optimization model also include: the robot foot always maintains contact with the ground during the take-off phase, the contact force between the foot and the ground satisfies the friction cone constraint, and the motion space constraint of the robot foot.

5. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 1, characterized in that: When the robot meets the landing detection conditions, it is considered that the robot is in the landing stage; the landing detection conditions are as follows: (t≥t h )and(p X -0.5L)≥x obs Among them, t represents the time, t h represents the time it takes for the robot to reach its highest point, L represents the length of the robot, and p X Indicates the position of the robot's body mass center in the X-axis direction, x obs Indicates the position of the obstacle boundary in the X-axis direction, with the robot's wheel rolling direction as the X-axis.

6. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 1, characterized in that: The joint torque of the robot motion is obtained by solving the whole machine dynamics model, and the whole machine dynamics model is expressed as: Where τ represents the joint torque of the robot, M(q) represents the generalized mass matrix of multi-rigid body dynamics, represents the generalized Coriolis force, G(q) represents the generalized gravity vector of the multi-rigid body system, J T (q) represents the rigid body Jacobian matrix of the quadruped robot; q, They represent the robot's joint angle, angular velocity, and angular acceleration respectively; F represents the external force at the robot's foot end.

7. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 6, characterized in that: The calculation method of the external force distribution at the foot end of the robot is: According to the current posture of the robot, the motion state of the robot in the future is predicted, and the predicted state is as close as possible to the expected motion trajectory. Combined with the foot-end contact force constraint, the external force distribution of the robot's foot is obtained online.

8. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as claimed in claim 7, characterized in that: The wheel-leg hybrid robot is modeled as a single rigid body in advance to obtain a single rigid body dynamics model; when calculating the external force distribution at the foot end of the robot, the motion state of the robot in the future is predicted based on the single rigid body dynamics model, and it is assumed that within the predicted time, the position of the contact point of the foot end of the wheel-leg hybrid robot relative to the body center of mass remains unchanged.

9. The rolling jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization according to any one of claims 1 to 8, characterized in that: After calculating the joint torque of the robot motion, the feedback torque is generated through proportional-differential control to compensate for the motor angle error and optimize the motor response.

10. A rolling jumping motion control system of a wheel-leg hybrid robot based on minimization of maximum torque, characterized in that: It includes a processor, which is used to execute the rolling and jumping motion control method of a wheel-leg hybrid robot based on maximum torque minimization as described in any one of claims 1-9.

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