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

Abstract

The present application 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, which comprises: in the design of a jumping trajectory, determining a desired motion trajectory of a robot in a jumping process according to the positional relationship between the robot and an obstacle and the height of the obstacle, the motion trajectory comprising a take-off trajectory, a flight trajectory and a landing trajectory, wherein the take-off trajectory is optimized with maximum torque minimization as the optimization objective; in the aspect of jumping control, determining the desired angle, angular velocity and angular acceleration of each joint of the robot according to the desired motion trajectory of the robot in the jumping process, and then combining the external force distribution at the foot end of the robot to obtain the joint torque of the robot motion, thereby realizing the control of the whole jumping process of the robot. The present application can optimize the jumping motion trajectory of the wheel-legged hybrid robot and realize the safe and efficient movement of the wheel-legged hybrid robot in a complex scene.

Description

TECHNICAL FIELD

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

[0002] The motion control of wheel-legged hybrid robots has always been a hot topic in the field of robot research. When the robot faces extreme terrains, such as steep slopes, high obstacles or dramatic changes in terrain, the traditional single movement mode limits the robot's obstacle crossing performance due to the lack of flexibility and adaptability. In order to solve this problem, jumping technology is considered as an innovative solution to deal with complex terrains. For wheel-legged hybrid robots, jumping technology not only helps them to quickly cross obstacles, but also enhances their ability to move flexibly on rough terrains. However, the jumping control of wheel-legged hybrid robots has significant difficulties. Precise trajectory planning is required during jumping to ensure the stability and safety of the robot in different terrains, and the complex dynamics model and highly nonlinear torque control also pose higher requirements for real-time control of the system.

[0003] Therefore, how to achieve efficient and accurate jumping control becomes a core problem in the jumping technology of wheel-legged hybrid robots. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides a wheel-legged hybrid robot rolling and jumping motion control method and system based on maximum torque minimization, which aims to realize safe and efficient jumping motion of wheel-legged hybrid robots in complex environments.

[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, a wheel-legged hybrid robot rolling and jumping motion control method based on maximum torque minimization is proposed, which includes the following steps:

[0006] Determine the desired motion trajectory of the robot during the jumping process 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] Construct a jumping trajectory optimization model with the minimum maximum torque of the joint motor as the optimization objective, and solve the jumping trajectory optimization model to obtain the take-off trajectory of the robot;

[0008] Determine the maximum take-off height of the robot during flight according to the detected take-off speed of the robot, and then combine the height of the obstacle to adjust the joint angle of the robot during flight by inverse kinematics to obtain the flight trajectory;

[0009] When it is detected that the robot is in the landing stage, according to the real-time height of the robot body centroid from the ground, the joint angle of the robot when landing is solved through inverse kinematics, the landing pose of the robot is adjusted, and the landing trajectory is obtained;

[0010] According to the expected motion trajectory of the robot in the jumping process, the expected angle, angular velocity and angular acceleration of each joint of the robot are determined, and then the joint torque of the robot motion is obtained in combination with the external force distribution of the foot end of the robot, so as to realize the control of the whole jumping process of the robot.

[0011] As a further optimization, the objective function J and the constraint condition of the jumping trajectory optimization model are:

[0012]

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

[0014] As a further optimization, when the jumping trajectory optimization model is solved iteratively, for the kth iteration, the upper limit function and the lower limit function respectively take the maximum value and the minimum value of the joint torque in the optimization result obtained in the (k-1)th iteration.

[0015] As a further optimization, the constraint condition of the jumping trajectory optimization model further includes: the constraint that the foot end of the robot always keeps in contact with the ground in the take-off stage, the constraint that the contact force between the foot end and the ground satisfies the friction cone, and the motion space constraint of the foot end of the robot.

[0016] As a further optimization, when the robot satisfies the landing detection condition, it is considered that the robot is in the landing stage; the landing detection condition is as follows:

[0017] (t≥t h )and(p z -0.5L)≥x obs

[0018] Wherein, t represents time, t h represents the time when the robot flies to the highest point, L represents the length of the robot body, p X represents the position of the robot body centroid in the X-axis direction, x obs represents the position of the obstacle boundary in the X-axis direction, and the X-axis is the rolling forward direction of the robot wheel.

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

[0020]

[0021] Wherein, 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, respectively represent the joint angle, angular velocity and angular acceleration of the robot; F represents the external force at the foot end of the robot.

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

[0023] According to the current pose of the robot, the motion state of the robot in the future period of time is predicted, and the robot foot end external force distribution is solved online by combining the foot end contact force constraint and taking the predicted state as close as possible to the expected motion trajectory as the goal.

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

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

[0026] According to another aspect of the present application, a wheel-legged hybrid robot rolling jump motion control system based on maximum torque minimization is provided, which comprises a processor for executing the above-mentioned wheel-legged hybrid robot rolling jump motion control method based on maximum torque minimization.

[0027] Overall, compared with the prior art, the above technical solutions conceived by the present application mainly have the following technical advantages:

[0028] 1、The present application divides the jumping process into three stages of take-off, flight and landing, generates the jumping trajectory of the robot with the optimization target of minimizing the maximum torque, can effectively improve the motion efficiency and stability of the robot, and then combines the external force distribution of the foot end of the robot to realize efficient and accurate control of the whole jumping process of the wheel-leg hybrid robot, and can be applied to mobile inspection, operation and other tasks in energy chemical industry, power, fire fighting, underground pipe gallery and other working environments.

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

[0030] Figure 1 It is a rolling jumping motion control method flowchart of the wheel-leg hybrid robot based on maximum torque minimization in the embodiment of the present application;

[0031] Figure 2 It is a specific implementation flowchart of environment information extraction and jumping action judgment in the embodiment of the present application;

[0032] Figure 3 It is a specific implementation flowchart of the jumping process analysis in the embodiment of the present application;

[0033] Figure 4a It is a specific implementation flowchart of the modeling process of the take-off stage trajectory optimization model in the embodiment of the present application;

[0034] Figure 4b It is a specific implementation flowchart of the solving process of the take-off stage trajectory optimization model in the embodiment of the present application;

[0035] Figure 5a It is a specific implementation flowchart of the flight process analysis in the embodiment of the present application;

[0036] Figure 5b It is a specific implementation flowchart of the flight state detection and attitude adjustment in the embodiment of the present application;

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

[0038] Figure 6b It is a specific implementation flowchart of the landing stage landing state detection and landing attitude adjustment in the embodiment of the present application;

[0039] Figure 6cis a specific embodiment flow diagram of the inverse dynamics of the robot in the embodiment of the present application;

[0040] Figure 7 is a specific embodiment flow diagram of the single rigid body modeling process in the embodiment of the present application;

[0041] Figure 8a is a specific embodiment flow diagram of the foot end contact force modeling in the embodiment of the present application;

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

[0043] Figure 9a is a specific embodiment flow diagram of the robot whole machine dynamics model establishment in the embodiment of the present application;

[0044] Figure 9b is a specific embodiment flow diagram of the robot whole machine dynamics model solving joint torque in the embodiment of the present application;

[0045] Figure 10 is a specific embodiment flow diagram of the motor torque calculation combined with the PD control method in the embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0047] The wheel-leg hybrid robot rolling and jumping motion control method based on maximum torque minimization provided by the embodiment of the present application comprises the following steps: the robot determines the minimum take-off speed and height of the robot jumping according to the position, size and other information of the obstacles fed back by the environmental information, designs the take-off trajectory of the robot with the optimization target of maximum torque minimization, adjusts the leg position in real time during the flight process, extends the leg after entering the landing stage to better land stably, optimizes and solves the foot end external force of the robot in real time during the whole jumping process, solves the joint torque of the robot according to the whole machine dynamics model combined with the proportional-differential controller, adjusts the attitude of the robot, and makes the robot realize the jumping action safely and efficiently.

[0048] In the embodiment, the motion control method is based on an environmental information module, a jumping trajectory generation module, a model prediction control (MPC) module and a motion control module based on whole machine dynamics, as shown inFigure 1 As shown in the following, the specific implementation is as follows.

[0049] I. Environment information module

[0050] The environment information module mainly provides real-time environmental data support for the planning and adjustment of the jumping trajectory through the perception of the environment by the wheel-legged hybrid robot, so that the robot can adjust the jumping posture in real time according to the obstacles and complete stable and efficient jumping actions.

[0051] As shown in the following, the wheel-legged hybrid robot obtains information through sensors such as laser radar, depth camera or ultrasonic sensor, and uses methods such as extended Kalman filter for information fusion to realize self-positioning and acquisition of three-dimensional data of the surrounding environment, and models the obstacles through algorithms to estimate their geometric characteristics and determine whether the robot should jump over the obstacles. Then, based on the geometric analysis, the distance between the robot and the obstacles, the height of the obstacles 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 obstacles to complete stable and efficient jumping actions. Figure 2 II. Jumping trajectory generation module

[0052] The jumping trajectory generation module determines the motion trajectory of the robot during the jumping process according to the positional relationship between the robot and the obstacles in the environmental information and the height of the obstacles, which includes a take-off module, a flight module and a landing module for generating take-off trajectory, flight trajectory and landing trajectory respectively. The whole jumping process of the robot is shown in the following.

[0053] Figure 3 During the take-off process, the robot starts from the initial position to prepare for jumping. First, the robot accumulates energy by squatting or compressing the elastic structure of the legs, and in this process, the robot generates sufficient vertical ground reaction force by adjusting the leg joints. When reaching the optimized squatting pose, the robot quickly extends the legs to obtain vertical speed to achieve take-off, while the wheel-legged hybrid robot provides forward horizontal speed by actively driving the wheels. After the body obtains sufficient vertical and horizontal speed, the robot retracts the legs into the flight stage, adjusts the center of gravity and prepares for 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 performs vertical motion and does not produce obvious horizontal displacement. In jumping forward, the robot not only performs vertical jumping, but also uses the wheels to produce forward horizontal speed to obtain additional horizontal displacement.

[0055] ​The wheels provide the horizontal speed of the robot during the jumping process. The jumping height of the robot determines the flight time of the robot, and the forward speed of the wheel-legged robot in the movement is obtained according to the environmental information c The wheels are rotated to provide:

[0056] v c = ω w r w

[0057] Where ω w is the angular speed of the wheel, and r w is the wheel radius.

[0058] 1. Take-off module

[0059] The take-off module mainly generates the motion trajectory of the robot that can meet the take-off speed as much as possible through the optimization method by combining the obstacle information fed back by the environmental information, the dynamic characteristics of the robot and the movement characteristics of the take-off process, and at the same time, the robot body is kept horizontal during the take-off process to ensure the stability of the fuselage.

[0060] The robot take-off trajectory generation method is shown in Figure 4a and Figure 4b During the jumping process, the take-off speed of the robot determines the jumping height of the robot. Influenced by the mechanical structure of the wheel-legged robot, the legs account for a certain proportion in the weight of the whole machine, which leads to the decrease of the vertical speed of the robot body center of mass when the foot end of the wheel-legged robot leaves the ground due to the gravity of the lower leg and the wheel. At this time, the lower leg and the wheel can be regarded as a whole, and it is assumed that the total momentum of the lower leg and the wheel is zero at the moment of leaving the ground, the speed of the wheel is zero at the moment of take-off, and the speed of the lower leg joint is also close to zero. Based on the principle of momentum conservation, it can be deduced that the speed of the robot body center of mass at the moment of leaving the ground is

[0061]

[0062] Where m b is the mass of the robot excluding the wheel and the lower leg joint, m is the whole mass of the robot, and are the vertical speeds of the robot body center of mass before and at the moment of leaving the ground, respectively. In the jumping task, the height of the jumping obstacle of the robot is h obs , and the take-off speed of the robot can be obtained by the energy conservation theorem as

[0063]

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

[0065] The modeling process of the take-off trajectory optimization model is shown in FIG. 1. Figure 4a The constraint conditions are that the robot foot end is always in contact with the ground during the take-off stage, the foot end-ground contact force satisfies the friction cone constraint, and the movement space of the robot foot end is also limited by the robot configuration. Specifically, according to the feedback information of the robot system, the constraint conditions in the entire trajectory optimization process are set as follows:

[0066] Dynamics constraint:

[0067] Foot end contact constraint:

[0068] Leg movement space constraint: r e [r min , r max ]

[0069] Friction constraint:

[0070] Joint angle constraint: q e [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-body dynamics, is the generalized Coriolis force, G(q) represents the generalized gravity vector of the multi-body system, J T (q) represents the rigid body Jacobian matrix of the quadruped robot. is the foot end position of the i-th leg of the robot in the Z-axis direction in the world coordinate system, μ is the friction coefficient, and respectively represent the reaction force of the robot foot end with the ground in the X, Y, and Z directions.

[0073] In the take-off stage of the robot, in order to meet the minimum take-off speed, the joint angular velocity of the robot increases significantly, and a large joint torque is required. However, joint torque overload not only accelerates motor wear and shortens the service life of the motor, but also may cause the robot to fail to complete the task. At the same time, in order to ensure that the energy consumption of the robot in the movement process is minimized, the energy integral of the maximum joint torque is considered as the optimization index. Therefore, the objective function can be expressed as

[0074]

[0075] where τ i(t) is the motor torque of joint i. The maximum torque of joint motor is minimized as the optimization objective, aiming to control the joint torque in a narrow range under the premise of meeting the trajectory requirements, thereby preventing the motor from being overloaded due to excessive torque, reducing the burden of the motor, and improving the stability and reliability of the overall system of the robot.

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

[0077] In the jump trajectory optimization objective function, it is difficult to find a suitable optimization method by directly using the maximum torque minimization objective function for optimization. Therefore, the objective function needs to be further transformed into

[0078]

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

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

[0081]

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

[0083] In order to facilitate better optimization, two upper and lower limit functions are introduced to limit the maximum and minimum values 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 upper limit function of the maximum τ max (t), and τ l (t) is the lower limit function of the minimum τ min (t). However, it is difficult to directly obtain the optimal solution by introducing the upper and lower limit functions to achieve the optimization objective of maximum torque minimization. Therefore, through a retractable boundary function, the feasible region range is refined, and the maximum torque function is gradually contracted to approach the optimal upper and lower limit functions. In the process of initial optimization, the objective function of the optimization model is expressed as:

[0087]

[0088] In order to refine the feasible region range, the maximum and minimum values of the moment function are reduced in the iteration process, and the maximum value in the optimization result obtained in the (k-1) th iteration is used in the k th iteration And the minimum value As a new boundary constraint, the optimization model of the iteration process is as follows:

[0089]

[0090] The specific process of the take-off trajectory optimization is as shown in Figure 4b The trajectory optimization model can be solved by a nonlinear optimization solver such as CasADi, and the upper limit function and the lower limit function of the moment are updated in the iteration process, that is, the optimization purpose of minimizing the maximum moment is met, and no new nonlinear constraint is added to the original model, and at the same time, due to the introduction of the iteration optimization, the dependence of the optimization model on the initial value is greatly reduced.

[0091] The maximum moment minimization proposed in the application as the core optimization objective is suitable for the design of the jump trajectory, and can also be used in the trajectory optimization and reinforcement learning training scenes, thereby effectively improving the motion efficiency and stability of the robot.

[0092] 2, flight module

[0093] The flight module mainly detects the take-off speed of the robot through the IMU feedback information of the robot, adjusts the leg pose in combination with the obstacle height feedback by the environment information, and ensures the smooth jump.

[0094] When the four-legged robot takes off, it formally enters the flight stage. In this stage, the robot is separated from the ground support, the feet are completely suspended, and the motion state is completely determined by the kinetic energy and potential energy accumulated during take-off. Since the robot is only affected by gravity, the motion trajectory will present a parabolic shape.

[0095] The attitude adjustment of the flight stage of the robot is as shown in Figure 5a After take-off, the robot retracts the legs to take off and enter the flight stage, and the highest point h of the take-off of the robot foot end is:

[0096] h=h obs +Δh

[0097] Where Δh is the retraction distance of the robot leg after take-off, and h obs is determined by the height of the obstacle.

[0098] The flight stage robot attitude adjustment process is as shown in Figure 5bThe retraction distance Δh of the robot's leg needs to consider the robot's avoidance of obstacles during the air phase. 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 becomes farther. During flight, the size of Δh is adjusted in combination with the obstacle to adjust the position of the robot's foot during the flight phase.

[0099] 3. Landing module

[0100] The landing module detects landing by combining robot joint information with environmental information to determine whether the robot has successfully landed. Based on the detection results, the robot's pose during landing is further adjusted to ensure smooth landing.

[0101] During the landing phase, the robot actively extends its legs to a certain length when it starts to descend from the highest point of flight to reduce the impact force during landing. During the jump, in order to ensure that the robot completes the landing quickly and stably, it is necessary to precisely control its motion state during the flight phase, while meeting the task requirements and maximizing the stability of the landing.

[0102] (1) Landing detection module

[0103] The landing detection module detects whether the robot is in the landing phase to better adjust the robot's landing pose and ensure the stability of the robot's landing.

[0104] During the jump, the robot needs to complete the flight phase and land quickly to reduce the challenges posed by flight time on attitude control. Prolonging the flight time can cause the pitch angle to change too much, affecting the stability of the landing pose and increasing the risk of imbalance or overturning. In addition, a prolonged flight phase can cause the pre-designed reference trajectory to deviate from the actual requirements, especially when landing, making it difficult to achieve smooth contact with the ground.

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

[0106] if(t≥t h )and(p X -0.5L)≥x obs

[0107] then adjust the robot's leg joint angle

[0108] where t h is the time when the robot flies to the highest point, L is the length of the robot's body, p x is the position of the robot's body center of mass in the X-axis direction, and xobs is the position of the obstacle boundary along the X-axis direction. Condition 1 is to determine whether the robot is in the landing 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 in the landing stage is shown in Figure 6b The landing posture adjustment module is to ensure the robot to land smoothly by solving the joint angles of the robot at the time of landing through inverse kinematics after detecting that the robot is in the landing state.

[0111] When it is detected that the robot is in the landing stage, the height h of the robot from the landing plane is calculated through the IMU data LA When adjusting the position of the landing leg, the joint angles of the four legs are kept consistent, the height of the body center of mass from the landing plane is taken as the height of the foot end from the body, the wheel center is adjusted to be directly below the shoulder joint of the robot, and the joint angles of the robot are solved through inverse kinematics. The joint angles solved through inverse dynamics are shown in Figure 6c

[0112]

[0113] where q1 and q2 represent the angles of the thigh joint and the shank joint of the robot respectively, and l1 and l2 are the lengths of the thigh and the shank of the robot respectively.

[0114] III. Model Predict Control (MPC) module

[0115] The MPC module is to predict the motion state in the future period of time according to the current pose of the robot, and to solve the external force distribution of the foot end of the robot online.

[0116] 1. Single rigid body dynamics modeling

[0117] The single rigid body dynamics modeling is performed in advance, which simplifies the robot as a single rigid body system, and retains part of the dynamic characteristics to meet the requirement of calculation efficiency for solving the external force of the foot end by MPC.

[0118] The structure of the wheel-legged hybrid robot is a multi-rigid body structure connected by movable joints, and the dynamics model is complex, which leads to the calculation time that cannot meet the requirement of real-time control. The simplified dynamics model can meet the requirement of the dynamics characteristics of the wheel-legged hybrid robot, and also significantly reduces the required time for solving.

[0119] To establish the simplified dynamics model of the wheel-legged hybrid robot, the following assumptions are made:

[0120] ​(1) The rotation angle and angular velocity of the robot's body in the take-off phase are small.

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

[0122] (3) The robot does not generate external moments at the contact with the ground.

[0123] (4) Changes in the mass distribution of the legs due to changes in joint positions are ignored.

[0124] According to the above assumptions, the wheel-legged robot is modeled as a single rigid body, as shown in Figure 7 , the rotation angle Z-Y-X of the body is expressed by Euler angles as Θ = [α β γ] T . The rotation matrix from the body coordinate system to the world coordinate system can be expressed as

[0125]

[0126] where R n (θ) represents the rotation matrix of θ angle 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-legged robot is established as

[0128]

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

[0130] When cosβ ≠ 0, the angular velocity of the robot and the differential mapping of Euler angles can be approximately expressed as

[0131]

[0132] Here R Z (γ) denotes the rotation matrix that rotates by an angle γ about the z-axis. Based on the above simplifications, the equation of motion can be combined into the continuous state equation of the single rigid body system

[0133]

[0134] where F i ∈R 3×1 is the contact force of the i-th leg of the robot with the ground, and the values of A, B are

[0135]

[0136] where I 3×3 is the identity matrix, e = [0 0 -1] T , [r i ] × is the skew-symmetric matrix of the vector r i .

[0137] 2. Foot end external force calculation

[0138] To ensure real-time online operation of the control system, a single rigid body dynamics model is used. Within a small prediction time interval, the position change of the foot end relative to the center of mass can be ignored, so it can be assumed that the position of the 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 the MPC, while maintaining accurate control of the robot's motion state.

[0139] The model predictive control module predicts a future period of time at each control cycle and establishes an optimization problem equation according to the prediction equation. The state equation is recursively propagated to k prediction intervals using the single rigid body dynamics discrete state equation

[0140]

[0141] The state and control variables 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] Further, the recursive process is integrated as

[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 by sensors and state estimator.

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

[0148]

[0149] Since the friction constraint is a nonlinear constraint, it is divided into a linear constraint for simplification, and the size of the foot bottom reaction force in the vertical direction is limited. In order to simplify the expression, the constraint is written in matrix form

[0150] c F i ≤ d

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

[0152] In order to track the desired trajectory, the control amount U that satisfies the condition is needed to make the future system state X as close as possible to the desired trajectory. The optimization problem can be established as follows

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

[0154] s.t.c F i ≤ d, i = 1, 2, 3, 4

[0155] where: Q is the weight matrix of the reaction force, and W is the weight matrix of the control amount.

[0156] The flowchart of the MPC for solving the robot foot end force is shown in Figure 8b . This optimization model can be quickly solved by using a general quadratic programming solver to solve the optimal foot end force of the wheel-foot end.

[0157] Four, motion control module based on whole machine dynamics

[0158] 1, torque control module of whole machine dynamics

[0159] The torque control module of the whole machine dynamics solves the robot's desired angle, angular velocity and angular acceleration based on the robot's jump trajectory designed by the trajectory generator and the robot's feedback information. Combined with the foot external force optimized by the MPC module, the desired joint torque of the robot's motion is solved through the whole machine dynamics model.

[0160] In the process of establishing the overall dynamics model, six virtual coordinate systems are set up for the robot body, corresponding to the translation along the X, Y, and Z axes and the rotation around the X, Y, and Z axes in the world coordinate system (with the vertical direction as the Z axis and the horizontal movement direction of the wheels as the X axis). Based on this, starting from the body 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] To simplify the robot's dynamics modeling process, a closed-form inverse dynamics model is established using Newton-Euler recursion. Starting from the body coordinate system, the rotational force and generalized acceleration vector of the link are recursively calculated towards the end of each leg. Then, starting from the end of the wheel of the wheel-leg hybrid robot, the rotational force of each joint is recursively calculated. The contact force between the wheel and the ground is converted into joint torque using the Jacobian matrix. Finally, the overall dynamic equations of the robot are obtained as follows:

[0162]

[0163] Solving for the joint torques of the robot using a whole-machine dynamics model, such as... Figure 9b As shown, in solving for joint torques, to achieve precise control of the wheel-leg hybrid robot, the force between the wheel and the ground is calculated using the MPC module. Based on the jump trajectory generator, the changes in robot joint angles during the robot's control cycle Δt are considered as uniformly accelerated linear motion. Therefore, the desired 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] Where, q ref The joint motion trajectory is obtained from the trajectory optimization generator. It is the joint angular velocity at the current moment.

[0167] 2. PD control module

[0168] The PD control module is a module unit for tracking control of the robot according to a jump trajectory designed according to a trajectory generation and 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 by using the whole robot dynamics model of the wheel-legged hybrid robot, the current joint angle fed back by the motor is used to dynamically adjust the control strategy. The PD control module for the expected rotation angle of the robot joint motor is introduced to compensate the angle error, and the response of the motor is further optimized.

[0170] Figure 10 The solving process of the joint motor torque of the robot is given. After the joint motor command is calculated by using the inverse dynamics of the wheel-legged hybrid robot, the feedback torque is estimated by the joint angle fed back by the motor, and is combined with the feedforward torque τ provided by the whole robot dynamics torque control module. The comprehensive adjusted torque is:

[0171]

[0172] Wherein: K p and K d are the parameters of the PD controller.

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

[0174] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not used to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A rolling-spring motion control method for a wheel-leg hybrid robot based on maximum torque minimization, characterized in that, The method comprises the following steps: According to the position relationship between the robot and the obstacle and the height of the obstacle, a desired motion trajectory of the robot in the jumping process is determined; the motion trajectory comprises a take-off trajectory, a flight trajectory and a landing trajectory, wherein: A jumping trajectory optimization model is constructed with the minimum maximum torque of the joint motor as the optimization objective, and the take-off trajectory of the robot is obtained by solving the jumping trajectory optimization model; According to the detected take-off speed of the robot, the maximum take-off height of the robot in flight is determined, and then the joint angle of the robot in flight is solved by inverse kinematics in combination with the height of the obstacle, so as to adjust the flight pose of the robot and obtain the flight trajectory; When it is detected that the robot is in the landing stage, the joint angle of the robot in landing is solved by inverse kinematics according to the real-time height of the body center of mass of the robot from the ground, so as to adjust the landing pose of the robot and obtain the landing trajectory; According to the desired motion trajectory of the robot in the jumping process, the desired angle, angular velocity and angular acceleration of each joint of the robot are determined, and then the joint torque of the robot motion is obtained in combination with the external force distribution of the foot end of the robot, so as to realize the control of the whole jumping process of the robot. The objective function of the jump trajectory optimization model and the constraint condition is: wherein denotes an upper limit function of the maximum value of the joint torque, denotes a lower limit function of the minimum value of the joint torque; denotes the time instant, denotes the initial time instant of the take-off phase, denotes the end time instant of the take-off phase.​​ 2. The maximum torque minimization-based rolling-springing motion control method of a wheel-legged hybrid robot according to claim 1, wherein When iteratively solving the jump trajectory optimization model, for the first iteration, the upper bound function and the lower bound function respectively take the maximum and minimum joint torque values in the optimization result obtained in the first iteration.

3. The maximum moment minimization based wheel-leg hybrid robot rolling hopping motion control method according to claim 2, wherein, The constraint conditions of the jumping trajectory optimization model further comprise: the foot end of the robot always keeps contact with the ground in the take-off stage, the contact force between the foot end and the ground satisfies the friction cone constraint, and the motion space of the foot end of the robot is constrained.

4. The maximum moment minimization based wheel-leg hybrid robot rolling hopping motion control method according to claim 1, wherein, When the robot satisfies the landing detection condition, it is considered that the robot is in the landing stage; the landing detection condition is as follows: wherein, represents the time of the moment, represents the time of the moment the robot flies to the highest point, represents the length of the robot body, represents the position of the robot body mass center in the X axis direction, represents the position of the obstacle boundary in the X axis direction, with the direction of the robot wheel rolling forward as the X axis.

5. The maximum moment minimization based wheel-leg hybrid robot rolling hopping motion control method according to claim 1, wherein, The joint torque of the robot motion is solved by an overall dynamics model, and the overall dynamics model is represented as: wherein, denotes the joint torque of the robot, denotes the generalized mass matrix of the multi-body dynamics, denotes the generalized Coriolis force, denotes the generalized gravity vector of the multi-body system, denotes the rigid body Jacobian matrix of the quadruped robot; , , denote the joint angle, angular velocity, angular acceleration of the robot, respectively; denotes the external force at the robot foot.

6. The maximum torque minimization-based rolling-springing motion control method of a wheel-legged hybrid robot according to claim 5, wherein, The calculation method of the external force distribution of the foot end of the robot is as follows: According to the current pose of the robot, the motion state of the robot in the future period of time is predicted, and the external force distribution of the foot end of the robot is solved online with the goal of making the predicted state as close as possible to the desired motion trajectory and combining the foot end contact force constraint.

7. The maximum torque minimization-based rolling-springing motion control method of a wheel-legged hybrid robot according to claim 6, wherein The wheel-legged hybrid robot is modeled as a single rigid body in advance to obtain a single rigid body dynamics model; when the external force distribution of the foot end of the robot is calculated, the motion state of the robot in the future period of time is predicted according to the single rigid body dynamics model, and it is considered that the position of the contact point of the foot end of the wheel-legged hybrid robot relative to the body center of mass remains unchanged within the prediction time.

8. The maximum moment minimization based wheel-leg hybrid robot rolling hopping motion control method according to any one of claims 1-7, wherein, After the joint torque of the robot motion is calculated, a feedback torque is generated by proportional-differential control to compensate for the motor angle error and optimize the motor response.

9. A rolling-springing motion control system of a wheel-leg hybrid robot based on maximum torque minimization, characterized in that, The method comprises a processor for executing the wheel-legged hybrid robot rolling jumping motion control method based on maximum torque minimization according to any one of claims 1-8.

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