Dynamic robust motion control method and system for wheeled biped robot

Abstract

The invention provides a wheeled biped robot dynamic robust motion control method and system, and relates to the technical field of robot motion control, the method comprises the following steps: receiving a user input instruction; a wheel expected position is obtained according to a user input instruction; according to the robot integrated kinetic model, the robot state, the user input instruction and the expected wheel position, optimal control input is obtained; robot control parameters are obtained according to the robot integrated kinetic model and the optimal control input; performing motion control on the robot based on the robot control parameters; wherein in the integrated dynamic model, the relative positions of the robot trunk and the robot wheels in the advancing direction serve as control variables, and the relative positions of the robot trunk and the robot wheels in the advancing direction are obtained according to the robot wheels and the dynamic analysis result of the robot trunk. According to the invention, dynamic coordination control of the wheeled biped robot can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of robot motion control, and in particular to a dynamic robust motion control method and system for a wheeled bipedal robot. Background Art

[0002] The combination of wheeled and legged mechanisms is considered to be an effective solution for mobile robots to cope with complex terrain. In the field of mobile robots, traditional wheeled robots have been widely used due to their high movement speed and energy efficiency on flat ground, but their adaptability is obviously limited when facing complex terrain. Relatively speaking, although legged robots have better stability and adaptability in complex terrain, their movement speed and efficiency are relatively low. Wheeled bipedal robots combine the advantages of wheeled and legged movements, integrate wheeled and legged movement modes, make up for the shortcomings of a single movement mode, and significantly improve the robot's mobility and adaptability, enabling it to smoothly cope with stairs, slopes and various unstructured terrains.

[0003] However, as a typical underactuated system, wheeled bipedal robots face multiple challenges in control. In existing work, wheeled bipedal robots are usually simplified as wheeled inverted pendulum models to maintain balance and achieve velocity tracking, but this oversimplified assumption is only applicable to specific types of tasks and cannot fully capture the complex motion behavior of wheeled bipedal robots. In addition, the response lag caused by the non-minimum phase characteristics increases the control complexity. At the same time, the strong coupling and nonlinearity of the system complicate the mutual influence of the moving parts, which puts higher requirements on the control strategy. Summary of the invention

[0004] In order to solve at least one of the deficiencies of the prior art, the purpose of the present invention is to provide a dynamic robust motion control method and system for a wheeled bipedal robot, by constructing a robot integrated dynamics model suitable for the wheeled bipedal robot to achieve dynamic coordinated control of the wheeled bipedal robot.

[0005] In order to achieve the above objectives, according to some embodiments, a first aspect of the present invention provides a dynamic robust motion control method for a wheeled biped robot, comprising: Receive user input instructions; Obtaining the desired wheel position according to the user input command; Obtain the optimal control input based on the robot's integrated dynamics model, robot state, user input commands, and desired wheel positions; According to the robot integrated dynamics model and the optimal control input, the robot control parameters are obtained; Controlling the robot's motion based on the robot's control parameters; Among them, in the integrated dynamics model, the relative position of the robot trunk and the robot wheels in the forward direction is used as the control variable, and the relative position of the robot trunk and the robot wheels in the forward direction is obtained according to the dynamics analysis results of the robot wheels and the robot trunk.

[0006] A second aspect of the present invention provides a dynamic robust motion control system for a wheeled bipedal robot, comprising: An input module, configured to receive user input instructions; A dynamic programming module is configured to obtain a desired wheel position according to a user input instruction; A predictive control module is configured to obtain an optimal control input based on an integrated dynamics model of the robot, a state of the robot, a user input command, and a desired position of the wheel; A whole body control module is configured to obtain robot control parameters according to the robot integrated dynamics model and the optimal control input; A motion control module is configured to perform motion control on the robot based on the robot control parameters; Among them, in the integrated dynamics model, the relative position of the robot trunk and the robot wheels in the forward direction is used as the control variable, and the relative position of the robot trunk and the robot wheels in the forward direction is obtained according to the dynamics analysis results of the robot wheels and the robot trunk.

[0007] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a dynamic robust motion control method and system for a wheeled bipedal robot. Aiming at the problem that the existing wheeled inverted pendulum model is difficult to fully capture the complex motion behavior of the wheeled bipedal robot, based on rolling constraints and interactive force transmission, the wheel dynamics and the bipedal body center of mass dynamics are integrated to construct a robot integrated dynamics model suitable for the wheeled bipedal robot to achieve dynamic coordinated control between the wheels and the trunk (base), thereby achieving accurate trajectory tracking, adapting to various terrains, and having strong robustness to interference.

[0008] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0010] Figure 1 A schematic diagram of the structure of a robot in an embodiment of the present invention; Figure 2Schematic diagram of a wheeled inverted pendulum model of a robot in an embodiment of the present invention; Figure 3 Schematic diagram of the overall control flow of the robot in an embodiment of the present invention. DETAILED DESCRIPTION

[0011] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0012] Embodiment 1 Embodiment 1 of the present invention, as Figure 1-Figure 3 As shown, a dynamic robust motion control method for a wheeled biped robot is provided, comprising: S1, receiving user input instructions; S2, obtaining the desired wheel position according to the user input command; S3, obtaining an optimal control input according to the robot integrated dynamics model, the robot state, the user input command and the desired position of the wheel; S4, obtaining robot control parameters according to the robot integrated dynamics model and the optimal control input; S5, controlling the motion of the robot based on the robot control parameters; Among them, in the integrated dynamics model, the relative position of the robot trunk and the robot wheels in the forward direction is used as the control variable, and the relative position of the robot trunk and the robot wheels in the forward direction is obtained according to the dynamics analysis results of the robot wheels and the robot trunk.

[0013] First, define the coordinate system. Inertial coordinate system { }The x-axis is horizontally forward, the z-axis is vertically upward, and the y-axis is perpendicular to the xoz surface. The base coordinate system (base coordinate system) { The origin of} is located at the center of mass of the trunk, and the initial direction is consistent with the inertial coordinate system, and it rotates with the rotation of the trunk. Represents the interaction force spinor between the wheel and the leg, which is composed of the interaction force and interaction torque Composition, corner mark and Used to distinguish between left and right legs, such as Figure 1 As shown. Generalized coordinate matrix , velocity matrix and the drive torque matrix is represented as: ; in, , , , represents the number of joints of the robot, and denote the translation and rotation of the torso, respectively. and represent the linear velocity and angular velocity of the torso respectively.

[0014] In addition, define the control coordinate system The origin of the coordinate system is located at the midpoint of the line connecting the two wheels of the robot, and the x-axis points in the direction of the robot's movement.

[0015] Controlling the coordinate system With inertial coordinate system The rotation relationship between them is given by the rotation matrix Indicates that , represents the yaw angle of the robot trunk, Indicates the rotation angle around the z axis The corresponding rotation matrix. Indicates the control coordinate system The vector in the inertial coordinate system The mapping of Represents the inertial coordinate system The vector in the control coordinate system Controlling coordinate system The definition of contains the non-holonomic constraint characteristics of the wheeled biped robot, which facilitates the extension of motion analysis from the sagittal plane to three-dimensional space. In this embodiment, in order to distinguish different coordinate systems, the coordinate system of each symbol is marked in the upper left corner of each symbol. Symbols without a coordinate system marked in the upper left corner are represented in the world coordinate system by default.

[0016] Aiming at the problems existing in the control of existing wheeled bipedal robots and solving the challenges brought by under-actuated characteristics and complex dynamic coupling, this embodiment develops a new control framework for wheeled bipedal robots. Based on rolling constraints and interactive force transmission, the wheel dynamics and the bipedal body center of mass dynamics are integrated to construct an integrated dynamic model suitable for wheeled bipedal robots to achieve dynamic coordinated control between wheels and base. In addition, considering the non-minimum phase behavior of the wheeled bipedal robot, online dynamic programming is designed to generate wheel position constraints to adapt to the dynamic balance requirements under the current center of mass height. Furthermore, considering the robot's whole-body dynamics, non-complete constraints, optimal interactive forces and multi-task coordination, a hierarchical optimization control framework combining model predictive control and whole-body control is proposed to compensate for the potential errors brought by the simplified model and enhance the real-time control stability of the robot. The algorithm can achieve accurate trajectory tracking, adapt to various terrains, and has strong robustness to interference.

[0017] Based on the dynamic analysis of the robot's wheels and base, an integrated dynamic model is constructed.

[0018] Figuratively speaking, a wheeled bipedal robot can be seen as a pair of roller skates with active drive capabilities integrated at the end of the legs of a bipedal robot. The wheels are subject to contact force from the ground, and at the wheel-leg connection point The force and torque are transmitted to the upper body. For simplicity, the left and right wheels are not distinguished in the following motion analysis. The wheel dynamics equation in the control coordinate system is: ; ; in, and is the weight and inertia tensor of the wheel, represents the acceleration of the wheel in the control coordinate system, Indicates the support force provided by the ground in the control coordinate system. and They represent the interaction force and torque between the wheels and legs in the world coordinate system, represents the vector from the wheel center to the wheel-ground contact point, represents the wheel radius, is the wheel angular velocity, represents the wheel angular velocity around the y-axis in the control coordinate system, and g represents the acceleration due to gravity. Assume that there is no relative slip between the wheel and the ground, and the following constraints are satisfied: .

[0019] Combined with the above formula, the ground contact force is eliminated And get the inertial coordinate system The wheel dynamics equation in the x-axis direction is: ; In the formula, the numbers in the brackets in the upper right corner of the matrix represent specific rows of the matrix, for example, That is, it represents the first row of the rotation matrix. For a wheeled biped robot, the wheels and torso need to be coordinated at all times. If the positions of the two are controlled separately, the cumulative error will continue to increase over time. This error accumulation will cause system instability, resulting in the robot being unable to maintain dynamic balance or even falling. Therefore, we use the relative position relationship between the wheels and the torso as a control variable to achieve coordinated control of the entire system. Determined by the mechanical structure of the robot, the distance between the two wheels in the y-axis direction in the control coordinate system is constant. Through forward kinematics derivation, the vector , as well as The relationship between them in the acceleration layer can be expressed by the following equation: ; in, The first two terms represent the rolling angular velocity and pitching angular velocity of the trunk, but do not include the yaw angular velocity of the trunk. Since the pitch and roll angular velocities of the robot are small and can be ignored during the movement, the above formula can be approximated as: ; in, In the control coordinate system In the figure, the distance between the robot torso and the robot wheels in the x-axis direction (i.e. the direction in which the robot moves forward).

[0020] Constructing the optimal control problem (OCP) in a model-based manner to achieve robot motion control is a widely used and effective method. Considering the high dimension and nonlinearity of the whole-body dynamics model, the optimization problem will take a long time to calculate and will be difficult to solve in predictive control, which will put forward strict requirements on the real-time performance and computing resources of the onboard controller. In order to ensure real-time performance, it is necessary to use a simplified model to reduce the scale of the optimization problem. Since the mass of the robot is mainly concentrated in the torso and wheels, and the limbs are relatively light, when simplifying the whole-body dynamics model, this embodiment removes the constraints of the joint space, ignores the influence of the joint velocity on the center of mass momentum and the influence of the limb link movement on the system inertia tensor. Assume that the center of mass of all links except the wheels is concentrated at the center of mass of the torso, and the robot torso is modeled as a floating base. In the world coordinate system, the single rigid body dynamics model of the torso is as follows: ; ; in, represents the mass of the torso, represents the inertia tensor of the trunk, subscript Indicates left and right wheel legs, e.g. and They represent the vectors of the trunk mass center pointing to the points of action of the left and right wheel-leg interaction forces, and They represent the interaction forces between the left and right wheels and the legs in the world coordinate system, and They represent the interaction torque between the left and right wheels and the legs in the world coordinate system respectively.

[0021] Assuming that the roll and pitch velocities are small and the off-diagonal terms of the inertia tensor are negligible, the above equation can be approximated as: ; Since the pitch angle and roll angle are small, the inertia tensor in the inertial system can be obtained by the following formula: ; in, represents the fixed inertia tensor in the base coordinate system B.

[0022] After the dynamics of the wheels and trunk are characterized, it can be found that the motion state of the wheels and trunk is determined by the interaction force spinor, and the interaction force is equal in magnitude and opposite in sign. According to the previous analysis, replacing the wheel position with the relative position of the trunk and the wheel in the forward direction as the control variable not only reduces the dimension of the state vector to shorten the settlement time of MPC (Model Predictive Control), but also effectively realizes the coordinated control of the wheel and leg. Combining the above formula, we can get: ; in, It represents the acceleration of the distance between the wheel and the trunk along the x-axis in the control coordinate system, and is defined as , and They represent the distance between the left and right wheels and the trunk along the x-axis in the control coordinate system. The state variables are selected as ,by As control input, the integrated dynamic equations satisfying nonholonomic constraints and internal force and torque transmission are obtained as follows: ; in: ; ; ; in, and The row permutation operation is involved, namely: , and Same reason.

[0023] In step S2, the desired position of the wheel is obtained through an online dynamic planner.

[0024] A system with non-minimum phase characteristics may initially exhibit opposite output changes upon receiving a control signal, and then eventually converge to the desired result. This behavior is reflected in a wheeled biped robot, where during forward or backward acceleration, the wheels move a certain distance in the opposite direction to satisfy the dynamic constraints of the wheeled inverted pendulum model. Intuitive Conditions Applicable only to static equilibrium conditions, where and They represent the desired distances between the left and right wheels and the trunk along the x-axis in the control coordinate system, respectively. At this time, the system is at rest or in uniform motion, and is not applicable to acceleration conditions. Therefore, when selecting the reference state, the position, velocity, and angular velocity commands can be specified based on user input or predefined trajectories, while the desired position of the wheels should be dynamically planned in real time based on the basic dynamics of the wheeled bipedal robot.

[0025] As a variation of the standard linear inverted pendulum model, the wheeled inverted pendulum model uses dynamic equations of a similar form: ; like Figure 2 As shown in Figure 2, we take the geometric midpoint of the line connecting the two wheel rotation centers as the equivalent wheel axle, where represents the vector pointing from the center of mass of the torso to the equivalent wheel axis in the control coordinate system, represents the height of the torso relative to the equivalent wheel axle in the z direction, , and They represent the displacement, acceleration and equivalent wheel displacement of the center of mass of the torso in the control coordinate system. The above dynamic equation reveals the acceleration of the center of mass of the torso and the relative distance between the trunk and the equivalent wheel axle The linear relationship between them can be expressed in state space form as: ; in, , , , and Respectively represent the state vector, the inverse of the state vector with respect to time, the input vector, the state transfer matrix and the input matrix, Depends on The value of The known quantities are calculated in advance to obtain the linearized state space equations. Since the system is linear, a linear quadratic regulator (LQR) can be used to achieve system stability by minimizing a specific quadratic cost function to calculate the optimal state feedback control of the continuous-time system: ; in, and are the weight matrices of state and input, respectively. Since the system is highly sensitive to control input, it is necessary to increase To suppress its influence. Considering the varying torso height, we sample equally in the range [0.1, 0.3] Based on the algebraic Riccati equation, LQR solution is implemented to obtain the optimal gain matrix. The feedback gain matrix is ​​obtained by polynomial fitting This strategy is conducive to shortening the planning process and improving the control bandwidth of the system. The expected position of the equivalent wheel axle that satisfies the dynamics of the wheeled inverted pendulum model at the current center of gravity height can be obtained by the following formula: ; in, represents the expected value of the state vector.

[0026] Therefore, the online planning conditions for the left and right wheel positions are: .

[0027] In step S3, the optimal control input is obtained according to the model predictive controller. In this embodiment, the desired force spin of the interaction between the wheel and the trunk is generated by a discrete time finite horizon model predictive controller. When facing a multi-input multi-output (MIMO) system, MPC (Model Predictive Control) can coordinate multiple control variables to ensure the overall coordination and optimal performance of the system. Based on the constructed reduced-order system dynamics model (i.e., the integrated dynamics model) and the current system state (i.e., the state quantity in the integrated dynamics model), the rolling optimization window is used to predict the future system behavior and take control measures in advance, thereby improving the response speed and accuracy of the system. By integrating constraints directly into the optimization problem, MPC can effectively process input and state constraints, thereby achieving the desired trajectory tracking. The optimization process is continuously looped, and each iteration only applies the optimal control input at the current moment and recalculates at the next moment.

[0028] The gravity term is integrated into the state variable, and the state variable is taken as , the discrete state space form of the integrated dynamics equation can be expressed as: ; in, , is the coefficient matrix, and represents the system state and control input at time k (i.e., the interaction force and torque between the wheels and legs), represents the system state at time k+1. Assume that the prediction step is , the MPC optimization problem is constructed as follows: ; in, represents the system state referenced at time k+1, represents the control input of the system at time k, , and represents a diagonal positive semidefinite weight matrix, The term imposes a penalty on abrupt changes in the control input between consecutive time steps to prevent robot instability. To prevent wheel motor current overload and wheel slip, a safety constraint is used to limit the wheel reaction force to the conical boundary: ; in, It represents the components of the wheel-leg interaction force in the x, y, and z axes, represents the driving coefficient, and its size is related to the performance of the wheel motor. The above constraint equation is linearized using the friction cone approximation as follows: ; In addition, due to the non-holonomic constraint, the wheels cannot actively provide lateral driving force and driving torque around the x-axis and z-axis in the control coordinate system. Therefore, this constraint needs to be incorporated into the framework of the optimization problem, expressed as: ; The optimization problem is solved in real time using the qpOASES solver, where As the optimal input vector for the current control cycle.

[0029] In step S4, the control task is processed by a weighted multi-task whole-body controller to obtain control parameters to achieve motion control of the robot. Robotic systems usually show significant advantages in multi-tasking capabilities, especially when the legs have redundant degrees of freedom, which can be used to complete specific control tasks. Ignoring the dynamic characteristics of the legs may lead to reduced reliability and accuracy of task execution, thereby affecting the effective synchronization of multiple tasks. Taking these factors into account, integrating leg dynamics into the whole-body control framework can improve the stability and accuracy of task execution and optimize the overall dynamic performance and response speed of the system.

[0030] Executing multiple tasks simultaneously is very complicated in control because there may be conflicts between tasks. There are many methods to solve this problem. For example, in the null space projection method, by assigning priorities to multiple tasks, low priority tasks are solved in the null space of high priority tasks. However, this method involves high-dimensional matrix calculations, which is time-consuming and may not have enough computational space to solve low priority tasks.

[0031] This embodiment proposes a weighted multi-task whole-body controller that formulates the control problem as a weighted optimization, where each task is assigned a specific weight. This approach allows the controller to handle all tasks simultaneously, simplifying the optimization process by eliminating sequential optimization and null space projection. In the controller, the acceleration in the action space can be converted to the acceleration in the joint space by differential forward kinematics, as shown below: ; in, and Indicates the speed and acceleration of the control quantity corresponding to the task, and Represents the Jacobian matrix corresponding to the task and its derivative with respect to time.

[0032] In order to achieve generalized acceleration that meets multiple mission requirements while balancing optimization performance and constraint satisfaction, a quadratic optimization problem is formulated: ; The first constraint is a dynamic equation constraint, which is generated by the dynamics library based on the robot's full-body dynamics model. , , , and They are the inertia matrix, centrifugal force and Coriolis force matrix, gravity matrix, drive joint selection matrix and contact Jacobian matrix. represents the wheel-leg interaction force and torque optimized by the model predictive controller, represents the slack variable, represents the final desired wheel-leg interaction force and moment, Representation Task The corresponding weight matrix is, represents the nonholonomic constraint matrix, represents the force and joint torque constraint matrix. Each task is described as In order to satisfy the dynamic constraints and coordinate the balance between model predictive control and systemic control, the slack variables are introduced. It is used to relax the constraints and thus increase the solvability of the problem. The optimization variables are defined as: ,Next, each task is described in detail.

[0033] (1) Task space motion tracking. This task is used to track the desired motion trajectory of the human body, including translation and rotation, as well as the target position of the wheels.

[0034] ① Trunk translation, the trunk translation task in the acceleration layer is defined as: ; ; in, represents the Jacobian matrix corresponding to the torso translation task, is the desired acceleration of the torso, , and denote the displacement, velocity and acceleration of the trunk reference, respectively. and Represents the feedback gain matrix. The desired trunk acceleration is generated by the reference trajectory containing displacement, velocity and acceleration through the PD control rate, and the corresponding current trunk motion state is estimated by the Kalman filter fusing the feedback information such as IMU and joint encoder.

[0035] ②Trunk rotation, the trunk rotation task in the acceleration layer is defined as: ; ; in, represents the Jacobian matrix corresponding to the torso rotation task, represents the desired angular acceleration of the torso, and Represents the quaternion corresponding to the reference rotation direction and the quaternion corresponding to the current rotation direction. represents the reference angular velocity. The error in the rotation direction is calculated using the minus box operator Definition, which computes the difference between two quaternions and converts it into a three-dimensional rotation.

[0036] ③ Leg swing: For a wheeled biped robot, leg swing has the ability to adjust the position of the wheels relative to the base trunk along the forward direction. The leg swing task in the acceleration layer is defined as: ; ; in, represents the desired acceleration of the wheel relative to the torso, A reference value indicating the relative distance between the wheels and the torso.

[0037] The Jacobian matrix for this task It can be obtained by the following equation: ; in, and They represent the Jacobian matrices corresponding to the wheel and torso positions in the world coordinate system respectively. By subtracting the two and converting them to the control coordinate system, the Jacobian matrix of the leg swing task can be obtained.

[0038] (2) Energy efficiency and relaxation optimization: To optimize the joint torque output, an energy efficiency function is introduced. Compared with the leg joints, the wheel joints are assigned larger weight coefficients, which reduces the significant oscillations in the system. In addition, minimizing the relaxation variables maintains the predictive performance of the system while ensuring that the constraints are strictly adhered to during the optimization process. The task can be described as: .

[0039] Embodiment 2 This embodiment provides a dynamic robust motion control system for a wheeled bipedal robot, comprising: An input module, configured to receive user input instructions; A dynamic programming module is configured to obtain a desired wheel position according to a user input instruction; A predictive control module is configured to obtain an optimal control input based on an integrated dynamics model of the robot, a state of the robot, a user input command, and a desired position of the wheel; A whole body control module is configured to obtain robot control parameters according to the robot integrated dynamics model and the optimal control input; A motion control module is configured to perform motion control on the robot based on the robot control parameters; Among them, in the integrated dynamics model, the relative position of the robot trunk and the robot wheels in the forward direction is used as the control variable, and the relative position of the robot trunk and the robot wheels in the forward direction is obtained according to the dynamics analysis results of the robot wheels and the robot trunk.

[0040] It should be noted here that the various modules in this embodiment correspond one-to-one to the steps of the method in Example 1, and the specific implementation process is the same, which will not be repeated here.

[0041] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A dynamic robust motion control method for a wheeled bipedal robot, characterized in that: include: Receive user input instructions; Obtaining the desired wheel position according to the user input command; Obtain the optimal control input based on the robot's integrated dynamics model, robot state, user input commands, and desired wheel positions; According to the robot integrated dynamics model and the optimal control input, the robot control parameters are obtained; Controlling the robot's motion based on the robot's control parameters; Among them, in the integrated dynamics model, the relative position of the robot trunk and the robot wheels in the forward direction is used as the control variable, and the relative position of the robot trunk and the robot wheels in the forward direction is obtained according to the dynamics analysis results of the robot wheels and the robot trunk.

2. A wheeled biped robot dynamic robust motion control method as claimed in claim 1, characterized in that: The relative position of the robot torso and the robot wheels in the forward direction is constrained by the following formula: ； in, In the control coordinate system , the distance between the robot trunk and the robot wheels in the forward direction; represents the first row of the rotation matrix, V represents the linear velocity of the torso, Represents the first row of the wheel acceleration matrix in the control coordinate system.

3. A wheeled biped robot dynamic robust motion control method as claimed in claim 2, characterized in that: The integrated dynamics equation of the robot is: ； in, and denote the translation and rotation of the torso, respectively. and denote the linear velocity and angular velocity of the trunk, respectively. , and They represent the distances between the left and right wheels and the trunk along the x-axis in the control coordinate system. Indicates left and right wheels, and There are row permutation operations involved. and There are row permutation operations involved. represents the mass of the torso, represents the inertia tensor of the torso, and They represent the vectors of the trunk mass center pointing to the points of action of the left and right wheel-leg interaction forces, and They represent the interaction forces between the left and right wheels and the legs in the world coordinate system, and They represent the interaction torque between the left and right wheels and the legs in the world coordinate system, and g represents the acceleration due to gravity; , ， ， Indicates the rotation angle around the z axis The corresponding rotation matrix is, represents the wheel radius, and is the weight and inertia tensor of the wheel, with the superscript Represents the controlling coordinate system.

4. A wheeled biped robot dynamic robust motion control method as claimed in claim 1, characterized in that: The expected position of the wheel is obtained based on the wheeled inverted pendulum model at the current center of gravity height: ， in, and They represent the desired distances between the left and right wheels and the trunk along the x-axis in the control coordinate system, , is the feedback gain matrix, represents the state vector, represents the expected value of the state vector.

5. A wheeled biped robot dynamic robust motion control method as claimed in claim 1, characterized in that: The optimal control input is the desired force rotation of the interaction between the wheel and the trunk, which is obtained according to the model predictive controller.

6. A method for dynamic robust motion control of a wheeled bipedal robot as claimed in claim 5, characterized in that: The prediction step length is , the optimization problem of the model predictive controller for the optimal control input is constructed as follows: ； in, represents the system state at time k+1, represents the system state referenced at time k+1, represents the control input of the system at time k, , and represents a diagonal positive semidefinite weight matrix, The term imposes a penalty on abrupt changes in the control input between consecutive time steps to prevent the robot from becoming unstable. , is the coefficient matrix, and represents the system state and control input at time k.

7. A wheeled biped robot dynamic robust motion control method as claimed in claim 1, characterized in that: According to the robot's integrated dynamics model and the optimal control input, the control tasks are processed by a weighted multi-task whole-body controller to obtain the robot's control parameters.

8. A wheeled biped robot dynamic robust motion control method as claimed in claim 7, characterized in that: The control tasks are processed by a weighted multi-task whole-body controller to obtain the robot control parameters, including assigning specific weights to each control task, formulating a quadratic optimization problem, describing each control task in the form of an equality constraint, and solving the quadratic optimization problem to obtain the robot control parameters.

9. A wheeled biped robot dynamic robust motion control method as claimed in claim 8, characterized in that: The control task includes task-space motion tracking including trunk translation, trunk rotation, and leg swinging, as well as energy efficiency and relaxation optimization.

10. A dynamic robust motion control system for a wheeled bipedal robot, characterized in that: include: An input module, configured to receive user input instructions; A dynamic programming module is configured to obtain a desired wheel position according to a user input instruction; A predictive control module is configured to obtain an optimal control input based on an integrated dynamics model of the robot, a state of the robot, a user input command, and a desired position of the wheel; A whole body control module is configured to obtain robot control parameters according to the robot integrated dynamics model and the optimal control input; A motion control module is configured to perform motion control on the robot based on the robot control parameters; Among them, in the integrated dynamics model, the relative position of the robot trunk and the robot wheels in the forward direction is used as the control variable, and the relative position of the robot trunk and the robot wheels in the forward direction is obtained according to the dynamics analysis results of the robot wheels and the robot trunk.

Images