Adaptive model predictive control method for quadruped robot based on disturbance observer

Abstract

The present invention relates to the field of robot control technology, and in particular to a method for adaptive model predictive control of a quadruped robot based on a disturbance observer, the method comprising the following steps: S1, establishing a dynamic model of the quadruped robot; S2, obtaining motion state information of the quadruped robot through a sensor; S3, calculating control information of the quadruped robot using adaptive model predictive control according to the state information, wherein the adaptive model predictive control calculation process is optimized using the dynamic model combined with the disturbance observer; S4: adjusting the control information to the quadruped robot in real time through a robot controller to control the motion of the quadruped robot. The present invention achieves better motion performance by compensating for unknown interference in the motion of the quadruped robot.

Description

Technical Field

[0001] The invention relates to the technical field of robot control, and in particular to an adaptive model predictive control method for a quadruped robot based on a disturbance observer. Background Art

[0002] Quadruped robots are a class of robotic systems that focus on emulating the flexible movements of animals such as dogs and cheetahs, allowing them to traverse challenging terrains in an adept manner. Such robots have a wide range of applications in areas such as transportation, search and rescue, emergency response, and environmental monitoring. In order to successfully perform a variety of locomotion tasks, quadruped robots must have the ability to accurately track desired trajectories in the presence of unknown disturbances.

[0003] In actual robotic applications, the disturbances to which the robot is subjected are usually uncertain, such as carrying extra loads, uncertain mass and inertial characteristics, etc. Unknown disturbances affect the dynamic characteristics and control performance of the robot system, so it is necessary to model and compensate for the disturbance forces and torques to achieve stable control and good performance. Summary of the invention

[0004] The present invention provides a quadruped robot adaptive model predictive control method based on a disturbance observer, aiming to supplement unknown disturbances in the movement process of the quadruped robot so as to optimize the performance of the quadruped robot.

[0005] The present invention provides a disturbance observer-based adaptive model predictive control method for a quadruped robot, comprising the following steps:

[0006] S1. Establish the dynamic model of the quadruped robot;

[0007] S2, obtaining the motion state information of the quadruped robot through sensors;

[0008] S3, according to the state information, using an adaptive model predictive control algorithm to predict and control and calculate the control information of the quadruped robot, wherein the adaptive model predictive control algorithm predictive control calculation process is optimized by using the dynamic model in combination with a disturbance observer;

[0009] S4: Using the control information to adjust the quadruped robot in real time through the robot controller to control the movement of the quadruped robot.

[0010] Furthermore, the kinetic model satisfies:

[0011]

[0012]

[0013] Where m represents the mass of the quadruped robot, represents the quadruped robot's center of mass acceleration, r i Represents the position vector of the origin of the inertial system, r c represents the position vector of the center of mass of the quadruped robot, i = 1, 2, 3, 4, representing the different feet of the quadruped robot, F b ∈R 3 represents the external force disturbance of the quadruped robot, F i represents the contact force on each foot, and F=(F1 T ,F2 T ,F3 T ,F4 T ) T , I G ∈R 3×3 represents the inertia matrix of the quadruped robot, and d represents the torque disturbance experienced by the quadruped robot.

[0014] Furthermore, the kinetic model has the following assumptions without loss of generality:

[0015] External force disturbance F b , the time derivative of the torque disturbance d has an upper bound and:

[0016]

[0017] in, represents the angular acceleration, w b Represents angular velocity.

[0018] Furthermore, the interference observer is specifically:

[0019] Defining Acceleration The first composite error in, e p =p c -p c,d and Represent the direction error and angular velocity error respectively, λ p ∈R 3×3 Represents a positive definite diagonal matrix used to estimate the external force perturbation F b The first disturbance observer is designed as:

[0020]

[0021]

[0022] in, Yes A b The estimated value of Λ1=diag([λ11 ,λ 12 ,λ 13 ])∈R 3×3 represents a positive definite matrix, ξ1 is an auxiliary variable;

[0023] definition Second composite error Among them, e o =log(R T R d )and represent the direction error and angular velocity error respectively, and Represent the actual fuselage direction and the expected fuselage direction respectively, log(·): Represents a rotation matrix mapped to the corresponding rotation vector, represents the actual angular velocity, represents the desired angular velocity, represents a positive definite diagonal matrix, and the second disturbance observer for estimating the torque disturbance d is designed as:

[0024]

[0025]

[0026] in is the estimated value of d, Λ2=diag([λ 11 ,λ 12 ,λ 13 ])∈R 3×3 represents a positive definite matrix, and ξ2 is an auxiliary variable.

[0027] Furthermore, it is used to estimate the external disturbance F b The first disturbance observer is calculated by the following method:

[0028] Define the first error estimate signal:

[0029]

[0030] The first error estimation signal is derived as follows:

[0031]

[0032]

[0033] Define the first Lyapunov function V p (t) used to construct the first virtual control information A:

[0034]

[0035]

[0036] Substitute the first virtual control information A into the first Lyapunov function V p (t) time inverse and define:

[0037]

[0038] So that the first Lyapunov function V p (t) time inverse satisfy:

[0039]

[0040] The first Lyapunov function V p (t) time inverse Substitute into the first disturbance observer to solve;

[0041] The second disturbance observer for estimating the torque disturbance d is calculated by the following method:

[0042] Define the second error estimate signal:

[0043]

[0044] Derivative the second error estimate signal:

[0045]

[0046]

[0047] Define the second Lyapunov function V o (t) used to construct the second virtual control information T B :

[0048]

[0049]

[0050] The second virtual control information T B Substitute the second Lyapunov function V o (t) time inverse and define:

[0051]

[0052] So that the second Lyapunov function V o (t) time inverse satisfy:

[0053]

[0054] The second Lyapunov function V o (t) time inverse Substitute into the second disturbance observer and solve it.

[0055] Furthermore, the adaptive model predictive control algorithm is specifically:

[0056] Substitute the first disturbance observer and the second disturbance observer into the dynamic model to obtain a dynamic model based on state representation:

[0057]

[0058] in:

[0059]

[0060]

[0061]

[0062]

[0063] The external force F b , torque d are combined into a state vector and discretized to establish the cost function, equality constraints and inequality constraints of the adaptive model predictive control algorithm:

[0064]

[0065]

[0066] Where n represents the total number of time steps, represents the estimation error of the system at time step i, X i and X i,d Represent the actual state and expected state of the system at time step i, respectively, and F i represents the ground reaction force, R i and S i represent diagonal positive semidefinite matrices, and Both represent the dynamical matrix of the discrete-time system, F ix 、F iy and F iz Represent the components of the contact force vector of each foot in the x, y, and z directions, μ represents the friction coefficient between the quadruped robot and the ground, and J i represents the Jacobian matrix of the i-th leg of the quadruped robot, D iRepresents the matrix used to select the swing leg and the stance leg.

[0067] Furthermore, the control information includes joint torque, and the feedback term of the joint torque is defined as τ i , which satisfies:

[0068]

[0069] in, represents the Jacobian matrix of each leg, represents a diagonal positive definite matrix, represents the position and velocity of the ith leg, represent the position and velocity of the reference swing leg, respectively;

[0070] Define the feedforward term of joint torque as τ ff,i , which satisfies:

[0071] τ ff,i =J T f d ;

[0072]

[0073] in, represents a diagonal positive definite matrix, p 0f and p 0d Represent the actual foot position and the expected foot position in the hip joint coordinate system, respectively. and represent the actual foot speed and the expected foot speed, respectively.

[0074] The beneficial effect achieved by the present invention lies in designing an interference observer used in the kinematic equations of a quadruped robot to offset the interference of the robot system, enhancing the system's ability to suppress interference by estimating the forces and torques generated by the external environment on the robot, and integrating the forces and torques observed by the observer into the model predictive control method for operation, establishing an optimization framework that can be cyclically controlled to suppress interference during operation while maintaining the performance of the overall movement, and at the same time, through rolling optimization, stable dynamic gait control of the quadruped robot can be achieved, and unknown interference can be compensated to achieve better movement performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a schematic diagram of the steps of the adaptive model predictive control method of a quadruped robot based on a disturbance observer provided by an embodiment of the present invention;

[0076] Figure 2 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 6 kg moves linearly at a speed of 1.5 m / s in a simulation environment in a simulation experiment provided by an embodiment of the present invention;

[0077] Figure 3 is a schematic diagram of the changes in the body of a quadruped robot when a load of 10 kg moves linearly at a speed of 1.5 m / s in a simulation environment in a simulation experiment provided by an embodiment of the present invention;

[0078] Figure 4 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 6 kg rotates at a speed of 2.0 rad / s in a simulation environment in a simulation experiment provided by an embodiment of the present invention;

[0079] Figure 5 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 10 kg rotates at a speed of 2.0 rad / s in a simulation environment in a simulation experiment provided by an embodiment of the present invention;

[0080] Figure 6 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 4.5 kg moves in a straight line at a speed of 0.8 m / s in a real machine environment in a simulation experiment provided by an embodiment of the present invention;

[0081] Figure 7 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 6 kg moves linearly at a speed of 0.8 m / s in a real machine environment in a simulation experiment provided by an embodiment of the present invention;

[0082] Figure 8 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 4.5 kg rotates at a speed of 0.8 rad / s in a real machine environment in a simulation experiment provided by an embodiment of the present invention;

[0083] Fig. 9 It is a schematic diagram of the changes in the body of a quadruped robot when a load of 6 kg rotates at a speed of 0.8 rad / s in a real machine environment in a simulation experiment provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solution 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.

[0085] Please refer to Figure 1 , Figure 1 1 is a schematic diagram of the steps of a quadruped robot adaptive model predictive control method based on a disturbance observer provided by an embodiment of the present invention. The quadruped robot adaptive model predictive control method based on a disturbance observer comprises the following steps:

[0086] S1. Establish a dynamic model of the quadruped robot.

[0087] S2. Obtain the motion state information of the quadruped robot through sensors.

[0088] S3. According to the state information, the control information of the quadruped robot is calculated by predictive control using an adaptive model predictive control algorithm, wherein the predictive control calculation process of the adaptive model predictive control algorithm is optimized by using the dynamic model in combination with a disturbance observer.

[0089] S4: Using the control information to adjust the quadruped robot in real time through the robot controller to control the movement of the quadruped robot.

[0090] Specifically, the kinetic model satisfies:

[0091]

[0092]

[0093] Where m represents the mass of the quadruped robot, represents the quadruped robot's center of mass acceleration, r i Represents the position vector of the origin of the inertial system, r c represents the position vector of the center of mass of the quadruped robot, i = 1, 2, 3, 4, representing the different feet of the quadruped robot, F b ∈R 3 represents the external force disturbance of the quadruped robot, F i represents the contact force on each foot, and F=(F1 T ,F2 T ,F3 T ,F4 T ) T , I G ∈R 3×3 represents the inertia matrix of the quadruped robot, and d represents the torque disturbance experienced by the quadruped robot.

[0094] The kinetic model has the following assumptions without loss of generality:

[0095] External force disturbance F b , the time derivative of the torque disturbance d has an upper bound and:

[0096]

[0097] in, represents the angular acceleration, w b Represents angular velocity.

[0098] A widely used simplification in quadruped robot dynamics ignores the conical and gyroscopic terms w in relation (3) b ×(I Gw b ). This component is usually discarded because its contribution to the robot dynamics is considered to be small. However, the embodiment of the present invention optimizes this.

[0099] The disturbance observer is specifically:

[0100] Define acceleration:

[0101]

[0102] First composite error:

[0103]

[0104] in, e p =p c -p c,d and Represent the direction error and angular velocity error respectively, λ p ∈R 3×3 Represents a positive definite diagonal matrix used to estimate the external force perturbation F b The first disturbance observer is designed as:

[0105]

[0106]

[0107] in, Yes A b The estimated value of Λ1=diag([λ 11 ,λ 12 ,λ 13 ])∈R 3×3 represents a positive definite matrix, ξ1 is an auxiliary variable;

[0108] Used to estimate the external disturbance F b The first disturbance observer is calculated by the following method:

[0109] Define the first error estimate signal:

[0110]

[0111] Derivative (8):

[0112]

[0113] Combining (4), (6) and (7), we can obtain:

[0114]

[0115] Define the first Lyapunov function Vp (t) used to construct the first virtual control information A:

[0116]

[0117] Substitute the first virtual control information A into the first Lyapunov function V p (t) time inverse By differentiating V p (t), its time derivative is obtained as:

[0118]

[0119] Among them I 3×3 is the unit matrix, α1=min{η 11 ,η 12 ,η 13}-1>0;

[0120] The first virtual control information A satisfies:

[0121]

[0122] Substituting (13) into (12), we obtain:

[0123]

[0124] According to the previous assumptions, we can get:

[0125]

[0126] And define:

[0127]

[0128] So that the first Lyapunov function V p (t) time inverse satisfy:

[0129]

[0130] The first Lyapunov function V p (t) time inverse Substitute into the first disturbance observer and solve it.

[0131] definition:

[0132]

[0133] Second composite error:

[0134]

[0135] Among them, eo =log(R T R d )and represent the direction error and angular velocity error respectively, and Represent the actual fuselage direction and the expected fuselage direction respectively, log(·): Represents a rotation matrix mapped to the corresponding rotation vector, represents the actual angular velocity, represents the desired angular velocity, represents a positive definite diagonal matrix, and the second disturbance observer for estimating the torque disturbance d is designed as:

[0136]

[0137]

[0138] in is the estimated value of d, Λ2=diag([λ 11 ,λ 12 ,λ 13 ])∈R 3×3 represents a positive definite matrix, and ξ2 is an auxiliary variable.

[0139] The second disturbance observer for estimating the torque disturbance d is calculated by the following method:

[0140] Define the second error estimate signal:

[0141]

[0142] Deriving equation (21):

[0143]

[0144] Combining (17), (19) and (20), we can obtain:

[0145]

[0146] Define the second Lyapunov function V o (t) used to construct the second virtual control information T B :

[0147]

[0148] The second virtual control information T B Substitute the second Lyapunov function V o (t) time inverse By differentiating Vo (t), its time derivative is obtained as:

[0149]

[0150]

[0151] The second virtual control information T B satisfy:

[0152]

[0153] Substituting (26) into (25), we obtain:

[0154]

[0155] Among them I 3×3 is the unit matrix, α2=min{η 21 ,η 22 ,η 23}-1>0;

[0156] According to the previous assumptions, we can get:

[0157]

[0158] And define:

[0159]

[0160] So that the second Lyapunov function V o (t) time inverse satisfy:

[0161]

[0162] The second Lyapunov function V o (t) time inverse Substitute into the second disturbance observer and solve it.

[0163] The adaptive model predictive control algorithm is specifically:

[0164] Substitute the first disturbance observer and the second disturbance observer into the dynamic model to obtain a dynamic model based on state representation:

[0165]

[0166] in:

[0167]

[0168]

[0169]

[0170]

[0171] The adaptive model predictive control algorithm in the embodiment of the present invention is a traditional method. Model predictive control (MPC) is a model-driven control method that guides current control decisions by predicting future system behaviors. In robot control, model predictive control is widely used in motion control. It predicts the system state in the future through the current state of the system and subsequent control inputs and optimizes the current control quantity. Model predictive control can provide efficient and accurate control solutions. Since linear MPC will predict dynamics within a limited time range, it requires linear discrete-time dynamics. However, to use traditional discretization methods, such as zero-order hold, the external force F should be b and torque d are combined into a state vector. b , torque d are combined into a state vector and discretized.

[0172] Therefore, equation (30) can be written as follows:

[0173]

[0174]

[0175]

[0176]

[0177] Discretized state equation:

[0178]

[0179] The cost function, equality constraints and inequality constraints of the adaptive model predictive control algorithm are established:

[0180]

[0181]

[0182] Where n represents the total number of time steps, represents the estimation error of the system at time step i, X i and X i,d Represent the actual state and expected state of the system at time step i, respectively, and F i represents the ground reaction force, R i and S i represent diagonal positive semidefinite matrices, and Both represent the dynamical matrix of the discrete-time system, F ix 、F iy and F iz Represent the components of the contact force vector of each foot in the x, y, and z directions, μ represents the friction coefficient between the quadruped robot and the ground, and J i represents the Jacobian matrix of the i-th leg of the quadruped robot, D i Represents the matrix used to select the swing leg and the stance leg.

[0183] The control of the swing leg mainly consists of calculating the joint torques of the leg. Prior to this, the foot positions of the leg need to be planned to obtain the desired joint angles and joint velocities. The trajectory of foot placement follows the trajectory in the world coordinate system. The calculation of the joint torques of the swing leg consists of two components: feedback terms and feedforward terms.

[0184] The control information includes joint torque, and the feedback term of joint torque is defined as τ i , which satisfies:

[0185]

[0186] in, represents the Jacobian matrix of each leg, represents a diagonal positive definite matrix, represents the position and velocity of the ith leg, represent the position and velocity of the reference swing leg, respectively;

[0187] Define the feedforward term of joint torque as τ ff,i , which satisfies:

[0188] τ ff,i =J T f d (43);

[0189]

[0190] in, represents a diagonal positive definite matrix, p 0f and p 0d Represent the actual foot position and the expected foot position in the hip joint coordinate system, respectively. and represent the actual foot speed and the expected foot speed, respectively.

[0191] To demonstrate the technical effect, the embodiments of the present invention conducted simulations and actual experiments under different effective loads. These experiments tested the effects of external loads of different masses on the height of the robot body.

[0192] The simulation experiment uses the GO1 robot in Unitree. The controller is implemented using ROS and Gazebo is used as the simulator. The goal of the simulation experiment is to prove that the GO1 robot can maintain a stable body height under different mass loads. To achieve this, the robot is commanded to carry a time-varying load for linear and rotational motion during the simulation. The force and torque effects of the load on the robot during the motion are compensated by the interference observer. Then the body height, linear speed and rotation speed of the robot are observed and compared with the data obtained by traditional MPC. The results are shown in Figure 2. Figures 2 to 9 As shown, in the experiment, two angles were tried: adapting to the uncertainty of the object, testing the GO1 robot by manipulating a time-varying load, specifically by commanding the robot to move forward at a speed of 0.8m / s, and rotating at a rotation speed of 0.8rad / s, and then recording the change in its body height and the speed tracking curve. Then gradually increase the load on the robot and repeat the above steps. Similarly, the traditional MPC was used as the control group, and the effectiveness of the adaptive model predictive control method for a quadruped robot based on a disturbance observer provided by an embodiment of the present invention was proved through data comparison.

[0193] The beneficial effect achieved by the present invention lies in designing an interference observer used in the kinematic equations of a quadruped robot to offset the interference of the robot system, enhancing the system's ability to suppress interference by estimating the forces and torques generated by the external environment on the robot, and integrating the forces and torques observed by the observer into the model predictive control method for operation, establishing an optimization framework that can be cyclically controlled to suppress interference during operation while maintaining the performance of the overall movement, and at the same time, through rolling optimization, stable dynamic gait control of the quadruped robot can be achieved, and unknown interference can be compensated to achieve better movement performance.

[0194] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0195] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0196] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, a magnetic disk, or an optical disk), and includes a number of instructions for enabling a terminal (which can be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to execute the methods described in each embodiment of the present invention.

[0197] The embodiments of the present invention are described above in conjunction with the accompanying drawings. What is disclosed is only the preferred embodiment of the present invention. However, the present invention is not limited to the above-mentioned specific implementation manner. The above-mentioned specific implementation manner is only illustrative rather than restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms and equivalent changes without departing from the scope of protection of the purpose of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for adaptive model predictive control of a quadruped robot based on a disturbance observer, characterized in that: The following steps are involved: S1. Establish the dynamic model of the quadruped robot; S2, obtaining the motion state information of the quadruped robot through sensors; S3, according to the state information, using an adaptive model predictive control algorithm to predict and control and calculate the control information of the quadruped robot, wherein the adaptive model predictive control algorithm predictive control calculation process is optimized by using the dynamic model in combination with a disturbance observer; S4: using the control information to adjust the quadruped robot in real time through a robot controller to control the movement of the quadruped robot; Wherein, the kinetic model satisfies: ； ； Where m represents the mass of the quadruped robot, represents the quadruped robot's center of mass acceleration, represents the position vector of the origin of the inertial frame, represents the position vector of the quadruped robot's center of mass, =1, 2, 3, 4, representing the different feet of the quadruped robot, represents the external force disturbance on the quadruped robot, represents the contact force on each foot, and , represents the inertia matrix of the quadruped robot, represents the torque disturbance experienced by the quadruped robot; The kinetic model has the following assumptions without loss of generality: External disturbance , torque disturbance The time derivative of ,and: ； in, represents the angular acceleration, represents the angular velocity; The disturbance observer is specifically: Defining Acceleration , the first composite error ,in, , , and represent the direction error and angular velocity error respectively, Represents a positive definite diagonal matrix used to estimate the external forces The disturbance observer is designed as: ； ； in, yes The estimated value of represents a positive definite matrix, is an auxiliary variable; definition , the second composite error ,in, and represent the direction error and angular velocity error respectively, and Represent the actual fuselage direction and the expected fuselage direction respectively, Represents a rotation matrix mapped to the corresponding rotation vector, represents the actual angular velocity, represents the desired angular velocity, represents a positive definite diagonal matrix used to estimate the torque disturbance The disturbance observer is designed as: ； ； in yes The estimated value of represents a positive definite matrix, is an auxiliary variable; To estimate external forces The first disturbance observer is calculated as follows: Define the first error estimate signal: ； The first error estimation signal is derived as follows: ； ； Define the first Lyapunov function Used to construct the first virtual control information : ； ； The first virtual control information Substitute the first Lyapunov function Countdown of time and define: ； The first Lyapunov function Countdown of time satisfy: ； The first Lyapunov function Countdown of time Substitute into the first disturbance observer to solve; For estimating torque disturbance The second disturbance observer is calculated as follows: Define the second error estimate signal: ； Derivative the second error estimate signal: ； ； Define the second Lyapunov function Used to construct the second virtual control information : ； ； The second virtual control information Substitute the second Lyapunov function Countdown of time and define: ； The second Lyapunov function Countdown of time satisfy: ； The second Lyapunov function Countdown of time Substitute into the second disturbance observer to solve; The adaptive model predictive control algorithm is specifically: Substitute the first disturbance observer and the second disturbance observer into the dynamic model to obtain a dynamic model based on state representation: ； in: ； ； ； ； The external force , Torque Combined into a state vector, and discretized, the cost function, equality constraints and inequality constraints of the adaptive model predictive control algorithm are established: ； ； in, represents the total number of time steps, Represents the system at time step The estimation error on and Represents the system at time step actual and expected status, represents the ground reaction force, and represent diagonal positive semidefinite matrices, and Both represent the dynamical matrices of discrete-time systems, , and Represents the contact force vector of each foot. , , The weight in direction, represents the friction coefficient between the quadruped robot and the ground, The quadruped robot The Jacobian matrix of the foot, represents the matrix used to select the swing leg and the stance leg; The control information includes joint torque, and the feedback term of joint torque is defined as , which satisfies: ； in, represents the Jacobian matrix of each leg, represents a diagonal positive definite matrix, , Representative The position and velocity of the legs, , represent the position and velocity of the reference swing leg, respectively; The feedforward term of the joint torque is defined as , which satisfies: ； ； in, represents a diagonal positive definite matrix, and Represent the actual foot position and the expected foot position in the hip joint coordinate system, respectively. and represent the actual foot speed and the expected foot speed, respectively.

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