A design method of a model reference adaptive based humanoid walking gait stability controller and a robot control device

Abstract

The application discloses a design method and a control device of a human-imitating walking stability controller based on model reference self-adaption, and comprises the following steps: S1, a dynamic equation of a continuous swing stage of a biped robot and a mapping model of a discrete collision stage are established; S2, a virtual constraint function y=h(q) is designed to make the motion of drive joints and under-actuated joints of the biped robot coupled; S3, input / output feedback linearization processing is performed on the virtual constraint function; S4, a PD tracking controller is designed for a linear subsystem; S5, an adaptive reference model is established; S6, based on an energy minimization criterion, parameters of a desired joint trajectory of the biped robot are optimized by combining a Bezier polynomial fitting method to generate an energy-saving periodic desired trajectory; and S7, the asymptotic stability of a closed-loop system is proved by using a control Lyapunov function and a Poincare mapping to ensure that the system is periodically stable in walking.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and in particular relates to a design method and robot control device for a humanoid walking stability controller based on model reference adaptation. Background Technology

[0002] Virtual constraint control couples the system output with the internal state by constructing geometric constraints, and is used for dimensionality reduction and trajectory planning. The traditional PID method is one of the most basic and widely used control algorithms in classical feedback control theory. Its core idea is to generate a control signal by linearly combining the proportional, integral and derivative components of the system error to achieve stable tracking of the desired target by the system output. The energy minimization optimization criterion is a performance index design method used in the trajectory planning stage. Its core objective is to minimize the energy consumption of the robot in a walking cycle while satisfying gait feasibility and stability.

[0003] The shortcomings of existing technologies are as follows: underactuated robots have fewer control inputs than degrees of freedom, and the system exhibits nonlinear, high-dimensional, and strongly coupled characteristics, making it difficult to directly construct accurate dynamic models. This results in high model uncertainty, which easily leads to the accumulation of extended tracking errors in joint trajectory tracking, affecting walking stability. Furthermore, traditional PID control methods do not incorporate online parameter adjustment mechanisms, relying solely on pre-designed trajectories and fixed control laws, failing to compensate for model errors in real time, thus causing a decrease in trajectory tracking accuracy.

[0004] Based on this, we hope to obtain new methods to achieve nonlinear system control, model reference adaptive optimization, and joint trajectory tracking and stability analysis. These methods can be applied to robot systems that require periodic and asymptotically stable walking, enabling bipedal robots to walk stably on uneven ground or in dynamic environments, and to improve the adaptability and robustness of models with uncertain systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a design method and robot control device for a humanoid walking stability controller based on model reference adaptation, thereby achieving nonlinear system control, model reference adaptive optimization, joint trajectory tracking and stability analysis. This makes it applicable to robot systems requiring periodic and asymptotically stable walking, enabling bipedal robots to walk stably on uneven ground or in dynamic environments, and to improve the adaptability and robustness of the system in models with uncertainties.

[0006] To achieve the above objectives, this invention proposes a design method for a model reference adaptive humanoid walking stability controller, the design method comprising the following steps: Step S1: Establish the dynamic equations of the continuous swinging phase of the bipedal robot and the mapping model of the discrete collision phase, and construct the bipedal robot walking system as a hybrid system; Step S2: Design a virtual constraint function y = h(q) to couple the motion of the driven joints and underactuated joints of the bipedal robot; Step S3: Perform input / output feedback linearization processing on the virtual constraint function to decompose the nonlinear system of the bipedal robot into a linear subsystem and zero dynamics; Step S4: Design a PD tracking controller for the linear subsystem; Step S5: Establish an adaptive reference model, design an adaptive law for parameters based on joint trajectory tracking error, and adjust the controller parameters online in real time to compensate for the uncertainty of the system model; Step S6: Based on the energy minimization criterion, the parameters of the desired joint trajectory of the bipedal robot are optimized by combining the Bezier polynomial fitting method to generate an energy-saving periodic desired trajectory; Step S7: Prove the asymptotic stability of the closed-loop system using the control Lyapunov function and the Poincaré mapping to ensure the periodic stable walking of the bipedal robot walking system; The parameter adaptive rate is designed and adjusted according to the following formula: ; In the formula, This represents the parameter update law. It is an adaptive gain constant symmetric matrix used to adjust the adaptive speed and stability of the parameters, Y. T The transpose of the regression matrix is ​​given, s represents the extended tracking error used to combine position and velocity errors, e represents the tracking error, i.e., the deviation between the actual trajectory and the desired trajectory, and K... d This represents the positive definite gain matrix, used to adjust the weight of the velocity term in the tracking error to ensure the convergence of the error dynamics.

[0007] Preferably, in step S1, the expression of the hybrid system satisfies the local Lipschitz condition, the dynamic equation includes the inertia matrix, the centrifugal force and Coriolis force matrix, the gravity matrix, the driving torque of each joint of the robot and the torque distribution matrix, and the mapping model of the discrete collision stage includes the collision switching mapping relationship between joint angular displacement and angular velocity.

[0008] Preferably, in step S2, the virtual constraint function is a virtual integrity constraint, which selects the angle between the line segment from the robot's hip joint to the contact point between the swing foot and the ground and the ground as the constraint reference quantity, specifies one or more (e.g., four) drive joints to apply the virtual constraint, and defines the synchronization relationship function between the drive joints and the constraint reference quantity so that the gait satisfies the periodic characteristics.

[0009] Preferably, in step S3, the input / output feedback linearization process is as follows: the inertia matrix is ​​inverted and multiplied on the left by the dynamic equation, and the state feedback control law is derived by combining the Jacobian matrix of the output equation. New input quantities and state vectors are introduced to decouple the linear subsystem of the nonlinear system from the internal dynamics, and the zero dynamics are set to make the system output 0 to shut down external disturbances of the linear subsystem.

[0010] Preferably, in step S3, a PD control law is designed for the decomposed linear subsystem. The PD control law includes a positive definite gain matrix, the desired output trajectory, and the output error, so as to enable the linear subsystem to track the desired walking trajectory.

[0011] Preferably, in step S5, the adaptive reference model includes an adjustable parameter column vector, a parameter error vector, and an adaptive gain constant symmetric matrix. The parameter adaptive law updates the parameters at the sampling points of each walking cycle of the bipedal robot. The update formula is approximated by a first order. The asymptotic stability of the system is proved by constructing a control Lyapunov function and taking its derivative, combined with the Lasalle invariance principle.

[0012] Preferably, in step S5, the joint trajectory tracking error includes an extended tracking error. The gravity term and external torque of the dynamic equation are combined into a joint torque vector. Based on the equation relationship between centrifugal force and Coriolis force, a control law is designed that includes a constant gain matrix, an estimated value of the inertia matrix, and estimated values ​​of the centrifugal force and Coriolis force matrices, so that both the joint trajectory tracking error and the extended tracking error asymptotically converge to 0.

[0013] Preferably, in step S6, the Bezier polynomial fitting method optimizes the desired joint trajectory of the bipedal robot, specifically as follows: Based on the desired end-cycle motion trajectory of the desired joint, the trajectory parameters are optimized using the energy minimization criterion to minimize the robot's energy consumption within a walking cycle, while simultaneously satisfying gait feasibility and stability.

[0014] In a second aspect, the present invention provides a robot control device, which includes a memory and a processor; The memory is used to store computer programs; The processor, when executing the computer program, implements the above-described design method for a model reference adaptive humanoid walking stability controller.

[0015] Preferably, the processor includes one or more of the following modules: Hybrid system modeling module, used to build continuous-discrete dynamic models; The virtual constraint design module is used to generate constraint functions for coupled driven and underactuated joints; The feedback linearization module is used to implement linear decomposition of system input / output; An adaptive optimization module is used to adjust control parameters and optimize energy consumption online. And a trajectory generation module, used to generate the desired trajectory based on Bezier polynomials and energy minimization criteria.

[0016] Thirdly, the present invention proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described design method for a model reference adaptive humanoid walking stability controller.

[0017] Compared with the prior art, the present invention has the following advantages and beneficial effects: This invention introduces a model reference adaptive law to adjust controller parameters online in real time, compensate for system model uncertainties, thereby extending the tracking error s to converge to zero within 0.8 seconds, and accurately tracking the desired trajectory with joint angles and angular velocities, achieving high-precision periodic gait.

[0018] Furthermore, the adaptive reference model used in this case can be updated online as environmental and system parameters change. Combined with Lyapunov stability proof, the system can still maintain stable movement and smooth ground force changes under model uncertainty, ground disturbance or load changes. In the trajectory planning stage, the energy minimization optimization criterion is adopted to generate an energy-saving Bezier desired trajectory. Adaptive control further optimizes torque distribution.

[0019] Furthermore, this case achieves linearization of input / output feedback through virtual constraints and zero dynamics, decomposing the nonlinear system into a linear subsystem and internal dynamics, which greatly simplifies online calculations. Even after a collision, the system can quickly recover stability after the state jumps, achieving smooth control of the continuous-discrete hybrid process.

[0020] It should be emphasized that the control structure in this case is clearly layered (i.e., from trajectory optimization to feedback linearization to adaptive PD control), and the physical meaning of the parameters is clear, making it valuable for engineering application. Attached Figure Description

[0021] Figure 1Control chart for linearized input / output feedback system; Figure 2 A block diagram illustrating the principle of adaptive parameter optimization for model reference; Figure 3 It represents the periodic trajectory of the joint angle; Figure 4 A phase diagram showing joint angles and angular velocities; Figure 5 To expand the tracking error. Detailed Implementation

[0022] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several adjustments and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0023] Example 1 In this embodiment, a design method for a humanoid walking stability controller based on model reference adaptation is proposed. The design method includes the following steps: Step S1: Establish the dynamic equations of the continuous swinging phase of the bipedal robot and the mapping model of the discrete collision phase, and construct the bipedal robot walking system as a hybrid system; Step S2: Design a virtual constraint function y = h (q) to couple the motion of the driven joints and underactuated joints of the bipedal robot, thereby reducing the system dimensionality. Step S3: Perform input / output feedback linearization processing on the virtual constraint function to decompose the nonlinear system of the bipedal robot into a linear subsystem and zero dynamics; Step S4: Design a PD tracking controller for the linear subsystem; Step S5: Establish an adaptive reference model, design an adaptive law for parameters based on joint trajectory tracking error, and adjust the controller parameters online in real time to compensate for the uncertainty of the system model; Step S6: Based on the energy minimization criterion, the parameters of the desired joint trajectory of the bipedal robot are optimized by combining the Bezier polynomial fitting method to generate an energy-saving periodic desired trajectory; Step S7: Prove the asymptotic stability of the closed-loop system using the control Lyapunov function and the Poincaré mapping to ensure the periodic stable walking of the bipedal robot walking system; The parameter adaptive rate is designed and adjusted according to the following formula: .

[0024] Its design principle is as follows: To achieve dimensionality reduction for a multi-degree-of-freedom underactuated bipedal robot, a link dynamics model of the robot's legs is established based on the Lagrange principle. A suitable output function, y = h(q), is selected to establish geometric constraints between driven and underactuated joints, thereby reducing the system's dimensionality.

[0025] A state feedback control strategy based on virtual constraints and zero dynamics was adopted to linearize the input / output feedback of the robot system. The output function was differentiated, and a state feedback control law was introduced. The nonlinear system of the robot is decomposed into a linear subsystem and internal dynamics. The linear subsystem is then tracked using a linear controller PID control.

[0026] It should be noted that in the dynamic model, a complete walking phase can be divided into two stages: the swing leg swing and the ground impact. The dynamic equations for the swing stage and the mapping for the impact stage are established as follows: (1) (2) in, The angular displacement of each joint is taken as clockwise. Let be the angular velocity of each joint. Switch mappings for collisions. The inertia matrix, Centrifugal force and Coriolis force matrix For the gravity matrix, The driving torque for each joint of the robot. Assign a torque matrix.

[0027] Define continuous state variables ,So , The entire bipedal walking model can be represented as a hybrid system. (3) in, To switch surfaces for collisions, , , All satisfy the local Lipschitz condition.

[0028] The design concept for the control strategy of the pedestrian system in this case is as follows: To achieve stable human-like walking in a bipedal robot, it is necessary to generate a desired motion that prevents falls and determine the stability of this motion. This invention employs a combination of virtual integrity constraints and hybrid zero dynamics to complete the trajectory planning and stability control algorithm design.

[0029] The main steps of controller design are as follows: First, write a set of virtual integrity constraints with system parameters, then use partial feedback linearization to make them asymptotically converge to the robot's constraint space, and use numerical optimization to select the parameters of the virtual constraints to achieve the purpose of adjusting the system to zero dynamics and realizing stable walking with low energy consumption.

[0030] First, connect the robot's hip joint to the point of contact between the swinging foot and the ground, and denote the angle between the line segment and the ground as . Therefore, within one walking cycle, The Cartesian coordinates of the value are monotonically increasing. The virtual integrity constraint is taken as... (4) in, Four drive joints were specified to be subject to virtual constraints. The function to be designed describes the independent drive joint and The synchronization relationship.

[0031] Because the gait needs to satisfy periodicity and the thigh and calf lengths need to be equal, it is further defined as follows: (5) (6) in, , ,So Using virtual constraints, the output is... (7) Next, the system is linearized for input / output feedback. See the relevant results. Figure 1 .

[0032] like Figure 1 As shown, the input / output feedback linearization processing system includes a nonlinear feedback inner loop of static state feedback control and a linear feedback outer loop of PD control law. In the technical solution described in this invention, the purpose of state feedback linearization is to decompose the robot's nonlinear system into a linear subsystem and internal dynamics. The linear part uses PD control, and the significance of introducing zero dynamics is to artificially make the system output 0, which is equivalent to shutting down the linear subsystem.

[0033] In other words, in step S3, the input / output feedback linearization process is as follows: the inertia matrix is ​​inverted and multiplied on the left by the dynamic equation, and the state feedback control law is derived by combining the Jacobian matrix of the output equation. New input quantities and state vectors are introduced to decouple the linear subsystem of the nonlinear system from the internal dynamics, and zero dynamics is set to make the system output 0 to shut down external disturbances to the linear subsystem.

[0034] The specific calculation process is as follows: Due to the inertia matrix It is always non-singular, multiplied by the left side of both sides of equation (1). inverse matrix (8) From the output equation as well as , can be obtained ,in, It is a Jacobian matrix.

[0035] Equation (8), then multiplied on the left have to, (9) like If the system is nonsingular, then the system state feedback control can be obtained from the following equation. (10) Among them, new input ,and , . At this point, let the new state vector Design a linear subsystem, define the PD control law, and track the desired trajectory of the walk. (11) in, To output the desired trajectory, This represents the output error. and It is a positive definite gain matrix.

[0036] In the technical solution described in this invention, the parameter optimization for model reference adaptation is as follows: For robot dynamics systems, the gravity matrix and inertia matrix The system contains uncertain parameters, and these uncertainties may affect the tracking performance of the joint trajectory. This design employs a model reference adaptive method to optimize the control strategy. The block diagram of the adaptive parameter adjustment principle is shown below. Figure 2 As shown.

[0037] First, establish an adaptive reference model. (12) in, It is a column vector containing adjustable parameters, the parameter error vector. , The sampling points are updated at each walking cycle. It does not contain any uncertain parameters. It is a symmetric matrix representing the adaptive gain constant. It is about , , and The function is obtained by calculating it using equation (13). (13) Next, the control law for the adaptive reference model is designed. The gravity term and external torque in the dynamic equation (1) are combined into a joint torque vector. Then equation (1) can be rewritten as follows: (14) The equations relating centrifugal force and Coriolis force are as follows: (15) in, Inertia derivative matrix. The end-effector trajectory of each joint is defined as the output. The tracking error is To improve the accuracy of joint trajectory tracking, it is expected that... and All converge asymptotically to 0.

[0038] The control law of the design is as follows: (16) in, It is a constant gain matrix. and The inertia matrix is ​​respectively And the matrix of centrifugal force and Coriolis force The estimated value. and For the defined extended tracking error, and , .

[0039] Extended tracking error and The relationship is as follows: (17) The corresponding adaptive law is as follows: (18) The constructed control Lyapunov functions are as follows: (19) The derivative of the control Lyapunov function is calculated as follows: (20) in, Not always a symmetric matrix, substituting (17) into (20) yields: (twenty one) Then substitute the robot's dynamic equation (18) into (21). (twenty two) Based on the control law (16) and adaptive law (18) of the reference model, substituting (14) into (20), we get: (twenty three) in, In state space It is positive definite. According to the Lasalle invariance principle, it can be proven that the bipedal walking system based on model reference adaptation is asymptotically stable.

[0040] At each sampling point in each cycle, the parameters are updated using equation (21). The updated formula, after first-order approximation, yields: (twenty four) and Figure 3 Indicates joint angle The trajectory of change over time.

[0041] like Figure 3 As shown, this design exhibits smoothness and periodicity, satisfying the target gait. Among these, and There are distinct jumps within each cycle, indicating the switching between the swinging leg and the supporting leg. It is an underactuated joint.

[0042] Figure 4 Indicates joint angle and joint angular velocity The phase diagram shows a passive limit cycle, thus enabling periodically stable walking. The red dots are fixed points on the limit cycle, i.e., fixed points in the Poincaré regression map. The straight lines in the diagram represent collisions between the swinging leg and the ground, at which point the robot's joint angular velocity changes abruptly.

[0043] Figure 5 To extend the variation of the tracking error s over time, it is shown that the tracking error can be reduced by using an adaptive control law based on model reference.

[0044] The inventors of this case considered that, unlike fully actuated robots, underactuated robots primarily differ in that the underactuated phase lacks corresponding control inputs and can only obtain motion trajectories through joint kinematic constraints. Furthermore, the nonlinear, high-dimensional, and strongly coupled characteristics of robots increase the difficulty of control. Stable walking in bipedal robots is sensitive to the values ​​of the system's structural parameters and the walking environment. Bipedal robot systems in practical engineering also exhibit uncertainties, making it difficult to describe the robot system with a precise mathematical model, which poses a challenge to underactuated bipedal walking control. This invention applies a model reference adaptive optimization method to bipedal walking control to achieve stable walking in underactuated bipedal robots. A feedback controller was designed using a control strategy combining virtual constraints and hybrid zero dynamics, and the stability of the system was proven by designing a control Lyapunov function.

[0045] To achieve the tracking of the pre-defined joint trajectories, Bezier polynomials were used to fit the expected end-effector periodic motion trajectories of the robot's five joints. Trajectory optimization was performed using an energy minimization criterion. Simultaneously, a model reference adaptive law was introduced to adjust the model parameters and optimize joint trajectory tracking, addressing the parameter uncertainty issue in the robot's dynamics model and thus reducing the spread error of joint trajectory tracking. Related results and validation can be found in [link to relevant documentation]. Figure 5 .

[0046] like Figure 5 As shown, the extended tracking error s converges to zero within 0.8 seconds, and the joint angle and angular velocity accurately track the desired trajectory, achieving high-precision periodic gait.

[0047] As can be seen from the above embodiments, the adaptive reference model in this case updates online as the environment and system parameters change. Combined with Lyapunov stability proofs, the system can still maintain stable operation even under model uncertainty, ground disturbances, or load changes. Figure 5 It can be seen that the ground force changes smoothly.

[0048] Furthermore, an energy minimization optimization criterion is employed during the trajectory planning phase to generate an energy-efficient Bezier desired trajectory; adaptive control further optimizes torque distribution. Input / output feedback linearization is achieved through virtual constraints and zero dynamics, decomposing the nonlinear system into a linear subsystem and internal dynamics, significantly simplifying online computation at the collision moment (see...). Figure 4 (Linear segment), the system can quickly recover to stability after a state jump, achieving smooth control of the continuous-discrete hybrid process.

[0049] Furthermore, considering the technical solution of this case as a whole, it has the advantages of a clear and hierarchical control structure (trajectory optimization → feedback linearization → adaptive PD control), clear physical meaning of parameters, and engineering transfer value.

[0050] Example 2 In this embodiment, a robot control device is disclosed, which includes a memory and a processor; The memory is used to store computer programs; When the processor executes the computer program, it implements the design method of the humanoid walking stability controller based on model reference adaptation as described in Embodiment 1.

[0051] Example 3 In this embodiment, a computer-readable storage medium is disclosed, on which a computer program is stored. When the computer program is executed by a processor, it implements the design method of the humanoid walking stability controller based on model reference adaptation as described in Embodiment 1.

[0052] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A design method for a humanoid walking stability controller based on model reference adaptation, characterized in that, The design method includes the following steps: Step S1: Establish the dynamic equations of the continuous swinging phase of the bipedal robot and the mapping model of the discrete collision phase, and construct the bipedal robot walking system as a hybrid system; Step S2: Design a virtual constraint function y = h(q) to couple the motion of the driven joints and underactuated joints of the bipedal robot; Step S3: Perform input / output feedback linearization processing on the virtual constraint function to decompose the nonlinear system of the bipedal robot into a linear subsystem and zero dynamics; Step S4: Design a PD tracking controller for the linear subsystem; Step S5: Establish an adaptive reference model, design an adaptive law for parameters based on joint trajectory tracking error, and adjust the controller parameters online in real time to compensate for the uncertainty of the system model; Step S6: Based on the energy minimization criterion, the parameters of the desired joint trajectory of the bipedal robot are optimized by combining the Bezier polynomial fitting method to generate an energy-saving periodic desired trajectory; Step S7: Prove the asymptotic stability of the closed-loop system using the control Lyapunov function and the Poincaré mapping to ensure the periodic stable walking of the bipedal robot walking system; The parameter adaptive rate is designed and adjusted according to the following formula: ； In the formula, This represents the parameter update law. It is an adaptive gain constant symmetric matrix used to adjust the adaptive speed and stability of the parameters, Y. T The transpose of the regression matrix is ​​given, s represents the extended tracking error used to combine position and velocity errors, e represents the tracking error, i.e., the deviation between the actual trajectory and the desired trajectory, and K... d This represents the positive definite gain matrix, used to adjust the weight of the velocity term in the tracking error to ensure the convergence of the error dynamics.

2. The design method according to claim 1, characterized in that, In step S1, the expression of the hybrid system satisfies the local Lipschitz condition, the dynamic equation includes the inertia matrix, centrifugal force and Coriolis force matrix, gravity matrix, driving torque of each joint of the robot and torque distribution matrix, and the mapping model of the discrete collision stage includes the collision switching mapping relationship between joint angular displacement and angular velocity.

3. The control method according to claim 1, characterized in that, In step S2, the virtual constraint function is a virtual integrity constraint. It selects the angle between the line segment from the robot's hip joint to the contact point between the swing foot and the ground and the ground as the constraint reference quantity, specifies one or more drive joints to apply the virtual constraint, and defines the synchronization relationship function between the drive joints and the constraint reference quantity so that the gait satisfies the periodic characteristics.

4. The design method according to claim 1, characterized in that, In step S3, the input / output feedback linearization process is as follows: the inertia matrix is ​​inverted and multiplied on the left by the dynamic equation. The state feedback control law is derived by combining the Jacobian matrix of the output equation. New input quantities and state vectors are introduced to decouple the linear subsystem of the nonlinear system from the internal dynamics. Zero dynamics is set so that the system output is 0 to shut down external disturbances to the linear subsystem.

5. The control method according to claim 1, characterized in that, In step S3, a PD control law is designed for the decomposed linear subsystem. The PD control law includes a positive definite gain matrix, the desired output trajectory, and the output error, so as to enable the linear subsystem to track the desired walking trajectory.

6. The design method according to claim 1, characterized in that, In step S5, the adaptive reference model includes an adjustable parameter column vector, a parameter error vector, and an adaptive gain constant symmetric matrix. The parameter adaptive law updates the parameters at the sampling points of each walking cycle of the bipedal robot. The update formula is approximated by a first order. By constructing and differentiating the control Lyapunov function, combined with the Lasalle invariance principle, the asymptotic stability of the system is achieved.

7. The design method according to claim 1, characterized in that, In step S5, the joint trajectory tracking error includes the extended tracking error. The gravity term and external torque in the dynamic equation are combined into a joint torque vector. Based on the equation relationship between centrifugal force and Coriolis force, a control law is designed that includes a constant gain matrix, an estimated value of the inertia matrix, and estimated values ​​of the centrifugal force and Coriolis force matrices, so that both the joint trajectory tracking error and the extended tracking error asymptotically converge to 0.

8. The design method according to claim 1, characterized in that, In step S6, the Bezier polynomial fitting method optimizes the desired joint trajectory of the bipedal robot, and its specific operation is as follows: Based on the desired end-cycle motion trajectory of the desired joint, the trajectory parameters are optimized using the energy minimization criterion to minimize the robot's energy consumption within a walking cycle, while simultaneously satisfying gait feasibility and stability.

9. A robot control device, characterized in that, The robot control device includes a memory and a processor; The memory is used to store computer programs; The processor, when executing the computer program, implements the design method of the humanoid walking stability controller based on model reference adaptation as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the design method of the humanoid walking stability controller based on model reference adaptation as described in any one of claims 1 to 8.

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