Humanoid robot walking stability control method and system based on nonlinear model predictive control and readable medium

Abstract

The invention discloses a humanoid robot walking stability control method and system based on nonlinear model predictive control and a readable medium, and the method comprises the following steps: S1, carrying out gait planning based on the current parameters of a humanoid robot, the gait planning comprises delimiting a feasible region of a foothold and a ZMP reference value; s2, NMPC optimization is conducted on gait planning, compliance control is added, new walking parameters are output to control the walking track of the humanoid robot, and stable walking of the humanoid robot is achieved; wherein the walking parameters comprise the position of the final foothold and the optimized walking track, speed and / or acceleration. According to the technical scheme, the problem of robust and efficient walking of the humanoid robot is solved, the spring damping model is optimized, and a theoretical basis is provided for flexibility and stability of humanoid walking.

Description

Technical Field

[0001] This invention relates to the field of robot motion control technology, specifically to a method, system, and readable medium for stabilizing the walking of a humanoid robot based on nonlinear model predictive control. Background Technology

[0002] Humanoid robots, due to their natural compatibility with human environments, have broad application prospects in service, rescue, and industrial fields. However, humanoid robots are susceptible to external disturbances (such as uneven ground or external forces) during walking, leading to instability or even falls. Existing control methods mostly rely on zero-torque point tracking, but they perform poorly in complex terrain or under continuous disturbances, exhibiting prominent problems such as response lag and accumulation of tracking errors.

[0003] Existing technologies commonly use preview control methods based on ZMP (Zero Moment Point), which achieve walking stability by planning ZMP trajectories and combining them with linear model predictive control. Some methods employ a three-loop control structure with current loop, velocity loop, and position loop, where the position and velocity loops are placed in the host computer and the current loop is placed in the joint actuator. These methods are mostly limited to flat ground and small disturbance scenarios.

[0004] Although the aforementioned existing technologies have achieved stable walking for humanoid robots to a certain extent, they still have the following fundamental technical shortcomings when facing complex and dynamic real-world environments, and these shortcomings are causally related: 1) The core objective of existing technologies is to passively track a pre-set ZMP trajectory. When the robot is subjected to a continuous, unidirectional external force, such as when walking on a slope, the gravitational component generates a continuous lateral thrust, and the controller can only provide limited compensation. Due to the lack of an active "resistance" mechanism, the ZMP will continuously deviate towards the edge of the supporting polygon, eventually causing the robot to tilt or even fall.

[0005] 2) Due to sensor signal processing delays, time-consuming complex algorithm calculations, and actuator response inertia, the predictive control model is overly simplified and cannot accurately predict dynamics under disturbances. When sudden disturbances occur, the controller's response is slower than the robot's dynamic changes, leading to tracking errors in ZMP.

[0006] 3) Although existing technologies include error feedback in the control loop, the parameters of their control laws are usually fixed, and the optimization objective is mainly aimed at ideal trajectory tracking. For unexpected, time-varying ZMP tracking errors caused by the aforementioned lag and disturbances, there is a lack of a dedicated, robust error convergence mechanism. This means that once an error occurs, it may not converge quickly, but rather persist or even amplify over multiple gait cycles, ultimately disrupting the periodic stability of walking, manifesting as robot swaying or gait disorder.

[0007] Based on this, we hope to obtain a new method for stabilizing the walking of humanoid robots, which can withstand complex situations and is not easily affected by external disturbances. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the present invention aims to provide a method, system, and readable medium for stabilizing the walking of a humanoid robot based on nonlinear model predictive control.

[0009] To achieve the above objectives, the present invention proposes the following technical solution: In a first aspect, the present invention proposes a walking stability control method for a humanoid robot based on nonlinear model predictive control, the humanoid robot walking stability control method comprising the following steps: Step S1: Perform gait planning based on the current parameters of the humanoid robot, wherein gait planning includes delineating the feasible area of ​​the landing point and the ZMP reference value; Step S2: Optimize the gait planning using NMPC (NMPC refers to Nonlinear Model Predictive Control, hereinafter referred to as NMPC) and add compliant control to output new walking parameters to control the humanoid robot's walking trajectory, thereby achieving stable walking. The walking parameters include the final foot position, the optimized walking trajectory, velocity, and / or acceleration. The compliant control includes the following steps: Establish a virtual centroid model; The virtual force controller obtains virtual force through a virtual center of mass model. The virtual force resists the influence of external forces to achieve compliant control.

[0010] Preferably, in step S2, the NMPC optimization of gait planning includes the following steps: Get the landing point location parameters; The future landing point parameters are obtained using the following formula (1), and the final landing point location is obtained through NMPC optimization: Equation (1); in, This indicates the position of the support foot within each time step. The step size in the sampling interval is represented by m, the index of the sequence summation is represented by M, the step index in the prediction time domain is represented by T, and the walking period is represented by T.

[0011] Preferably, the virtual centroid model is obtained by establishing the following formula (2): Equation (2); in, m o For the quality of the robot, The location of the robot's center of mass. Let h represent the external force acting on the robot's center of mass, and g represent the norm of the gravity vector. This represents the expected value at the zero torque point. This represents the true value at the zero torque point.

[0012] Preferably, the virtual force is calculated using the following equations (3) and (4): Equation (3); Equation (4); in, This represents the virtual force actually output. K1 is a negative coefficient. Determine the critical damping of the robot system.

[0013] In a second aspect, the present invention proposes a robot control device, which includes a walking pattern generator, a disturbance-resistant compliant controller, and a nonlinear model predictive control optimizer. Among them, the anti-twist compliant controller uses the above-mentioned humanoid robot walking stability control method to perform flexible control and generate joint commands; The nonlinear model predictive control optimizer uses the above-mentioned humanoid robot walking stability control method to optimize the landing point position and generate the landing point position command. The walking pattern generator generates a walking trajectory based on joint commands and foot placement commands.

[0014] Thirdly, the present invention proposes a humanoid robot, which includes the aforementioned robot control device.

[0015] Fourthly, the present invention proposes a humanoid robot control system, which includes the following modules: A gait planning module performs gait planning based on the current parameters of the humanoid robot. The gait planning includes defining a feasible area for landing points and ZMP reference values. The optimization module performs NMPC optimization on gait planning and incorporates compliant control to output new walking parameters to control the humanoid robot's walking trajectory, thereby achieving stable walking. The walking parameters include the final foot position, the optimized walking trajectory, and velocity and / or acceleration. The compliant control includes the following steps: Establish a virtual centroid model; The virtual force controller obtains virtual force through a virtual center of mass model. The virtual force resists the influence of external forces to achieve compliant control.

[0016] Fifthly, the present invention proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described humanoid robot walking stability control method.

[0017] Based on an in-depth analysis of the shortcomings of existing technologies, this invention aims to systematically address the core stability challenges faced by humanoid robots when walking in complex and dynamic environments. Traditional ZMP tracking methods have limited control compensation when dealing with unidirectional and continuous thrust, such as the gravitational component of slopes or persistent lateral wind forces. This results in the zero-moment point (ZMP) continuously deviating towards the edge of the supporting polygon, ultimately causing the robot to tip over. The technical solution described in this invention provides an active, compliant, and disturbance-resistant control mechanism that enables the robot not only to "accommodate" instantaneous impacts but also to actively "resist" and counteract continuous external forces. This fundamentally enhances dynamic balance on non-flat and non-ideal surfaces, such as slopes and uneven ground, to maintain gait stability.

[0018] Furthermore, existing control methods suffer from sensor delays, computational time consumption, and model simplification, resulting in a lag in dynamic response to sudden disturbances. This causes the actual ZMP trajectory to deviate from the reference trajectory, and the error cannot be quickly eliminated over multiple gait cycles, even accumulating and disrupting the periodic stability of walking. Therefore, the technical solution described in this invention proposes a composite control strategy that integrates feedforward prediction and feedback correction. Nonlinear model predictive control (NMPC) is used to predict the impact of disturbances in advance and optimize future gait, while a high-gain, robust state feedback controller provides real-time, powerful correction of the current error, achieving rapid convergence and zeroing of ZMP tracking errors and preventing error accumulation.

[0019] In summary, compared with the prior art, the present invention has the following advantages and beneficial effects: 1) The compliant controller designed in this invention can actively estimate and generate a reverse virtual force to counteract continuous external forces, rather than passively following or providing limited compensation. This allows the robot to dynamically adjust its center of mass to generate a torque that resists the continuous thrust when subjected to it, thereby actively pulling the ZMP back to the center region of the supporting polygon and avoiding the risk of overturning caused by the ZMP continuously drifting to the edge.

[0020] 2) The actual trajectory of ZMP obtained by the technical solution described in this invention can closely and quickly track its reference trajectory, and the tracking error can converge to near zero within a few gait cycles, eliminating the divergence problem of error accumulation over time in traditional methods.

[0021] 3) In the technical solution described in this invention, NMPC optimization actually optimizes future gait using a look-ahead approach, reducing errors caused by planning mismatch. The compliant control employed serves as a high-bandwidth, robust feedback correction element. Therefore, the combination of NMPC optimization and compliant control ensures the system's stability and tracking accuracy.

[0022] 4) In the technical solution described in this invention, the NMPC framework directly integrates nonlinear dynamic constraints and complex environmental geometric constraints. Therefore, when solving each step of the control command, the optimizer can simultaneously consider the robot's own physical limits and external terrain limitations, thereby generating the optimal gait online that satisfies both dynamic stability and environmental feasibility, achieving a unity of stability and passability. Attached Figure Description

[0023] Figure 1 This is a block diagram illustrating the control principle of the technical solution described in this invention. Figure 2 The tracking effect of the trajectory in the X direction is shown, where A represents no TPC control and B represents with TPC control; Figure 3 The tracking effect of the trajectory in the X direction is shown, where A represents no TPC control and B represents with TPC control; Figure 4 This illustrates the change in trajectory tracking error over time in one embodiment of the humanoid robot walking stability control method described in this invention; Figure 5 The diagram shows the walking trajectory of the humanoid robot walking stability control method of the present invention in one embodiment; Figure 6 The centroid trajectory of the humanoid robot walking stability control method described in this invention under NMPC is shown in one embodiment. Detailed Implementation

[0024] 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.

[0025] The design concept of the technical solution described in this invention is as follows: 1. A hierarchical collaborative control system architecture integrating NMPC, active disturbance rejection control, and compliant control is proposed. Nonlinear model predictive control, trunk position compliant controller (TPC), and whole-body motion calculation module are integrated into a unified framework based on information flow and functional division of labor. Specifically, NMPC provides forward-looking, constrained optimization planning; the disturbance rejection controller handles persistent external disturbances; and the TPC achieves local interactive compliance. The three components collaboratively output and correct the final joint commands.

[0026] 2. The entire walking system architecture includes a walking pattern generator, a disturbance-resistant compliant controller, and a nonlinear model predictive control optimizer. The outputs of the disturbance-resistant compliant controller and the NMPC optimizer are used together to correct the reference trajectory generated by the walking pattern generator, and then converted into joint control commands by the whole-body motion solver.

[0027] 3. The humanoid robot walking stability control problem is constructed as a real-time optimization problem with multiple nonlinear constraints. The constraints include not only traditional ZMP stability constraints, but also dynamic constraints based on the robot's complete nonlinear inverted pendulum model, as well as non-convex environmental geometric constraints regarding the landing point position and orientation.

[0028] 4. A proactive disturbance rejection compliant control method based on virtual force estimation and impedance model is proposed. The virtual disturbance force is estimated online based on real-time ZMP deviation, and a disturbance rejection control law is designed to generate compensation commands to actively resist continuous external forces. The virtual disturbance force estimation formula and the proactive disturbance rejection control law with a specific coefficient range are the core algorithms for realizing the disturbance rejection function.

[0029] Example 1 In this embodiment, a walking stability control method for humanoid robots based on nonlinear model predictive control (NMPC) is proposed. This method is a hierarchical, closed-loop integrated control system designed to simultaneously achieve compliant interaction, active disturbance rejection, and dynamic stability.

[0030] Figure 1 This is a block diagram of the control principle.

[0031] like Figure 1 As shown, the gait planning module defines the feasible region for landing points and the ZMP reference value. The walking trajectory is given by a spring linear inverted pendulum model (SLIP) that generates a COM-ZMP trajectory. During walking, the impedance controller modifies the walking trajectory, velocity, and acceleration to adapt to external forces. The joint angle commands of the robot can be calculated using inverse kinematics methods. For the optimization of walking parameters, a nonlinear model predictive control method (NMPC) is used for optimization.

[0032] During gait planning, based on a given walking speed and direction target, a simplified model using a spring-loaded linear inverted pendulum can be used to generate an ideal ZMP reference trajectory and a center of mass (COM) reference trajectory offline or online. The ZMP trajectory is strictly constrained within the support polygon to ensure static stability. Algorithms such as ZMP predictive control are employed to adjust the robot's COM acceleration so that the actual ZMP tracks the reference ZMP trajectory generated in the previous step as closely as possible. The controller is typically designed as a PID linear feedback controller. The calculated desired COM trajectory and foot trajectory are converted into angle commands for each joint through inverse kinematics, which are then executed by the underlying servo drivers.

[0033] Example 2 In this embodiment, a method for stabilizing the walking motion of a humanoid robot is proposed, which includes the following steps: Step S1: Perform gait planning based on the current parameters of the humanoid robot, wherein gait planning includes delineating the feasible area of ​​the landing point and the ZMP reference value; Step S2: Optimize the gait planning using NMPC and add compliant control to output new walking parameters to control the humanoid robot's walking trajectory and achieve stable walking. The walking parameters include the final foot position, the optimized walking trajectory, speed and / or acceleration. The walking parameters include the final foot placement, the optimized walking trajectory, speed, and / or acceleration; the compliance control includes the following steps: Establish a virtual centroid model; The virtual force controller obtains virtual force through a virtual center of mass model. The virtual force resists the influence of external forces to achieve compliant control.

[0034] In some preferred embodiments, step S2, performing NMPC optimization on gait planning, includes the following steps: Get the landing point location parameters; The future landing point parameters are obtained using the following formula (1), and the final landing point location is obtained through NMPC optimization: Equation (1); in, This indicates the position of the support foot within each time step. The step size in the sampling interval is represented by m, the index of the sequence summation is represented by M, the step index in the prediction time domain is represented by T, and the walking period is represented by T.

[0035] In some preferred embodiments, in step S2, the compliance control includes the following steps: Establish a virtual centroid model; The virtual force controller obtains virtual force through a virtual center of mass model. The virtual force resists the influence of external forces to achieve compliant control.

[0036] In some preferred embodiments, the virtual centroid model is obtained by establishing the following equation (2): Equation (2) in, m o For the quality of the robot, The location of the robot's center of mass. The external force acting on the robot's center of mass. h Indicates the height of the center of gravity. g The norm of the gravity vector. This represents the expected value at the zero torque point. This represents the true value at the zero torque point.

[0037] In some preferred embodiments, the virtual force is calculated using the following equations (3) and (4): Equation (3); Equation (4); in, This represents the virtual force actually output. , K 1 is a negative coefficient. Determine the critical damping of the robot system.

[0038] Regarding the establishment of the TPC model, the inventor's design concept is as follows: The basic principle of trunk position control (TPC) is to enable the robot to react to errors in external forces and foot forces, producing a corresponding compliant effect. Based on the measured error of the actual ZMP (Zero-Minute Movement) and the planned ZMP, a compliant response to external forces and foot forces can be achieved.

[0039] Therefore, in the technical solution described in this invention, a three-dimensional inverted pendulum model is used to model the humanoid robot.

[0040] The following time-step progression is achieved by mapping the current state to the future state: Equation (5); in, Represents the angular velocity of the center of mass. This represents the coefficient matrix with respect to period T. This represents a column vector with respect to T.

[0041] By establishing the positional relationship between COM and ZMP, we can derive the following equation (6): Equation (6); in, h Indicates the height of the center of gravity, through Calculated The norm of the gravity vector.

[0042] Substituting equation (6) into equation (5) yields equation (7): Equation (7); This allows us to obtain the ZMP reference value. Of course, in some other implementations, considering that robot systems typically delay their response to measurement signals, a first-order inertial segment is used to simulate the delay effect. Therefore, the ZMP measurement value can also be used. Calculate the true value of ZMP (See Equation 8), that is, the ZMP reference value is obtained by calculating the following formula: Equation (8) This allows us to obtain the ZMP reference value.

[0043] The above steps can solve the problems of disturbance resistance and compliant control for slow walking on flat ground with small disturbances. Considering that when the robot is subjected to continuous external disturbances, or when the walking contact surface is sloping, it may tilt to one side, causing walking instability, a compliant control with resistance is adopted to counteract this. Specifically, the robot is simulated to be subjected to a thrust, first making a compliant movement in accordance with the thrust, and then making a reverse movement to resist the thrust. This invention uses a combination of virtual force control and virtual model control.

[0044] The basic idea of ​​resistant compliance control is to first establish a virtual center of mass model, then apply virtual force control and external force together to this model, generating the torso's adjustment range through impedance control. By establishing a three-dimensional inverted pendulum model of the robot, the magnitude of the external force acting on the center of mass is estimated based on the ZMP value, as shown in the following formula. Equation (2) Where, m o For the quality of the robot, The location of the robot's center of mass. The external force acting on the robot's center of mass. and These are the expected value and the actual value of the robot's ZMP, respectively. The expected value can be either a reference value for ZMP or the actual value of ZMP.

[0045] Therefore, the expression for the external force acting on the robot is: Equation (9); Impedance control is used to simulate the effect of external force as an expression for the output position. First, a virtual model of spring-damped mass block is established to describe the dynamics of impedance control.

[0046] Equation (10); Where Kp is the spring constant, Kd is the damping coefficient of the system, and Km is the mass of the model.

[0047] It should be noted that the virtual force controller can be divided into two parts: a virtual resistance controller and a model predictive control (MMC) component. The former is mainly used to naturally resist motion effects, while the latter ensures that the actual ZMP value tracks the expected value of the reference ZMP during robot movement. When using virtual force control for ZMP, future ZMP values ​​should be considered in advance, and responses should be made ahead of time to overcome hysteresis. In other words, virtual resistance control is mainly used to naturally resist motion effects. The resistance virtual force control takes the external force as input and outputs the resistance virtual force as the control variable, as expressed below. Equation (4); in, K1 is a negative coefficient. Determine the critical damping of the robot system.

[0048] Since the resistance effect occurs after the compliance effect, the resistance force lags behind the external force. A first-order inertial element is used to simulate the lag effect: Equation (3); in, This represents the actual output of the resistance virtual force.

[0049] To further illustrate the NMPC optimization process, the explanation is as follows: To ensure the robot's balance under external disturbances, it is necessary to optimize the landing point location. The model prediction method for balance control, based on the ZMP criterion, transforms a set of constraints acting on ZMP into an optimization problem, thereby improving robustness to strong disturbances.

[0050] Suppose there is a point P inside the supporting leg, and its current position and orientation on the ground are determined by... Given, where, Therefore, the future gait can be represented as: Equation (1); in, This indicates the position of the support foot within each time step. This indicates the step size within the sampling interval.

[0051] The cost function in NMPC is designed as follows: Equation (11); in, and The weights represent the cost function. The definition is as follows: Equation (12); This represents the cost function associated with linear velocity tracking. Equation (13); This represents the cost function related to angular velocity tracking. Equation (14); It is the cost function that minimizes the distance between COP and the projection of the ankle onto the sole of the foot. Equation (15).

[0052] Example 3 To better observe performance changes, a robot system without TPC control was used as a comparative simulation. Simulation results for TPC control and NMPC optimization can be found in [reference needed]. Figures 2-6 .

[0053] in, Figure 2 and Figure 3 The trajectory tracking effects in the X and Y directions are depicted respectively.

[0054] Combination Figure 2 and Figure 3 It can be seen that the actual ZMP trajectory can track its reference trajectory, and the tracking effect is even better after adding TPC control.

[0055] Depend on Figure 4 It can be seen that the tracking error of ZMP will converge to 0 after a period of time.

[0056] Depend on Figure 5 As can be seen, after adopting the technical solution described in this invention, the phase diagrams of angle and angular velocity exhibit the form of limit cycles, indicating that the robot can achieve periodic and stable walking. Simulation results show that under the action of external forces, TPC control can achieve good tracking performance.

[0057] Depend on Figure 6 The humanoid robot can move freely forward. The key to the proposed TPC control is generating appropriate ZMP reference inputs by modifying the position, velocity, and acceleration of the landing point. The overall performance of the proposed compliant control is verified through the humanoid robot's motion trajectory.

[0058] 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 method for stabilizing the walking motion of a humanoid robot based on nonlinear model predictive control, characterized in that, The humanoid robot walking stability control method includes the following steps: Step S1: Perform gait planning based on the current parameters of the humanoid robot, wherein gait planning includes delineating the feasible area of ​​the landing point and the ZMP reference value; Step S2: Optimize the gait planning using NMPC and add compliant control to output new walking parameters to control the humanoid robot's walking trajectory, achieving stable walking. The walking parameters include the final foot position, the optimized walking trajectory, and velocity and / or acceleration. The compliant control includes the following steps: Establish a virtual centroid model; The virtual force controller obtains virtual force through a virtual center of mass model. The virtual force resists the influence of external forces to achieve compliant control.

2. The humanoid robot walking stability control method according to claim 1, characterized in that, In step S2, NMPC optimization of gait planning includes the following steps: Get the landing point location parameters; Based on the landing point location parameters, the future landing point parameters are obtained using the following formula (1), and the final landing point location is obtained through NMPC optimization: Equation (1); in, This indicates the position of the support foot within each time step. The step size in the sampling interval is represented by m, the index value of the sequence summation is represented by M, the step index in the prediction time domain is represented by T, and the walking period is represented by T.

3. The humanoid robot walking stability control method according to claim 1, characterized in that, The virtual centroid model is obtained by establishing the following equation (2): Equation (2); in, m o For the quality of the robot, The location of the robot's center of mass. The external force acting on the robot's center of mass. h Indicates the height of the center of gravity. g The norm of the gravity vector. This represents the expected value at the zero torque point. This represents the true value at the zero torque point.

4. The humanoid robot walking stability control method according to claim 1, characterized in that, The virtual force is calculated using the following equations (3) and (4): Equation (3); Equation (4); in, This represents the virtual force actually output. , K 1 is a negative coefficient. Determine the critical damping of the robot system.

5. A robot control device, characterized in that, The robot control device includes a walking pattern generator, a disturbance-resistant compliant controller, and a nonlinear model predictive control optimizer. Among them, the anti-bending compliant controller uses the humanoid robot walking stability control method as described in any one of claims 1 to 4 to perform flexible control and generate joint commands; The nonlinear model predictive control optimizer uses the humanoid robot walking stability control method as described in any one of claims 1 to 4 to optimize the landing point position and generate the landing point position command. The walking pattern generator generates a walking trajectory based on joint commands and foot placement commands.

6. A humanoid robot, characterized in that, The humanoid robot includes the robot control device as described in claim 5.

7. A humanoid robot control system, characterized in that, The humanoid robot control system includes the following modules: A gait planning module performs gait planning based on the current parameters of the humanoid robot. The gait planning includes defining a feasible area for landing points and ZMP reference values. The optimization module performs NMPC optimization on gait planning and incorporates compliant control to output new walking parameters to control the humanoid robot's walking trajectory, thereby achieving stable walking. The walking parameters include the final foot position, the optimized walking trajectory, and velocity and / or acceleration. The compliant control includes the following steps: Establish a virtual centroid model; The virtual force controller obtains virtual force through a virtual center of mass model. The virtual force resists the influence of external forces to achieve compliant control.

8. The humanoid robot control system according to claim 7, characterized in that, In the optimization module, NMPC optimization of gait planning includes the following steps: Get the landing point location parameters; Based on the landing point location parameters, the future landing point parameters are obtained using the following formula (1), and the final landing point location is obtained through NMPC optimization: Equation (1); in, This indicates the position of the support foot within each time step. The step size in the sampling interval is represented by m, the index value of the sequence summation is represented by M, the step index in the prediction time domain is represented by T, and the walking period is represented by T.

9. The humanoid robot control system according to claim 7, characterized in that, The virtual centroid model is obtained by establishing the following equation (2): Equation (2); in, m o For the quality of the robot, The location of the robot's center of mass. The external force acting on the robot's center of mass. h Indicates the height of the center of gravity. g The norm of the gravity vector. This represents the expected value at the zero torque point. This represents the true value at the zero torque point.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the humanoid robot walking stability control method as described in any one of claims 1 to 4.

Images