Robot assembly distributed control method and system based on disturbance observer

Abstract

The application belongs to the field of robot control, and discloses a robot assembly distributed control method and system based on a disturbance observer, which acquires the motion state of the robot assembly, obtains an initial robot dynamics model based on the motion state, establishes a discrete disturbance observer to acquire internal disturbance forces between the robots, establishes a local extended observer to acquire internal and external disturbance forces of the robots, establishes a disturbance-based probability trigger model, switches the discrete disturbance observer and the local extended observer when the disturbance force observed by the discrete disturbance observer reaches a certain threshold, corrects the initial robot dynamics model based on the observed disturbance force, establishes an optimal quadratic programming problem and solves it based on the corrected robot dynamics model according to the requirements of the task, and acquires the input foot force of the assembly motion. Through internal and external disturbance estimation, the application realizes the motion control of the leg-foot robot, and makes the leg-foot robot assembly have high flexibility and robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot control, in particular to a robot assembly distributed control method and system based on disturbance observer. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] Legged robots have great potential for flexible movement in unstructured terrain, so they are very suitable for application in the field or factory. However, the current legged bionic robots are often limited by stability and flexibility in practical application. In order to solve the above limitations, the existing methods mainly solve from two ideas of hardware and control method. One is to improve the ability of the driven joint, which may greatly increase the weight of the single robot; the other is to increase the number of legs, such as hexapod robot or multi-legged robot, which sacrifices some flexibility inherent in biped or quadruped design. Therefore, the challenge faced by the legged robot is how to make the legged robot not only maintain the adaptability of individual movement, but also support the cooperation behavior between individuals, so as to maximize the stability. This challenge highlights the demand for a legged robot assembly platform, which should balance between stable movement and movement flexibility to meet various needs in the field, factory or any other working environment.

[0004] Although some progress has been made in the control field of traditional robot assembly (wheel assembly, etc.) in the past, its application on the legged robot assembly still faces challenges. For example, although traditional assembly distributed control methods considering the computational burden have been developed, these methods often ignore the fact that in the cooperative task of the legged assembly, the lever effect of the connecting mechanism will greatly amplify the disturbance force brought by another module of the assembly, so that each module in the assembly is always under disturbance. Therefore, the control method for the traditional assembly cannot be applied to the legged robot assembly. In view of this problem, the control method of the legged robot assembly must ensure the movement ability of itself while resisting the influence of mutual interference caused by the connecting mechanism, so that the platform can realize higher flexibility and robustness. SUMMARY

[0005] In order to solve the above problems, the present application proposes a robot assembly distributed control method and system based on disturbance observer, which realizes internal and external disturbance estimation by establishing discrete disturbance observer and local extended observer, and realizes the movement control of the legged robot through the distributed model predictive control method, so that the legged robot assembly has high flexibility and robustness.

[0006] In order to achieve the above object, the present application adopts the following technical solutions:

[0007] In a first aspect, the present application provides a robot assembly distributed control method based on a disturbance observer, comprising the following steps:

[0008] Obtaining the motion state of each unit in the robot assembly at the current time, and obtaining an initial robot dynamics model based on the motion state;

[0009] Establishing a discrete disturbance observer to obtain the internal disturbance force between the robots, and establishing a local extended observer to obtain the internal and external disturbance forces of the robots;

[0010] Establishing a probability trigger model based on the disturbance, and switching the discrete disturbance observer and the local extended observer when the disturbance force observed by the discrete disturbance observer reaches a certain threshold;

[0011] Based on the observed disturbance force, the initial robot dynamics model is corrected, and based on the corrected robot dynamics model, an optimal quadratic programming problem is established according to the requirements of the task, the quadratic programming problem is solved, and the input foot force of the robot assembly motion is obtained.

[0012] As an optional implementation, the motion state of each unit in the robot assembly at the current time includes joint angle, self-pose, and joint torque.

[0013] As an optional implementation, the discrete disturbance observer is established, specifically:

[0014] The joint angle, self-pose, and joint torque are integrated into the generalized coordinates and generalized velocities of the robot assembly, the generalized momentum of the robot is obtained according to the generalized velocities, and the discrete disturbance observer is established according to the generalized coordinates, generalized momentum, and joint torque.

[0015] As an optional implementation, the internal disturbance force between the robots is obtained based on the discrete disturbance observer, specifically:

[0016] The observed torque of each driven joint is obtained based on the discrete disturbance observer, the ground reaction force received by the leg is converted from the observed torque, the disturbance dynamics model is established based on the ground reaction force, and the internal disturbance force between the robots is obtained.

[0017] As an optional implementation, whether to switch the observer is determined according to the calculation result of the probability trigger model, when the calculation result of the probability trigger model exceeds a certain value, it rapidly increases from 0 to 1, at this time the observer is switched to the local extended observer; when it is less than a certain value, it rapidly decreases from 1 to 0, at this time the observer is switched to the discrete disturbance observer.

[0018] As an alternative implementation, according to the requirements of the task, an optimal quadratic programming problem is established and solved to obtain the optimal input plantar force, the optimal input plantar force is changed in real time according to the size of the disturbance, and the input plantar force of the robot assembly motion is obtained.

[0019] In a second aspect, the present application provides a robot assembly distributed control system based on a disturbance observer, comprising:

[0020] The dynamic model construction module is configured to: obtain the motion state of each unit in the robot assembly at the current time, and obtain an initial robot dynamic model based on the motion state;

[0021] The disturbance observer establishment module is configured to: establish a discrete disturbance observer, obtain the internal disturbance force between each robot, establish a local extended observer, and obtain the internal and external disturbance forces of the robot;

[0022] The disturbance observer switching module is configured to: establish a probability trigger model based on the disturbance, and when the disturbance force observed by the discrete disturbance observer reaches a certain threshold, switch the discrete disturbance observer and the local extended observer;

[0023] The control output module is configured to: correct the initial robot dynamic model based on the observed disturbance force, establish an optimal quadratic programming problem based on the corrected robot dynamic model according to the requirements of the task, solve the quadratic programming problem, and obtain the input plantar force of the robot assembly motion.

[0024] In a third aspect, the present application provides an electronic device comprising a memory and a processor, and computer instructions stored in the memory and running on the processor, when the computer instructions are executed by the processor, the method of the first aspect is completed.

[0025] In a fourth aspect, the present application provides a computer readable storage medium for storing computer instructions, when the computer instructions are executed by the processor, the method of the first aspect is completed.

[0026] In a fifth aspect, the present application provides a computer program product comprising a computer program, when the computer program is executed by the processor, the method of the first aspect is completed.

[0027] Compared with the prior art, the present application has the following beneficial effects:

[0028] The application provides a robot combination distributed control method based on a disturbance observer, all internal and external disturbance forces suffered by a leg-foot robot combination can be acquired in real time without using an external force sensor through a discrete disturbance observer and a local expansion observer, and a change from anti-disturbance control to disturbance modeling control is realized; on the basis of acquiring all disturbance forces, a distributed model predictive controller is established, the leg-foot robot combination can be directly used on a single body and a combination, different controllers do not need to be designed separately, the control efficiency and motion effect of the leg-foot robot can be effectively improved, and an effective basis is provided for realizing stable motion of the robot in various complex environments.

[0029] The method has high robustness and scalability, the stable distributed controller can be directly deployed on various types of leg-foot robots, the deployment integration can significantly increase the motion performance, load bearing capacity and other abilities of the leg-foot robot, further application potential of the method is brought into play, the leg-foot robot can move in various complex environments, and finally the stability, flexibility and overall motion performance of the leg-foot robot are enhanced.

[0030] Advantages of the additional aspects of the application will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0031] The drawings accompanying the specification integrated into the specification of the application serve to provide further understanding of the application, the illustrative embodiments of the application and the description thereof serve to explain the application, and do not constitute an improper limitation on the application.

[0032] Figure 1 A framework flowchart of a robot combination distributed control method and system based on a disturbance observer is provided for the embodiment 1 of the application;

[0033] Figure 2 A schematic diagram of a robot combination is provided for the application.

[0034] Figure 3 A schematic diagram of a disturbance force transmission model is provided for the application. DETAILED DESCRIPTION

[0035] The application will be further described below in combination with the drawings and embodiments.

[0036] It should be pointed out that the following detailed description is exemplary and aims to provide further description of the application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as that generally understood by those skilled in the art to which the application belongs.

[0037] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments of this disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and "comprising", when used in this specification, specify the presence of stated features, integers, steps, or components, but do not preclude the presence or addition of one or more other features, integers, steps, components, or groups thereof.

[0038] The embodiments in the present disclosure and the features in the embodiments can be combined with each other without conflict.

[0039] Embodiment 1

[0040] In order to enable the leg-foot robot assembly to effectively move in both combined and separated states, the present embodiment provides a robot assembly distributed control method based on disturbance observer, which only uses the leg-foot robot body sensors to obtain joint rotation angle, self-pose, joint torque, generalized coordinates and other robot motion states, and realizes efficient estimation of all internal and external disturbances suffered by the robot through the establishment of a discrete disturbance observer and a local extended state observer. Based on the estimated internal and external disturbances, the robot dynamics model can further establish independent dynamics models, so that the simplified single rigid body dynamics model can obtain more accurate fuselage dynamics information, reducing the influence of modeling error and disturbance interference, thereby realizing a more reliable model predictive controller.

[0041] The leg-foot robot assembly distributed control method based on disturbance observer proposed in the present embodiment uses the encoders located at the joints of the leg-foot robot assembly and the inertial measurement unit on the robot body to obtain the generalized coordinates of the overall system, and obtains the current joint output torque through the joints equipped with torque feedback. The generalized coordinates and joint output torque are input into the discrete observer to obtain the reaction force of the ground against the end of the single body module, and the total reaction force is equivalent to the internal disturbance force transmitted through the connecting rod through the established kinematics and dynamics models, which is used to establish a model predictive controller based on disturbance observation for another leg-foot module in the assembly. Since this discrete observer cannot comprehensively cover all internal and external disturbance forces, a local state observer of the disturbance force of the connecting rod transmission model is proposed, and the disturbance force obtained by the observer is input into the distributed model predictive controller in the same way. In actual application, in order to reduce the calculation cost of the observer and increase the real-time performance of disturbance estimation, a probability trigger model based on error function is proposed to realize real-time switching of the discrete observer and the local disturbance observer.

[0042] The robot assembly distributed control method based on the disturbance observer of the embodiment, the assembly platform schematic diagram is as shown in Figure 2 The disturbance force transmission model is as shown in Figure 3 The following scheme is specifically adopted.

[0043] As shown in Figure 1 The robot assembly distributed control method based on the disturbance observer of the embodiment is provided, including the following steps:

[0044] Obtain the motion state of each unit in the robot assembly at the current time, and obtain the initial robot dynamics model based on the motion state;

[0045] Establish a discrete disturbance observer to obtain the internal disturbance force between each robot, and establish a local expansion observer to obtain the internal and external disturbance force of the robot;

[0046] Establish a disturbance-based probability trigger model, when the disturbance force observed by the discrete disturbance observer reaches a certain threshold, switch the discrete disturbance observer and the local expansion observer;

[0047] Based on the observed disturbance force, correct the initial robot dynamics model, based on the corrected robot dynamics model, establish an optimal quadratic programming problem according to the requirements of the task, solve the quadratic programming problem, and obtain the input foot force of the robot assembly motion.

[0048] The robot assembly distributed control method based on the disturbance observer of the embodiment is introduced as follows.

[0049] The joint rotation angle, self-pose feedback information of the leg-foot robot assembly at the current time are obtained by using the encoders located on the joints of the leg-foot robot assembly and the inertial measurement unit on the body, and are integrated into the generalized coordinates of the overall system That is,

[0050] (1);

[0051] Wherein, is the robot centroid position, is the robot centroid rotation angle; is the position of all joints of the robot, The value of is determined by the number of all joints of the robot; is the dimension of the robot generalized coordinates, and its size is ; the upper subscript represents the transpose of the vector or matrix. Similarly, the generalized velocity can be obtained by the above sensor:

[0052] (2);

[0053] wherein, is the robot centroid velocity, is the robot centroid angular velocity; is the velocity of all joints of the robot. In addition, the output torque of all joints of the robot is obtained by the joint motors of the leg-foot robot combination with torque feedback .

[0054] The robot state vector is obtained by integrating the generalized coordinates and the generalized velocities The initial robot single-rigid-body dynamics model (i.e., the initial robot dynamics model) can be obtained as:

[0055] (3).

[0056] wherein the variables , and the upper sign defines the derivative of the state with respect to time, is the identity matrix, is the rotation matrix, is the moment of inertia matrix, is the robot mass, is the robot final output foot force, which is obtained by step S6.

[0057] Based on the obtained generalized velocity, the generalized momentum of the leg-foot robot at the current time is:

[0058] (4).

[0059] wherein, is the mass matrix, which can be obtained by the Euler method or the Lagrange method. Based on the generalized coordinates, the generalized momentum and the joint output torque, a discrete disturbance observer can be established:

[0060] (5).

[0061] wherein, is the generalized torque observed by the observer, is the observer cutoff frequency, is the sampling time, is a selection matrix that sets the torque on the underactuated degree of freedom to zero, and is is the robot Coriolis force and centrifugal force matrix, which can also be solved by the Euler method or the Lagrange method, is the gravitational acceleration. The generalized torque obtained by the above observer can be converted into the ground reaction force at each foot end by the contact Jacobian , i.e.:

[0062] (6);

[0063] in For the first i The selection matrix for each leg For the first i The contact Jacobian matrix of each leg. Based on the perturbation force transmission model and the obtained ground reaction force, a perturbation dynamics model can be established for the center-of-mass velocity and angular velocity of the robot's state vector:

[0064] (7);

[0065] in, The ground reaction force obtained by the aforementioned observer from another module, For this reaction force to act on the robot's lever arm, The lever arm is the force by which the ground reaction force acts on the robot's center of mass.

[0066] Based on the established perturbation dynamics model, assuming the robot always operates in an ideal state without tipping over, the perturbation dynamics model is statistically analyzed over a period of time to obtain the average value. with standard deviation Then, a probability triggering model is established, as shown in the following formula.

[0067] (8);

[0068] in, Let be the Gaussian error function. This equation is... Exceeding a certain value (this value is determined by...) Statistical characteristics and When the value is determined, the value rapidly increases from zero to 1, at which point the observer switches to a local disturbance observer; when the value is less than a certain threshold, the value rapidly decreases from 1 to 0, at which point the observer switches to a discrete observer.

[0069] Formula (7) establishes a dynamic model of the reaction force from the ground, but it does not take into account the external influences that the fuselage may experience. However, considering the disturbances experienced by each robot in the legged robot assembly, the dynamic model can now be reformulated as follows:

[0070] (9);

[0071] in This represents external forces and torque disturbances acting on the robot, excluding internal disturbances caused by ground reaction forces. To estimate the disturbances... The local dilation observer can be designed as follows:

[0072] (10);

[0073] wherein, is the disturbance model observed by the local extended observer, is the disturbance model observation gain matrix, is the disturbance observation gain matrix, is defined as the difference between the actual disturbance model and the observed disturbance model, i.e.,

[0074] (11);

[0075] wherein the actual disturbance model is obtained by integrating formula (9).

[0076] Based on the observed disturbance force obtained by the discrete disturbance observer or the local state observer, the single rigid body dynamics model of the robot can be modified to (i.e., the robot dynamics model is corrected):

[0077] (12);

[0078] wherein, is the system state vector under disturbance, is the observed disturbance force obtained. By defining the state tracking error , the distributed model predictive controller can be constructed as a quadratic programming problem:

[0079] (13);

[0080] wherein, is the norm symbol, and are the terminal value and stage cost weight matrices, respectively, represent the weight matrix of the output .

[0081] By establishing a quadratic programming problem through the whole body control module, the joint torque solved based on the distributed model predictive controller is further optimized according to the requirements of tasks such as position, attitude angle, etc., so that the robot can move according to the given instructions.

[0082] Through the above method, it is ensured that the leg-foot robot combination can obtain the disturbance situation in real time based on the proprioceptive perception in the presence of internal and external disturbances, and can change the optimal foot output force in real time according to the size of the disturbance, effectively reducing the influence of internal disturbances generated by the leg-foot combination and the external environment, and has strong application potential.

[0083] Embodiment 2

[0084] The embodiment provides a robot assembly distributed control system based on a disturbance observer, comprising:

[0085] A dynamics model construction module is configured to acquire a motion state of each unit in the robot assembly at a current time, and obtain an initial robot dynamics model based on the motion state;

[0086] A disturbance observer establishment module is configured to establish a discrete disturbance observer, acquire internal disturbance forces between the robots, establish a local extended observer, and acquire internal and external disturbance forces of the robots;

[0087] A disturbance observer switching module is configured to establish a probability trigger model based on disturbance, and switch the discrete disturbance observer and the local extended observer when the disturbance force observed by the discrete disturbance observer reaches a certain threshold;

[0088] A control output module is configured to correct the initial robot dynamics model based on the observed disturbance force, establish an optimal quadratic programming problem based on the corrected robot dynamics model and the requirements of a task, solve the quadratic programming problem, and obtain an input foot force of robot assembly motion.

[0089] It should be noted that the modules correspond to the steps in Embodiment 1, and the modules have the same examples and application scenarios as the steps, but are not limited to the content disclosed in Embodiment 1. It should be noted that the modules can be executed in a computer system as part of the system.

[0090] In more embodiments, the following are also provided:

[0091] An electronic device comprises a memory and a processor, and computer instructions stored in the memory and running on the processor, and when the computer instructions are run by the processor, the method in Embodiment 1 is completed. For brevity, details are not repeated here.

[0092] It should be understood that in the embodiment, the processor can be a central processing unit CPU, and the processor can also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, field programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0093] A computer readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the method in Embodiment 1 is completed.

[0094] The method in embodiment 1 can be directly executed by a hardware processor, or executed by a combination of hardware and software modules in the processor. The software modules can be located in a storage medium mature in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, register, etc. The storage medium is located in a memory, and the processor reads information in the memory and combines hardware to complete the steps of the above method. To avoid repetition, no longer detailed description is made herein.

[0095] A computer program product comprising a computer program which, when executed by a processor, implements the method in embodiment 1.

[0096] The present application also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer executable instructions, for example, instructions embodied in program modules, executed by devices at the target real or virtual processor to perform processes / methods as described above. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform particular tasks or implement particular abstract data types. In various embodiments, the functions of the program modules can be combined or divided as desired in various embodiments. Machine executable instructions for program modules can be executed within a local or distributed device. In a distributed device, program modules can be located in local and remote storage media.

[0097] Computer program code for carrying out operations of the present application can be written in one or more programming languages. These computer program codes can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus, so that the program codes cause the functions / operations specified in the flowcharts and / or block diagrams to be performed when the computer or other programmable data processing apparatus executes the program codes. The program codes can be executed entirely on a computer, partially on a computer, as a standalone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0098] In the context of the present application, computer program code or related data can be carried by any appropriate carrier to enable a device, apparatus or processor to perform various processes and operations described above. Examples of the carrier include a signal, a computer readable medium, etc. Examples of the signal can include an electrical, optical, radio, sound or other forms of propagated signals, such as a carrier wave, an infrared signal, etc.

[0099] Those skilled in the art can understand that the units and algorithm steps of each example described in combination with the present embodiment can be realized in electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software manner depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0100] Although the specific embodiments of the present application are described above in combination with the drawings, it is not a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the scope of protection of the present application.

Claims

1. A robot assembly distributed control method based on a disturbance observer, characterized by, The method comprises the following steps: obtaining the motion state of each unit in the robot assembly at the current time, and obtaining an initial robot dynamics model based on the motion state; a discrete disturbance observer is established to obtain internal disturbance forces between the robots, a local extended observer is established to obtain internal and external disturbance forces of the robots, and the discrete disturbance observer is established in detail as follows: joint angles, self poses, and joint torques are integrated into generalized coordinates and generalized velocities of the robot assembly, generalized momentum of the robot is obtained according to the generalized velocities, and the discrete disturbance observer is established according to the generalized coordinates, the generalized momentum, and the joint torques; internal disturbance forces between the robots are obtained based on the discrete disturbance observer in detail as follows: observed torques of each driving joint are obtained based on the discrete disturbance observer, the observed torques are converted into ground reaction forces borne by the legs and feet, a disturbance dynamics model is established based on the ground reaction forces, and internal disturbance forces between the robots are obtained; a probability trigger model based on disturbance is established, and when the disturbance force observed by the discrete disturbance observer reaches a certain threshold, the discrete disturbance observer and the local extended observer are switched; the initial robot dynamics model is corrected based on the observed disturbance force, an optimal quadratic programming problem is established based on the corrected robot dynamics model according to the requirements of a task, the quadratic programming problem is solved, and input foot forces of the robot assembly motion are obtained.

2. The disturbance observer based robot assembly distributed control method according to claim 1, wherein, The motion state of each unit in the robot assembly at the current time comprises joint angles, self poses, and joint torques.

3. The disturbance observer based robot assembly distributed control method according to claim 1, wherein, Whether to switch the observer is determined according to the calculation result of the probability trigger model, the calculation result of the probability trigger model rapidly increases from 0 to 1 when the calculation result exceeds a certain value, at this time, the observer is switched to the local extended observer, and the calculation result of the probability trigger model rapidly decreases from 1 to 0 when the calculation result is less than a certain value, at this time, the observer is switched to the discrete disturbance observer.

4. The disturbance observer based robot assembly distributed control method according to claim 1, wherein, An optimal quadratic programming problem is established and solved according to the requirements of the task, optimal input foot forces are obtained, the optimal input foot forces are changed in real time according to the size of the disturbance, and input foot forces of the robot assembly motion are obtained.

5. A robot assembly distributed control system based on a disturbance observer, characterized by, The method comprises the following steps: a dynamics model construction module is configured to obtain the motion state of each unit in the robot assembly at the current time, and obtain an initial robot dynamics model based on the motion state; a disturbance observer establishment module is configured to establish a discrete disturbance observer to obtain internal disturbance forces between the robots, establish a local extended observer to obtain internal and external disturbance forces of the robots, and establish the discrete disturbance observer in detail as follows: joint angles, self poses, and joint torques are integrated into generalized coordinates and generalized velocities of the robot assembly, generalized momentum of the robot is obtained according to the generalized velocities, and the discrete disturbance observer is established according to the generalized coordinates, the generalized momentum, and the joint torques; internal disturbance forces between the robots are obtained based on the discrete disturbance observer in detail as follows: observed torques of each driving joint are obtained based on the discrete disturbance observer, the observed torques are converted into ground reaction forces borne by the legs and feet, a disturbance dynamics model is established based on the ground reaction forces, and internal disturbance forces between the robots are obtained; The disturbance observer switching module is configured to establish a disturbance-based probabilistic triggering model, and when the disturbance force observed by the discrete disturbance observer reaches a certain threshold, switching is performed between the discrete disturbance observer and the local extended observer; The control output module is configured to correct the initial robot dynamics model based on the observed disturbance force, establish an optimal quadratic programming problem according to the requirements of the task based on the corrected robot dynamics model, solve the quadratic programming problem, and obtain the input foot force of the robot assembly motion.

6. An electronic device, comprising: The computer program product comprises a memory and a processor, and computer instructions stored on the memory and run on the processor, and when the computer instructions are run by the processor, the method in any one of claims 1-4 is completed.

7. A computer readable storage medium characterized by A computer program product for storing computer instructions, which are executed by a processor to complete the method in any one of claims 1-4.

8. A computer program product, characterised in that, The computer program product comprises a computer program, which is executed by a processor to complete the method in any one of claims 1-4.

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