Impedance control method and device based on axis angle representation, equipment and storage medium

Abstract

The application discloses an impedance control method and device based on an axis angle representation, equipment and a storage medium. A Jacobian matrix of a rotation angle and a three-dimensional direction vector with respect to a joint angle and a matrix irrelevant to a joint angular velocity in a second-order derivative of a product of the rotation angle and the three-dimensional direction vector with respect to time are calculated according to the rotation angle and the three-dimensional direction vector. A mathematical relationship of a robot joint instruction torque is constructed according to a robot Jacobian matrix, the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle, the matrix irrelevant to the joint angular velocity in the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time, the rotation angle and the three-dimensional direction vector. The robot joint instruction torque is obtained by solving the mathematical relationship of the robot joint instruction torque according to a preset constraint function. The application aims to eliminate nonlinear factors of a dynamic relationship in impedance control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot automation, and in particular to an impedance control method and device based on an axis angle representation, a device, an apparatus and a storage medium. BACKGROUND

[0002] With the improvement of automation, the application scenarios of robots are no longer limited to tasks such as carrying and moving in free space. Robots are also required to perform some contact operations such as polishing. In addition, with the concept of human-robot symbiosis, robots are further required to perform some tasks in cooperation with humans, which requires robots to have safety features. Impedance control is a control algorithm that can meet the above two requirements.

[0003] Impedance control is to form a dynamic relationship between the robot end coordinate system error and the external force. The dynamic relationship is specified and usually has the form of a second-order differential equation. The robot end coordinate system error includes position error and angle error. In general impedance control, the angle error part of the first-order term and the second-order term in the specified dynamic relationship usually uses the angle velocity error and the angle acceleration error of the end, while the angle error part of the zero-order term in the dynamic relationship usually uses the Euler angle or the axis angle representation between the actual end coordinate system and the desired end coordinate system, which results in that the zero-order term and the first-order and second-order terms of the angle error part do not form a derivative relationship. This actually introduces a nonlinear factor in the dynamic relationship, which will cause difficulties in the angle control level of impedance control. SUMMARY

[0004] In view of the problems in the prior art, the present application provides an impedance control method and device based on an axis angle representation, an apparatus and a storage medium, which aims to eliminate the nonlinear factor of the dynamic relationship in impedance control.

[0005] To solve the above technical problems, the present application is implemented by the following technical solutions:

[0006] An impedance control method based on an axis angle representation, comprising:

[0007] Obtaining robot joint angles and joint angular velocities, and calculating a robot Jacobian matrix and a robot actual end coordinate system rotation matrix according to the joint angles and the joint angular velocities;

[0008] Calculating a rotation angle and a three-dimensional direction vector according to the robot actual end coordinate system rotation matrix and a preset desired end coordinate system rotation matrix;

[0009] Calculate the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle, as well as the matrix in the second derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is unrelated to the joint angular velocity, based on the rotation angle and the three-dimensional direction vector.

[0010] The mathematical relationship for the robot joint command torque is constructed based on the robot Jacobian matrix, the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle, the matrix in the second derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is not related to the joint angular velocity, and the rotation angle and the three-dimensional direction vector.

[0011] The robot joint command torque is obtained by solving the mathematical relationship of the robot joint command torque according to the preset constraint function.

[0012] Furthermore, the calculation of the rotation angle and three-dimensional direction vector based on the actual end-effector coordinate system rotation matrix and the preset desired end-effector coordinate system rotation matrix is ​​as follows:

[0013]

[0014]

[0015] In the formula: R is the rotation matrix of the robot's actual end-effector coordinate system. d is the rotation matrix of the desired end coordinate system; is the trace function, which is the sum of the diagonal elements of the matrix; θ is the rotation angle; l is the three-dimensional direction vector.

[0016] Furthermore, the calculation of the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle, and the matrix in the second derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is unrelated to the joint angular velocity, is as follows:

[0017]

[0018]

[0019]

[0020] In the formula: J o′ Γ is the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle; Γ is the matrix in the second derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is independent of the joint angular velocity; J o This represents the portion of the robot's Jacobian matrix J corresponding to the angular velocity. Joint angular velocity; is a time derivative of a preset desired end coordinate system rotation matrix, and β is a unit vector perpendicular to l and to each other, and α×l=β; represents the following operation:

[0021]

[0022] Further, the mathematical relationship of the robot joint instruction torque is as follows:

[0023]

[0024] wherein, and are the estimated robot inertia matrix, Coriolis force matrix, gravity matrix and joint friction torque respectively; F e is a six-dimensional vector composed of the force and torque exerted on the robot by the environment measured by the end torque sensor; τ is the robot joint instruction torque; τ d is an arbitrarily set three-dimensional real number vector; e is the torque exerted on the robot by the environment measured by the force sensor, which is a three-dimensional real number vector; M, B and K are arbitrarily set three-order real number matrices.

[0025] Further, the constraint function is specifically as follows:

[0026]

[0027] An impedance control device based on a shaft angle representation, comprising:

[0028] A first calculation module is configured to acquire robot joint angles and joint angular velocities, and calculate a robot Jacobian matrix and a robot actual end coordinate system rotation matrix according to the joint angles and the joint angular velocities;

[0029] A second calculation module is configured to calculate a rotation angle and a three-dimensional direction vector according to the robot actual end coordinate system rotation matrix and a preset desired end coordinate system rotation matrix;

[0030] A third calculation module is configured to calculate a rotation angle and a three-dimensional direction vector, a Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angles, and a matrix irrelevant to the joint angular velocity in a second-order derivative of a product of the rotation angle and the three-dimensional direction vector with respect to time;

[0031] A fourth calculation module is configured to construct a mathematical relationship of a robot joint instruction torque according to the robot Jacobian matrix, the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angles, the matrix irrelevant to the joint angular velocity in the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time, the rotation angle and the three-dimensional direction vector;

[0032] The fifth calculation module is configured to solve a mathematical relationship of the robot joint instruction torque according to a preset constraint function to obtain the robot joint instruction torque.

[0033] An apparatus includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the impedance control method based on the axis angle representation when executing the computer program.

[0034] A computer readable storage medium stores a computer program, and the computer program implements the steps of the impedance control method based on the axis angle representation when executed by a processor.

[0035] Compared with the prior art, the present application has at least the following beneficial effects:

[0036] The impedance control method based on the axis angle representation provided by the present application obtains robot joint angles and joint angular velocities, calculates a robot Jacobian matrix and a robot actual end coordinate system rotation matrix according to the joint angles and the joint angular velocities, calculates a rotation angle and a three-dimensional direction vector according to the robot actual end coordinate system rotation matrix and a preset expected end coordinate system rotation matrix, calculates a Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angles and a matrix of a second-order derivative of a product of the rotation angle and the three-dimensional direction vector with respect to time that is irrelevant to the joint angular velocities, constructs a mathematical relationship of robot joint instruction torque according to the robot Jacobian matrix, the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angles, the matrix of the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is irrelevant to the joint angular velocities, and the rotation angle and the three-dimensional direction vector, and solves the mathematical relationship of the robot joint instruction torque according to a preset constraint function to obtain the robot joint instruction torque, so that the specified second-order dynamic relationship is solved, the nonlinear factors of the dynamic relationship in the impedance control are eliminated, and the subsequent application of the impedance control is facilitated.

[0037] In order to make the above objectives, characteristics and advantages of the present application more apparent and understandable, the following preferred embodiments are described in detail below, and the accompanying drawings are described as follows. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the specific embodiments of the present application, the following will briefly introduce the drawings needed to be used in the description of the specific embodiments. Obviously, the drawings described below are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0039] Figure 1 is a flow chart of an impedance control method based on axis-angle representation of the present application;

[0040] Figure 2 is a schematic diagram of an impedance control device based on axis-angle representation in an embodiment of the present application;

[0041] Figure 3 is a calculation flow chart of an impedance control method based on axis-angle representation in an embodiment of the present application.

[0042] In the figure: 1-mechanical arm; 2-force sensor; 3-upper computer. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme of the present application will be described clearly and completely below in conjunction with the drawings. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0044] As a specific embodiment of the present application, in conjunction with Figure 1 shown, an impedance control method based on axis-angle representation is as follows:

[0045] a. Obtain the joint angle and joint angular velocity of the robot, and calculate the robot Jacobian matrix and the actual robot end coordinate system rotation matrix according to the joint angle and the joint angular velocity.

[0046] b. Calculate the rotation angle and three-dimensional direction vector according to the actual robot end coordinate system rotation matrix and the preset desired end coordinate system rotation matrix, specifically as follows:

[0047]

[0048]

[0049] In the formula: R is the actual robot end coordinate system rotation matrix, R d is the preset desired end coordinate system rotation matrix; is the trace function, that is, the sum of the diagonal elements of the matrix; θ is the rotation angle; l is the three-dimensional direction vector.

[0050] c. Calculate the rotation angle and three-dimensional direction vector Jacobian matrix about the joint angle and the second derivative of the product of the rotation angle and the three-dimensional direction vector about time which is irrelevant to the joint angular velocity, specifically as follows:

[0051]

[0052]

[0053] wherein J o′ is the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle; Γ is the matrix of the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is irrelevant to the joint angular velocity; J o is the part of the robot Jacobian matrix J corresponding to the angular velocity; is the joint angular velocity; is the derivative of the preset desired end coordinate system rotation matrix with respect to time, and β is a unit vector perpendicular to l and to each other, and α x l = β; represents the following operation:

[0054]

[0055] d. A mathematical relationship of the robot joint instruction torque is constructed according to the robot Jacobian matrix, the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle, the matrix of the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time that is irrelevant to the joint angular velocity, the rotation angle and the three-dimensional direction vector, and the mathematical relationship is specifically as follows:

[0056]

[0057] wherein, and are the estimated robot inertia matrix, the Coriolis force matrix, the gravity matrix and the joint friction torque, respectively; F e is a six-dimensional vector composed of the force and torque exerted on the robot by the environment measured by the end torque sensor; τ is the robot joint instruction torque; τ d is an arbitrarily set three-dimensional real number vector; e is the torque exerted on the robot by the environment measured by the force sensor, and is a three-dimensional real number vector; M, B and K are arbitrarily set three-order real number matrices.

[0058] e. The robot joint instruction torque is obtained by solving the mathematical relationship of the robot joint instruction torque according to the preset constraint function, and the constraint function is specifically as follows:

[0059]

[0060] A more detailed explanation is provided below.

[0061] As Figure 3 shown, an impedance control method based on the shaft angle representation includes the following steps:

[0062] Step one, according to the robot joint angle and joint angular velocity, the robot Jacobian matrix, the robot Jacobian matrix derivative, the robot actual end coordinate system rotation matrix and the robot actual end coordinate system rotation matrix derivative are calculated.

[0063] Step two, according to the robot actual end coordinate system rotation matrix and the given desired end coordinate system rotation matrix, the values of θ and l are calculated. Specifically, the calculation method is as follows:

[0064]

[0065]

[0066] In the formula: R is the robot actual end coordinate system rotation matrix, R d is the preset desired end coordinate system rotation matrix; is the trace function, that is, the sum of the diagonal elements of the matrix; θ is the rotation angle; l is a three-dimensional direction vector.

[0067] Step three, based on the above calculation results, α and β are calculated. The algorithm for calculating α and β is not unique, but the calculated results should satisfy: α and β are any mutually perpendicular and perpendicular to l unit vectors, and have α×l=β.

[0068] Step four, based on the above calculation results, the values of and are calculated, and the calculation method is as follows:

[0069]

[0070]

[0071] Step five, based on the above calculation results, the values of and are calculated, and the algorithm for calculating and is not unique, but the calculated results should satisfy: for the selected α and β, and are any three-dimensional vectors that satisfy and , wherein w l is any three-dimensional vector that satisfies ; represents the skew symmetric operator, that is, represents the operation

[0072]

[0073] Step six, based on the above calculation results, the values of J o′ and Γ are calculated, and the calculation method is as follows:

[0074]

[0075]

[0076]

[0077] J o is the part of the robot Jacobian matrix J corresponding to the angular velocity; is the joint angular velocity; is the derivative of the preset desired end coordinate system rotation matrix with respect to time; and are obtained by using the chain rule of derivation on J o′ and g.

[0078] Step seven, based on the calculation results above, combined with the measurement value of the force sensor, the mathematical relationship that the robot joint instruction torque τ should satisfy is constructed, specifically, the mathematical relationship is as follows:

[0079]

[0080] wherein, and are the estimated robot inertia matrix, Coriolis force matrix, gravity matrix and joint friction torque respectively; F e is the six-dimensional vector composed of the force and torque exerted on the robot by the environment measured by the end torque sensor; τ d is an arbitrarily set three-dimensional real number vector; e is the torque exerted on the robot by the environment measured by the force sensor, which is a three-dimensional real number vector; M, B and K are arbitrarily set three-order real number matrices.

[0081] Step eight, based on the calculation results above, the value of the joint instruction torque τ is solved according to the mathematical relationship that the robot joint instruction torque τ should satisfy, the solving method here is not unique, but the torque instruction τ solved makes the following mathematical relationship hold:

[0082]

[0083] As shown in Figure 2 , an impedance control system based on shaft angle representation, including a mechanical arm 1, a force sensor 2 and an upper computer 3, the force sensor 2 is installed at the end of the mechanical arm 1, and the upper computer 3 is in communication connection with the mechanical arm 1 and the force sensor 2.

[0084] The force sensor 2 is used to measure the force and torque exerted on the robot by the environment.

[0085] The host computer 3 is used to control the movement of the robot arm 1, and is also used to calculate the robot Jacobian matrix, the derivative of the robot Jacobian matrix, the actual end coordinate system rotation matrix, and the derivative of the actual end coordinate system according to the robot joint angle and the joint angular velocity; and is also used to calculate the values of theta and l according to the actual end coordinate system rotation matrix and the desired end coordinate system rotation matrix; and is also used to calculate the values of alpha and beta; and is also used to calculate the values of and ; and is also used to calculate the values of and ; and is also used to calculate the values of J o′ , and omega; and is also used to calculate the mathematical relationship that the robot joint instruction torque tau should satisfy in combination with the measurement value of the force sensor; and is also used to solve the feasible instruction torque tau according to the mathematical relationship, so as to form a specified second-order dynamic relationship between the robot end coordinate system error and the external force.

[0086] In this embodiment, the robot arm 1 is a seven-degree-of-freedom robot arm; the host computer 3 is a computer system; and the force sensor 2 is a six-dimensional force / torque sensor. The host computer 3 communicates with the robot arm 1 through a communication protocol, and the six-dimensional force / torque sensor feeds back data to the host computer 3 through a communication protocol. During operation, the robot arm 1 moves under the instruction of the host computer 3.

[0087] In one embodiment, the present application provides a computer device, which comprises a processor and a memory, the memory is used to store a computer program, the computer program comprises program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and 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 gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to realize a corresponding method flow or a corresponding function; the processor in the embodiment of the present application can be used to realize the operation of an impedance control method based on axis angle representation.

[0088] In one embodiment of the present application, the impedance control method based on the shaft angle representation can be stored in a computer readable storage medium if it is implemented in the form of a software functional unit and sold or used as an independent product. Based on such understanding, the present application can implement all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer readable storage medium, and the computer program can implement the steps of each method embodiment when executed by a processor. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or some intermediate forms, etc. The computer readable storage medium includes permanent and non-permanent, removable and non-removable media, and can be implemented by any method or technology to store information. The information can be computer readable instructions, data structures, program modules, or other data.

[0089] The computer storage medium can be any available medium or data storage device that can be accessed by a computer, including but not limited to magnetic storage (such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MO), etc.), optical storage (such as CDs, DVDs, BDs, HVDs, etc.), and semiconductor storage (such as ROM, EPROM, EEPROM, non-volatile memory (NAND FLASH), solid state disk (SSD), etc.).

[0090] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0091] The present application is described with reference to the flowcharts and / or block diagrams of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The device that implements the functions specified in one flow or multiple flows and / or blocks Figure 1 The device that implements the functions specified in one flow or multiple flows and / or blocks

[0092] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flow Figure 1 of the flow or flows and / or blocks Figure 1 of the block or blocks specified in the flow.

[0093] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 of the flow or flows and / or blocks Figure 1 of the block or blocks specified in the flow.

[0094] Finally, it should be noted that the above-described embodiments are merely exemplary implementations of the present application, and are used to explain the technical solutions of the present application, but are not intended to limit the present application. The protection scope of the present application is not limited thereto. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can make modifications or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some of the technical features, without departing from the technical scope disclosed by the present application. The modifications, changes or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method of impedance control based on a representation of shaft angle, characterized by, The method comprises the following steps: obtaining robot joint angle and joint angular velocity, calculating robot Jacobian matrix and robot actual end coordinate system rotation matrix according to the joint angle and the joint angular velocity; calculating rotation angle and three-dimensional direction vector according to the robot actual end coordinate system rotation matrix and preset expected end coordinate system rotation matrix; calculating rotation angle and three-dimensional direction vector about joint angle Jacobian matrix and the matrix irrelevant to joint angular velocity in the second order derivative of the product of rotation angle and three-dimensional direction vector with respect to time according to the rotation angle and three-dimensional direction vector; constructing mathematical relationship of robot joint instruction torque according to the robot Jacobian matrix, the rotation angle and three-dimensional direction vector about joint angle Jacobian matrix, the matrix irrelevant to joint angular velocity in the second order derivative of the product of rotation angle and three-dimensional direction vector with respect to time, the rotation angle and the three-dimensional direction vector; solving the mathematical relationship of the robot joint instruction torque according to the preset constraint function to obtain the robot joint instruction torque.

2. The impedance control method based on the shaft angle representation according to claim 1, wherein, The calculation of the rotation angle and the three-dimensional direction vector according to the robot actual end coordinate system rotation matrix and the preset expected end coordinate system rotation matrix is specifically as follows: In the formula: R is a robot actual end coordinate system rotation matrix, R d is a preset expected end coordinate system rotation matrix; tr is a trace function, that is, the sum of diagonal elements of a matrix; θ is a rotation angle; and l is a three-dimensional direction vector.

3. The impedance control method based on the shaft angle representation according to claim 2, characterized in that, The calculation of the rotation angle and the three-dimensional direction vector about joint angle Jacobian matrix and the matrix irrelevant to joint angular velocity in the second order derivative of the product of rotation angle and three-dimensional direction vector with respect to time according to the rotation angle and the three-dimensional direction vector is specifically as follows: wherein: J o′ is the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle; Γ is the matrix of the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time which is irrelevant to the joint angular velocity; J o is the part corresponding to the angular velocity in the robot Jacobian matrix J; is the joint angular velocity; is the derivative of the preset desired end coordinate system rotation matrix with respect to time, and α and β are arbitrary unit vectors which are perpendicular to each other and to l, and α x l = β; represents the following operation:

4. The impedance control method based on the shaft angle representation according to claim 3, characterized by, The mathematical relationship of the robot joint instruction torque is as follows: where and are the estimated robot inertia matrix, Coriolis force matrix, gravitational force matrix and joint friction torque, respectively; F e is a six-dimensional vector composed of the force and torque exerted on the robot by the environment as measured by the end-effector force / torque sensor; τ is the commanded joint torque of the robot; τ d is an arbitrary three-dimensional real vector; τ e is the torque exerted on the robot by the environment as measured by the force / torque sensor, a three-dimensional real vector; M, B and K are arbitrary third-order real matrices.

5. The impedance control method based on the shaft angle representation according to claim 4, characterized in that, The constraint function is specifically as follows:

6. An impedance control device based on a shaft angle representation, characterized by The method comprises the following steps: a first calculation module is configured to obtain robot joint angle and joint angular velocity, and calculate robot Jacobian matrix and robot actual end coordinate system rotation matrix according to the joint angle and the joint angular velocity; a second calculation module is configured to calculate rotation angle and three-dimensional direction vector according to the robot actual end coordinate system rotation matrix and preset expected end coordinate system rotation matrix; a third calculation module is configured to calculate rotation angle and three-dimensional direction vector about joint angle Jacobian matrix and the matrix irrelevant to joint angular velocity in the second order derivative of the product of rotation angle and three-dimensional direction vector with respect to time according to the rotation angle and the three-dimensional direction vector; a fourth calculation module is configured to construct mathematical relationship of robot joint instruction torque according to the robot Jacobian matrix, the rotation angle and three-dimensional direction vector about joint angle Jacobian matrix, the matrix irrelevant to joint angular velocity in the second order derivative of the product of rotation angle and three-dimensional direction vector with respect to time, the rotation angle and the three-dimensional direction vector; a fifth calculation module is configured to solve the mathematical relationship of the robot joint instruction torque according to the preset constraint function to obtain the robot joint instruction torque.

7. An apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein, The processor executes the computer program to realize the steps of the impedance control method based on the shaft angle representation according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, the computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 7. The computer program is executed by the processor to realize the steps of the impedance control method based on the shaft angle representation according to any one of claims 1 to 5.

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