Compliant control method and compliant control system for a robot

Abstract

The application provides a compliant control method and a compliant control system for a robot, the method comprising: according to Newton-Euler method, splitting the secondary term of a velocity vector into two different inputs, obtaining a recursive expression of the robot, and obtaining a dynamic equation of the robot according to the recursive expression; constructing a generalized momentum observer; applying an external force during the operation of the robot, obtaining the output of the generalized momentum observer, estimating the external torque in the physical interaction between the robot and the external environment according to the output; generating a reference position signal according to the external torque and an impedance control model, and performing compliant control of the robot according to the reference position signal. By constructing an accurate dynamic model of the robot and combining the generalized momentum observer, the application infers the external force generated in the interaction between the robot and the external environment, without relying on a physical force sensor, thereby significantly reducing the hardware cost, simplifying the design and maintenance process of the system, and improving the reliability and maintainability of the system.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, specifically to a compliant control method and a compliant control system for robots. Background Technology

[0002] Currently, robot teaching and operation imitation methods typically rely on force sensors to perceive the forces applied by the external environment in real time, thereby achieving precise control of the robot.

[0003] However, the high cost, complex installation process, and susceptibility to environmental interference of force sensors limit their widespread application in industrial and service robotics. Summary of the Invention

[0004] To solve the above-mentioned technical problems, the present invention provides a compliant control method and a compliant control system for robots.

[0005] The technical solution adopted in this invention is as follows:

[0006] A first aspect of the present invention proposes a compliant control method for a robot, comprising the following steps: constructing a link coordinate system for the robot using the DH parameter method; decomposing the second term of the velocity vector into two different inputs according to the Newton-Euler method, obtaining recursive expressions for the angular velocity and acceleration of each link of the robot, as well as the linear acceleration of the origin and center of mass of the coordinate system, and obtaining the robot's dynamic equations based on the recursive expressions; constructing a generalized momentum observer based on generalized momentum; applying an external force during the operation of the robot, obtaining the output of the generalized momentum observer based on the dynamic equations and robot operation data, estimating the external torque in the physical interaction between the robot and the external environment based on the output of the generalized momentum observer; obtaining an impedance control model, generating a reference position signal based on the external torque and the impedance control model, and performing compliant control of the robot based on the reference position signal.

[0007] The compliant control method for robots described above in this invention also has the following additional technical features:

[0008] According to an embodiment of the present invention, the recursive expression is obtained according to the following formula:

[0009]

[0010] in, Represents the angular velocity of joint i. ω represents the auxiliary angular acceleration of joint i. i Let be the angular velocity of link i. Let i be the auxiliary angular velocity of link i. This represents the linear acceleration at the origin of the coordinate system of link i; The linear acceleration at the center of mass of link i is represented by r. i-1,i This represents the vector from the (i-1)th joint to the ith joint. ω represents the vector from the i-th joint to the centroid of the link. i This represents the angular velocity of link i. This represents the angular acceleration of link i. τ represents the auxiliary angular velocity of link i. i f represents the torque at joint i. i f represents the force at joint i. i+1 I represents the force at joint i+1. i Let z represent the inertia matrix of link i. i This represents a vector along the i-axis, [0 0 1]. T , τ d This represents the driving torque of the robot.

[0011] According to one embodiment of the present invention, the dynamic equations of the robot are obtained specifically according to the following formula; Where q represents the joint angle. Represents joint angular velocity. M(q) represents the joint angular acceleration, and M(q) represents the inertia tensor. G(q) represents the centrifugal force and Coriolis torque, and τ represents the gravity vector. d Indicates driving torque; τ e This represents the torque that is mapped from the external input force to each joint.

[0012] According to one embodiment of the present invention, generalized momentum is obtained according to the following formula: Where p represents generalized momentum, M(q) represents the inertia tensor, and q represents the joint angle. Represents joint angular velocity.

[0013] According to one embodiment of the present invention, a generalized momentum observer is constructed based on the following formula: Where r(t) represents the output of the generalized momentum observer, and K represents the observer gain coefficient. for The transpose of the matrix, G(q) represents centrifugal force and Coriolis torque, G(q) represents gravity vector, and p represents generalized momentum.

[0014] According to an embodiment of the present invention, the impedance control model is obtained according to the following formula: Among them, M d D represents the mass matrix of the simulation. d Represents the damping matrix, K d Represents the stiffness matrix, q d q rτ represents the robot's reference position and actual position, respectively. e This represents the torque that is mapped from the external input force to each joint. Represents the joint angles during actual robot operation. This represents the joint angular velocity during actual robot operation.

[0015] According to one embodiment of the present invention, the robot is a six-degree-of-freedom robot.

[0016] A second aspect of this invention provides a compliant control system for a robot, comprising: a first construction module for constructing a link coordinate system of the robot using the DH parameter method; an acquisition module for obtaining recursive expressions for the angular velocity and acceleration of each link of the robot, as well as the linear acceleration of the origin and center of mass of the coordinate system, by splitting the secondary term of the velocity vector into two different inputs according to the Newton-Euler method; a second construction module for establishing the robot's dynamic equations based on the robot's driving torque and the external torque in the robot's physical interaction with the outside world; and a third construction module for obtaining the robot's centrifugal force and Coriolis torque terms according to the recursive expressions. The gravity vector G(q) is based on the generalized momentum p, centrifugal force, and Coriolis torque term. A generalized momentum observer is constructed using the gravity vector G(q); an estimation module is used to apply external force during the robot's operation, obtain the robot's driving torque based on the robot's current information, input the driving torque into the generalized momentum observer, and estimate the external torque in the robot's physical interaction with the external environment based on the output of the generalized momentum observer; a control module is used to obtain an impedance control model, generate a reference position signal based on the external torque and the impedance control model, and perform compliant control of the robot based on the reference position signal.

[0017] The beneficial effects of this invention are:

[0018] This invention constructs an accurate robot dynamics model and combines it with a generalized momentum observer to infer the external forces generated during the robot's interaction with the outside world. This model-based force estimation technology does not rely on physical force sensors, but also significantly reduces hardware costs, simplifies the system design and maintenance process, and improves the system's reliability and maintainability.

[0019] This invention employs an improved Newton-Euler method when obtaining the dynamic equations, splitting the secondary term of the velocity vector into two different inputs, thereby enabling its application to robots with more degrees of freedom. Attached Figure Description

[0020] Figure 1 This is a flowchart of a compliant control method for a robot according to an embodiment of the present invention;

[0021] Figure 2 This is a diagram illustrating the derivation principle of a recursive expression according to an embodiment of the present invention;

[0022] Figure 3 This is a block diagram of a generalized momentum observer according to an embodiment of the present invention;

[0023] Figure 4 This is a block diagram illustrating the control process of a robot according to an embodiment of the present invention;

[0024] Figure 5 This is a block diagram of a compliant control system for a robot according to an embodiment of the present invention. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0026] Within the framework of human-robot collaboration, the perception of external forces plays a crucial role in robot operation. Rapidly and accurately capturing external forces not only improves robot compliance but also optimizes controller performance through feedforward mechanisms, thereby enhancing the robot's resistance to interference in compliant control. Besides relying on accurate dynamic models as a foundation, the design of the external force observer is a key factor directly affecting the effectiveness of force detection.

[0027] The robot described in this invention can be a six-degree-of-freedom robot.

[0028] Figure 1 This is a flowchart of a robot compliance control method according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes the following steps:

[0029] S1, the link coordinate system of the robot is constructed using the DH parameter method.

[0030] Specifically, this invention focuses on a six-degree-of-freedom industrial robot and employs the Denavit-Hartenberg (DH) parameter method to construct a link coordinate system. By analyzing each joint of the six-degree-of-freedom industrial robot, its link length, torsion angle, offset, and joint angle are defined to form an accurate link coordinate system. The DH parameter method allows for more flexible handling of the relative positional relationship between joints and links, and is particularly suitable for the unique structural features of six-degree-of-freedom industrial robots.

[0031] S2, based on the Newton-Euler method, splits the secondary term of the velocity vector into two different inputs to obtain the recursive expressions for the angular velocity and acceleration of each link of the robot, as well as the linear acceleration of the origin and center of mass of the coordinate system.

[0032] Specifically, the Newton-Euler method utilizes the principles of particle dynamics and rotational dynamics to establish the overall dynamic equations by analyzing each joint and link of the robot step by step.

[0033] First, initialize the joint state variables of the six-DOF industrial robot, including joint position, velocity, and acceleration. The forward pass starts from the root joint, calculating the linear velocity and angular velocity of each joint. Using known joint angles and angular velocities, the linear velocity is derived through the connection relationships between joints. Then, calculate the linear acceleration and angular acceleration of each joint. By differentiating the linear and angular velocities, accurately reflecting joint motion is ensured. After obtaining the linear and angular accelerations, the linear forces and torques acting on each joint are calculated using the joint's mass and inertia matrix. Key variables include the joint's mass, center of gravity position, and inertial characteristics. The backward pass starts from the end effector, calculating the reaction forces and torques of each joint. The linear force and torque results of each joint are passed to the previous joint, updating its state. This step is implemented recursively, ensuring the transfer of dynamic information between successive joints. For each joint, the linear velocity and angular velocity are updated using its force conditions, ensuring the overall system state remains consistent.

[0034] The Newton-Euler algorithm is as follows: τ is the joint torque, and g is the acceleration due to gravity. Represents joint angular velocity. Represents joint angular acceleration, NE * The algorithm is the Newton-Euler algorithm.

[0035] like Figure 2 As shown, this invention modifies the Newton-Euler method, which can be simply described as a method with 5 inputs, namely... , of the 4 vector functions This refers to the joint auxiliary angular velocity.

[0036] By using velocity vector The term is split into two different inputs. and auxiliary This allows for application to more degrees of freedom, with the additional condition that: for have:

[0037]

[0038] Furthermore, the equations need to satisfy the oblique symmetry property, and when the algorithm NE... * Call When g=0, g represents the gravity term, and should produce: Represents the Coriolis force term;

[0039] matrix The i-th column is: And it must satisfy: For matrix The elements in.

[0040] Considering the above requirements, an auxiliary angular velocity for link i is introduced. It depends Through recursion: z i-1 This represents the vector along the (i-1) axis, denoted as [0 0 1]. T .

[0041] In addition, the following terms in the standard Newton-Euler recursive method with second-order velocity dependence are modified:

[0042] In the standard Newton-Euler recurrence relation, the forward recurrence relation for the angular velocity and acceleration of each link, as well as the linear acceleration of the origin and center of mass of the coordinate system, is as follows:

[0043]

[0044]

[0045] Here, r represents a position vector, used to describe the positional relationship between two points. r i-1,i =O i -O i-1 B i and O i Let ω be the origin of the i-th reference frame and the centroid of the i-th link, respectively. i This represents the angular velocity of link i. τ represents the angular acceleration of link i. i f represents the torque at joint i. i f represents the force at joint i. i+1 I represents the force at joint i+1. i Let z represent the inertia matrix of link i. i This represents the vector along the i-axis, defined as [0 0 1]. T .

[0046] In the positive recurrence relation ω i ×(ω i ×r i-1,i ), and ω i ×(I i ω i ) needs to be modified.

[0047] Equation (1) contains Multiply by ω i-1 It is The function exists as a vector product in the remaining equations. One of the factors depends on The other depends on In all four cases described above, the result will vary depending on the order of the substitutions. In fact, in the modified expression (1):

[0048] Due to the antisymmetric nature of the vector product, the torque expression will have a sign reversal, specifically m×n=-(m×n), where m and n are vectors. For the recursive equation of angular acceleration, equation (1) can be replaced with the following:

[0049] Therefore, in one embodiment of the present invention, the recursive expression is obtained according to the following formula.

[0050]

[0051] in, Represents the angular velocity of joint i. ω represents the auxiliary angular acceleration of joint i. i Let be the angular velocity of link i. Let i be the auxiliary angular velocity of link i. This represents the linear acceleration at the origin of the coordinate system of link i; The linear acceleration at the center of mass of link i is represented by r. i-1,i This represents the vector from the (i-1)th joint to the ith joint. ω represents the vector from the i-th joint to the centroid of the link. i This represents the angular velocity of link i. This represents the angular acceleration of link i. τ represents the auxiliary angular velocity of link i. i f represents the torque at joint i. i f represents the force at joint i. i+1 I represents the force at joint i+1. i Let z represent the inertia matrix of link i. i This represents the vector along the i-axis, defined as [0 0 1]. T u i This represents the torque in the z-direction required for the robot to move at the given speed and acceleration.

[0052] Therefore, a modified recursive Newton-Euler algorithm This can be represented by the recursive expression above.

[0053] S3. Establish the robot's dynamic equations based on the robot's driving torque and the external torque in the robot's physical interaction with the outside world.

[0054] Specifically, considering the force interaction between a 6-DOF robot and its external environment in real-world scenarios, in one embodiment of the present invention, the dynamic equations are rewritten as follows:

[0055]

[0056] Where q represents the joint angle. Represents joint angular velocity. M(q) represents the joint angular acceleration, and M(q) represents the inertia tensor. G(q) represents the centrifugal force and Coriolis torque, and τ represents the gravity vector. d This represents the driving torque, which consists of two parts: one part is acted upon by an external force, and the other part drives the motion of the body; τ e τ represents the external torque in the physical interaction between the robot and its surroundings, that is, the torque that is mapped from the external input force to each joint. e =J T F ext J represents the Jacobian matrix, F ext It represents the contact force in the physical interaction between the robot and the outside world.

[0057] τ d The external torque τ can be obtained by acquiring the servo motor current during robot operation. e The following generalized momentum observer is used to obtain it.

[0058] S4, Obtain the centrifugal force and Coriolis torque terms of the robot based on the recursive expression. The gravity vector G(q) is based on the generalized momentum p, centrifugal force, and Coriolis torque term. And the gravity vector G(q) is used to construct a generalized momentum observer.

[0059] To avoid the problems of numerical differentiation of the inertia tensor M(q) or calculation of the partial derivatives of each element, the residual expression of the generalized momentum observer needs to calculate a quadratic velocity term, which is of the form: This invention applies the modified Newton-Euler method described above to the generalized momentum observer studied in this paper, thereby simplifying the inertial terms in the dynamic expression.

[0060] According to one embodiment of the present invention, such as Figure 3 As shown, using the robot dynamics equations, the generalized momentum p is defined as: Where p represents generalized momentum, M(q) represents the inertia tensor, and q represents the joint angle. Represents joint angular velocity.

[0061] The antisymmetric property of the dynamics, that is, it can be obtained through the dynamic analysis of the Lagrangian form. Differentiating both sides of the above formula, we can obtain the dynamic equation that does not include angular acceleration:

[0062] The estimated value of the generalized momentum derivative for:

[0063] Define the residual r(t). The residual r(t) reflects the deviation between the model and the actual situation. This deviation is usually caused by the robot's contact with the outside world. Therefore, this residual can be regarded as the external torque τ that needs to be observed. e That is, the residual of the joint torque is generated by external forces. In a specific embodiment of the present invention, a generalized momentum observer is constructed according to the following formula:

[0064]

[0065] Where r(t) represents the output of the generalized momentum observer, and K represents the observer gain coefficient. for The transpose of the matrix, G(q) represents centrifugal force and Coriolis torque, G(q) represents gravity vector, and p represents generalized momentum.

[0066] In this invention, a modified recursive Newton-Euler algorithm is used, namely the recursive expression described above. The inertial terms in the calculation of the dynamic expression are as follows:

[0067] according to Calculate the gravity vector G(q);

[0068] according to Calculate the centrifugal force and Coriolis moment terms.

[0069] From the above derivation process and momentum observer, it can be seen that the deviation of and will lead to the deviation between and . In theoretical research, the equation After further Laplace transformation, the transfer functions for the residuals and external torque are obtained as: r(s) = Kτ e (s)[s+K) -1 s is the Laplace operator, and K is the gain coefficient. From the above equation, it can be seen that when the gain coefficient K approaches infinity, its value will be infinitely close to the actual external torque. Therefore, the external torque can be calculated based on the output of the momentum observer.

[0070] S5 applies an external force during robot operation, obtains the driving torque based on the robot's current information, inputs the driving torque into the generalized momentum observer, and estimates the external torque in the physical interaction between the robot and the outside world based on the output of the generalized momentum observer.

[0071] Specifically, by incorporating a generalized momentum observer into the robot's control system, and applying external forces during robot operation, the robot's driving torque τ can be obtained based on the current information generated during operation. d The driving torque τ of the robot will be obtained. d By inputting the generalized momentum observer and using its output, the external torque τ in the physical interaction between the robot and the external environment can be calculated using the residual and the transfer function of the external torque. e .

[0072] S6, acquire the impedance control model, generate a reference position signal based on the external torque and impedance control model, and perform compliant control of the robot based on the reference position signal.

[0073] According to an embodiment of the present invention, the impedance control model is obtained according to the following formula:

[0074]

[0075] Among them, M d D represents the mass matrix of the simulation. d Represents the damping matrix, K d Represents the stiffness matrix, q d q r τ represents the robot's reference position and actual position, respectively. e Indicates external torque. Represents the joint angles during actual robot operation. This represents the joint angular velocity during actual robot operation.

[0076] Specifically, such as Figure 4 As shown, the output of the generalized momentum observer can be substituted into the external torque τ in the external physical interaction of the impedance control model. e The reference position q of the generated robot d This signal is transmitted to the six-degree-of-freedom industrial robot through the robot controller, enabling it to perform the corresponding motion.

[0077] Therefore, by using dynamic models and observers to estimate external torque forces, it is possible to effectively support robots in achieving kinematic teaching and imitation operations when performing tasks. This innovative method can still accurately perceive external forces and perform complex tasks even without sensors, demonstrating stronger robustness and adaptability. This significantly improves the robot's operational performance and application versatility in variable and complex environments, laying a solid foundation for the further development of robotics technology.

[0078] In summary, the compliant control method for robots according to embodiments of the present invention, by constructing an accurate robot dynamics model and combining it with a generalized momentum observer, infers the external forces generated during the robot's interaction with the outside world, without relying on physical force sensors. This model-based force estimation technique not only significantly reduces hardware costs but also simplifies the system design and maintenance process, improving system reliability and maintainability. The present invention employs an improved Newton-Euler method when obtaining the dynamic equations, splitting the secondary term of the velocity vector into two distinct inputs, thereby enabling its application to robots with more degrees of freedom.

[0079] Corresponding to the aforementioned compliant robot control method, this invention also proposes a compliant robot control system. Since the system embodiments of this invention correspond to the method embodiments described above, details not disclosed in the system embodiments can be found in the method embodiments described above, and will not be repeated here.

[0080] Figure 5 This is a block diagram of a robot compliance control system according to an embodiment of the present invention, as shown below. Figure 5 As shown, the control system includes: a first construction module 10, an acquisition module 20, a second construction module 30, a third construction module 40, an estimation module 50, and a control module 60.

[0081] The first construction module 10 is used to construct the robot's link coordinate system using the DH parameter method; the acquisition module 20 is used to obtain the recursive expressions for the angular velocity and acceleration of each link of the robot, as well as the linear acceleration of the origin and center of mass of the coordinate system, by splitting the secondary term of the velocity vector into two different inputs according to the Newton-Euler method; the second construction module 30 is used to establish the robot's dynamic equations based on the robot's driving torque and the external torque in the robot's physical interaction with the outside world; and the third construction module 40 is used to obtain the robot's centrifugal force and Coriolis torque terms according to the recursive expressions. The gravity vector G(q) is based on the generalized momentum p, centrifugal force, and Coriolis torque term. A generalized momentum observer is constructed using the gravity vector G(q); the estimation module 50 is used to apply external force during robot operation, obtain the robot's driving torque based on the robot's current information, input the driving torque into the generalized momentum observer, and estimate the external torque in the robot's physical interaction with the outside world based on the output of the generalized momentum observer; the control module 60 is used to obtain the impedance control model, generate a reference position signal based on the external torque and the impedance control model, and perform compliant control of the robot based on the reference position signal.

[0082] In summary, the compliant control system for robots according to embodiments of the present invention, by constructing an accurate robot dynamics model and combining it with a generalized momentum observer, infers the external forces generated during the robot's interaction with the outside world, without relying on physical force sensors. This model-based force estimation technique not only significantly reduces hardware costs but also simplifies the system design and maintenance process, improving system reliability and maintainability. The present invention employs an improved Newton-Euler method when obtaining the dynamic equations, splitting the second term of the velocity vector into two distinct inputs, thereby enabling its application to robots with more degrees of freedom.

[0083] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. "A plurality of" means two or more, unless otherwise explicitly specified.

[0084] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0085] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0086] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of the invention pertain.

[0087] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0088] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any of the following techniques known in the art, or a combination thereof: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0089] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0090] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0091] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A compliant control method for a robot, characterized in that, Includes the following steps: The link coordinate system of the robot is constructed using the DH parameter method; Based on the Newton-Euler method, the secondary term of the velocity vector is split into two different inputs to obtain the recursive expressions for the angular velocity and acceleration of each link of the robot, as well as the linear acceleration of the origin and center of mass of the coordinate system. The robot's dynamic equations are established based on the robot's driving torque and the external torque in the robot's physical interaction with the outside world. Obtain the centrifugal force and Coriolis torque terms of the robot based on the recursive expression. Gravity vector Based on generalized momentum Centrifugal force and Coriolis torque terms and gravity vector Construct a generalized momentum observer; An external force is applied during the operation of the robot. The driving torque of the robot is obtained based on the robot's current information. The driving torque is input into a generalized momentum observer. The external torque in the physical interaction between the robot and the outside world is estimated based on the output of the generalized momentum observer. Obtain the impedance control model, generate a reference position signal based on the external torque and the impedance control model, and perform compliant control of the robot based on the reference position signal; The robot's dynamic equations are obtained using the following formula: ； in, Represents joint angle, Represents joint angular velocity. Represents joint angular acceleration. Represents the inertia tensor. Representing the centrifugal force and Coriolis torque terms, Represents the gravity vector. Indicates driving torque; This represents the external torque in the physical interaction between the robot and the outside world; The impedance control model is obtained using the following formula: ； in, The mass matrix represents the simulation. Represents the damping matrix. Represents the stiffness matrix. These represent the robot's reference position and actual position, respectively. Indicates external torque. Represents the joint angles during actual robot operation. This represents the joint angular velocity during actual robot operation.

2. The compliant control method for a robot according to claim 1, characterized in that, The recursive expression can be obtained using the following formula: ； in, Represents the angular velocity of joint i. Represents the auxiliary angular acceleration of joint i. Link angular velocity, Link Auxiliary angular velocity, This represents the linear acceleration at the origin of the coordinate system of link i; This represents the linear acceleration at the center of mass of link i; This represents the vector from the (i-1)th joint to the ith joint. Let represent the vector from the i-th joint to the centroid of the link. This represents the angular velocity of link i. This represents the angular acceleration of link i. Indicates the link Auxiliary angular velocity, This represents the torque at joint i. This represents the force at joint i. This represents the force at joint i+1. This represents the inertia matrix of link i. The vector along the i-axis is denoted as . , This represents the torque along the z-axis required for the robot to move at the given speed and acceleration.

3. The compliant control method for a robot according to claim 1, characterized in that, Generalized momentum can be obtained using the following formula: ； in, Represents generalized momentum. Represents the inertia tensor. Represents joint angle, Represents joint angular velocity.

4. The compliant control method for a robot according to claim 3, characterized in that, Construct a generalized momentum observer based on the following formula: ； in, This represents the output of the generalized momentum observer. Represents the observer gain coefficient. for The transpose of the matrix, Represents the centrifugal force and Coriolis torque terms. Represents the gravity vector. It represents generalized momentum.

5. The compliant control method for a robot according to any one of claims 1-4, characterized in that, The robot is a six-degree-of-freedom robot.

6. A compliant control system for a robot, employing the compliant control method for a robot according to claim 1, characterized in that, include: The first construction module is used to construct the robot's link coordinate system using the DH parameter method; The acquisition module is used to split the secondary term of the velocity vector into two different inputs according to the Newton-Euler method, and obtain the recursive expressions for the angular velocity and acceleration of each link of the robot, as well as the linear acceleration of the origin and center of mass of the coordinate system. The second construction module is used to establish the dynamic equations of the robot based on the driving torque of the robot and the external torque in the physical interaction between the robot and the outside world. The third construction module is used to obtain the centrifugal force and Coriolis torque terms of the robot according to the recursive expression. Gravity vector Based on generalized momentum Centrifugal force and Coriolis torque terms and gravity vector Construct a generalized momentum observer; An estimation module is used to apply external force during the operation of the robot, obtain the driving torque of the robot based on the robot's current information, input the driving torque into a generalized momentum observer, and estimate the external torque in the physical interaction between the robot and the outside world based on the output of the generalized momentum observer. The control module is used to acquire an impedance control model, generate a reference position signal based on the external torque and the impedance control model, and perform compliant control of the robot based on the reference position signal.

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