Active compliant interaction control method and system for collaborative robot without force sensor

Abstract

The invention relates to the field of collaborative robot control, in particular to an active compliant interaction control method and system for a collaborative robot without a force sensor. According to the method, the man-machine interaction force is estimated in real time through the interaction force estimation system, additional sensors are not needed, and the hardware cost is reduced; solving an optimal impedance model through strategy iteration by using an impedance model optimization system to adapt to an uncertain interaction environment; and the reference trajectory of the robot is corrected through the active compliant interaction control system, so that accurate and reliable compliant control is realized. According to the main scheme, the method comprises the steps of interaction force estimation based on generalized momentum, target impedance equation modeling, performance index function optimization and barrier Lyapunov function control input design. The method solves the problems that a traditional collaborative robot is high in hardware cost, poor in interaction adaptability, unstable in control and the like, and is suitable for man-machine interaction scenes in the fields of intelligent manufacturing, medical health and the like.

Description

Technical Field

[0001] The present invention relates to the field of collaborative robot control, and in particular to a method and system for active compliant interactive control of a collaborative robot without force sensors. Background Art

[0002] With the development of intelligent manufacturing, medical health and other fields and the growing demand for human-computer interaction, collaborative robots with good flexibility, light weight and high safety have received widespread attention, and interactive control has also become a hot topic of research. In order to ensure the smooth completion of interactive tasks, robots need to obtain interactive forces with people in real time. The traditional approach is to install a six-dimensional end force sensor on the robot wrist, but this not only increases the weight and size of the hardware system, but also increases the system cost. Moreover, when the robot contacts people outside the end effector, the sensor cannot sense it. Collaborative robots are generally composed of rigid links and joints containing motors and reducers. The application of harmonic reducers in joint structures increases the torque of the joints and reduces the stiffness of the joints, which improves safety to a certain extent. However, due to the low stiffness, it severely limits the robot's ability and stability to operate with high precision. In addition, when the robot interacts physically with the environment, the human is an unknown time-varying dynamic environment for the robot, and traditional interactive control methods based on known interactive environment information are difficult to apply. Summary of the invention

[0003] The purpose of the present invention is to solve the problem of how a collaborative robot can achieve accurate and reliable active and compliant interactive control by estimating the interactive force in real time, optimizing the impedance model and adjusting the control input in the absence of an external force sensor, thereby reducing hardware costs and improving the adaptability and stability of human-computer interaction.

[0004] In order to achieve the above purpose, the present invention adopts the following technical solutions: The present invention provides a method for active compliant interaction control of a collaborative robot without force sensors, comprising the following steps: Step 1: Based on the robot state, the interaction force in the interaction process of physical contact between humans and collaborative robots is estimated through the interaction force estimation system to obtain the interaction force information; Step 2: The robot state and the interaction force information obtained in step 1 are passed to the impedance model optimization system, and the optimal impedance model is returned through the strategy iteration solution module to adjust the dynamic characteristics of the robot to adapt to the uncertain interaction environment; Step 3: Substitute the robot's initial reference trajectory and the interaction force obtained in step 1 into the optimal impedance model obtained in step 2 to obtain the actual reference trajectory, and solve the robot's control input through the active and compliant interactive control system so that the collaborative robot can track the actual reference trajectory to achieve accurate and reliable active and compliant interactive control.

[0005] The reference trajectories include: Task space reference trajectory: the expected motion path of its end effector (such as the end of a robotic arm) in three-dimensional space; Joint space reference trajectory: defines how each joint moves over time to achieve the desired path in task space.

[0006] In the above scheme, step 1 comprises: Step 1.1: Establish the interactive force observation system model through the dynamic equation of the flexible joint collaborative robot and the generalized momentum of the robot. The dynamic equation of the flexible joint collaborative robot is as follows: represents the inertia matrix of the flexible joint manipulator, represents the Coriolis force matrix of the flexible joint manipulator, is the gravity acting on the robot, is the human-machine interaction torque on the robot, To control the torque, represents the inertia matrix of the motor, represents the stiffness matrix of the joint, represents the joint angle vector, represents the joint angular velocity vector, represents the joint angular acceleration vector, represents the motor angle vector, represents the motor angular acceleration vector, where “·” represents the first-order derivative and “··” represents the second-order derivative; The generalized momentum of the robot is: Therefore, the interactive force observation system model of the flexible joint collaborative robot can be written as: in express The transpose of Step 1.2: Based on the interaction force observation system model, an improved interaction force robust estimation method is designed, the robot state is input, and the interaction torque is estimated in real time; The interaction force estimation error is defined as: ,in is the estimated value of the interaction moment, which is calculated by the following formula: in represents the output of the generalized momentum observer, Indicates at time The robot system momentum at time , and are all positive definite diagonal matrices, and , represents the robust term.

[0007] In the above scheme, step 2 comprises: Step 2.1: Establish the target impedance equation to describe the state change relationship between the robot's position, velocity change, and interaction force with the human. Specifically, establish the following target impedance equation to model human-machine interaction: in are the unknown mass, damping and stiffness matrices respectively, where represents the change in the robot's position, Indicates the speed change, represents the change in acceleration, represents the interaction force; Step 2.2: Based on the target impedance equation, combined with the robot's position change and the interaction force with the human, determine the performance index function to form a quadratic programming problem. The performance index function The settings are as follows: The state quantity The following state equation is satisfied: in express The inverse matrix of express The identity matrix of in are all symmetric weight matrices. and is a known matrix, is an auxiliary variable; Step 2.3: Solve the quadratic programming problem through the iterative update of the calculation factors and the iterative process of the impedance parameters of the strategy iteration solution module to obtain the optimal impedance model: Step 2.3.1: State equation based on step 2.2 , design state feedback control input Make the performance indicator function of step 2.2 Minimize: in represents the optimal gain.

[0008] In the above scheme, step 3 comprises: Step 3.1: Substitute the initial reference trajectory of the robot and the interaction force information obtained in step 1 into the optimal impedance model obtained in step 2, solve the trajectory correction value of the robot, correct the initial reference trajectory of the robot, and obtain the actual reference trajectory; The trajectory correction value is a subvector of the optimization variables: So the initial reference trajectory can be Make corrections to obtain the actual reference trajectory : ; Step 3.2: Convert the actual reference trajectory of the robot into a numerical solution in the joint space through the joint space motion solution module to obtain the joint space reference trajectory ; right The joint space reference trajectory can be obtained by integration ,in represents the inverse matrix of the Jacobian matrix; Step 3.3: Based on the barrier Lyapunov function, the control input of the flexible joint collaborative robot is derived from the joint space reference trajectory using the backstepping method, so that the robot can track the actual reference trajectory; Step 3.3.1: Define the error on the connecting rod side as follows , Sliding mode signal and auxiliary semaphores : represents the desired joint angle vector, And the following are all positive definite matrices with diagonal constant coefficients; Step 3.3.2: Construct Lyapunov candidate function for: where 𝜀>0 is a constant, is the inertia matrix of the flexible joint manipulator; Step 3.3.3: Derivative the Lyapunov function and design the virtual control input. Take the derivative and substitute the sliding mode signal into the equation to obtain: Design a virtual control input , that is, the motor angle Expected value: is a positive definite diagonal constant coefficient matrix used to adjust the gain of the control input; Step 3.3.4: Define the error of the motor rotation angle and sliding mode semaphore for: Step 3.3.5: Construct Lyapunov function : Step 3.3.6: Derivative the Lyapunov function and design the control input: right Taking the derivative and substituting the semaphore and virtual control input, we get: The design control input is: is a positive definite matrix with diagonal constant coefficients, and Satisfies that its eigenvalue is greater than the joint stiffness matrix The maximum eigenvalue of ; Step 3.3.7: Verify system stability Through the above control inputs, ensure that: Thereby ensuring the stability of the system.

[0009] The present invention also provides a force-free sensor-free collaborative robot active compliant interactive control system, including an interactive force estimation system, an impedance model optimization system, and an active compliant interactive control system; Interaction force estimation system: estimates the interaction force during the physical contact between humans and collaborative robots based on the robot state to obtain interaction force information; Impedance model optimization system: returns the optimal impedance model through the strategy iteration solution module according to the robot state and interaction force information; Active compliant interactive control system: Substitute the robot's initial reference trajectory and interactive force into the optimal impedance model to obtain the actual reference trajectory, solve the robot's control input, and enable the collaborative robot to track the actual reference trajectory to achieve accurate and reliable active compliant interactive control.

[0010] Further in the above system, the interaction force estimation system includes: The interactive force observation system modeling module is used to establish an interactive force observation system model based on generalized momentum, in which the dynamic equation of the flexible joint collaborative robot is as follows: represents the inertia matrix of the flexible joint manipulator, represents the Coriolis force matrix of the flexible joint manipulator, is the gravity acting on the robot, is the human-machine interaction torque on the robot, To control the torque, represents the inertia matrix of the motor, represents the stiffness matrix of the joint, represents the joint angle vector, represents the joint angular velocity vector, represents the joint angular acceleration vector, represents the motor angle vector, represents the motor angular acceleration vector; The generalized momentum of the robot is: Therefore, the interactive force observation system model of the flexible joint collaborative robot can be written as: in express The transpose of An interaction force observation module, used for estimating the interaction torque in real time based on the interaction force observation system model and the improved interaction force robust estimation method; The interaction force estimation error is defined as: ,in is the estimated value of the interaction moment, which is calculated by the following formula: in represents the output of the generalized momentum observer, Indicates at time The robot system momentum at time , and are all positive definite diagonal matrices, and , represents the robust term.

[0011] Further in the above system, the impedance model optimization system includes: The target impedance equation establishment module is used to establish the target impedance equation that describes the relationship between the robot's position, velocity, and interaction force. Specifically, the following target impedance equation is established to model human-machine interaction: in are the unknown mass, damping and stiffness matrices respectively, where represents the change in the robot's position, Indicates the speed change, represents the change in acceleration, represents the interaction force; The performance indicator function determination module is used to determine the performance indicator function based on the target impedance equation, combined with the position change and interaction force of the robot, to form a quadratic programming problem. The performance indicator function The settings are as follows: The state quantity The following state equation is satisfied: in express The inverse matrix of express The identity matrix of in are all symmetric weight matrices. and is a known matrix, is an auxiliary variable; The strategy iteration solution module is used to solve the quadratic programming problem and obtain the optimal impedance model by iteratively updating the calculation factors and iteratively updating the impedance parameters. Specifically: Based on the equation of state , design state feedback control input Make the performance indicator function of step 2.2 Minimize: in represents the optimal gain.

[0012] Further in the above system, the active compliance interactive control system includes: Reference trajectory acquisition module: used to acquire the actual reference trajectory of the robot based on the optimal impedance model and the initial reference trajectory of the robot, specifically: Substitute the robot's initial reference trajectory and interaction force information into the optimal impedance model, solve the robot's trajectory correction value, correct the robot's initial reference trajectory, and obtain the actual reference trajectory; The trajectory correction value is a subvector of the optimization variables: So the initial reference trajectory can be Make corrections to obtain the actual reference trajectory : ; Joint space motion solution module: used to convert the actual reference trajectory into a numerical solution in joint space to obtain the joint space reference trajectory : right The joint space reference trajectory can be obtained by integration ,in represents the inverse matrix of the Jacobian matrix; The control rate update module, based on the barrier Lyapunov function, uses the backstepping recursion method to derive the control input of the flexible joint collaborative robot from the joint space reference trajectory, so that the robot can track the actual reference trajectory. Further in the above system, the active compliance interactive control system includes: the control rate update module is specifically implemented by the following steps: Step A: Define the error on the connecting rod side as follows , Sliding mode signal and auxiliary semaphores : represents the desired joint angle vector, And the following are all positive definite matrices with diagonal constant coefficients; Step B: Construct Lyapunov candidate function for: where 𝜀>0 is a constant, is the inertia matrix of the flexible joint manipulator; Step C: Derivate the Lyapunov function and design the virtual control input. Take the derivative and substitute the sliding mode signal into the equation to obtain: Design a virtual control input , that is, the motor angle Expected value: is a positive definite diagonal constant coefficient matrix used to adjust the gain of the control input; Step D: Define the error in the motor rotation angle and sliding mode semaphore for: Step E: Construct Lyapunov function : Step F: Derivative the Lyapunov function and design the control input: right Taking the derivative and substituting the semaphore and virtual control input, we get: The design control input is: , is a positive definite matrix with diagonal constant coefficients, and Satisfies that its eigenvalue is greater than the joint stiffness matrix The maximum eigenvalue of ; Step G: Verify system stability Through the above control inputs, ensure that: Thereby ensuring the stability of the system.

[0013] Because the present invention adopts the above technical means, it has the following beneficial effects: 1. The interactive force estimation system can observe the interactive force in real time, and can accurately obtain the interactive force information not limited to the end of the robot arm in real time when the interactive force varies with time, so as to realize safe and convenient human-computer interaction without external sensors, solve the problems of difficult integration and high cost in the traditional sensor-dependent method, and facilitate its large-scale application; 2. Through the impedance model optimization system, it is possible to preset the desired impedance model without the need for expert experience or prior knowledge, thus overcoming the difficulty in obtaining the real impedance parameters. At the same time, it can solve the problem that the interaction process is dynamic and changing, and it is difficult to maintain the optimal impedance control throughout the process; 3. Through the active compliant interactive control system, the control problems caused by the complex model of the flexible joint collaborative robot system and the uncertainty of dynamic parameters can be solved, the state of the robot can be kept within a feasible range, and the adaptability and stability of human-computer interaction can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a schematic diagram of the overall control system of the present invention; Figure 2 is a schematic diagram of an interaction force estimation system of the present invention; Figure 3 is a schematic diagram of an impedance model optimization system of the present invention; Figure 4 It is a schematic diagram of the active compliant interactive control system of the present invention; Figure 5 This is the workflow of the system of the present invention. DETAILED DESCRIPTION

[0015] The following is a detailed description of the embodiments of the present invention. Although the present invention will be described and illustrated in conjunction with some specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, modifications or equivalent substitutions made to the present invention should all be included in the scope of the claims of the present invention.

[0016] In addition, in order to better illustrate the present invention, numerous specific details are given in the following specific embodiments. It will be understood by those skilled in the art that the present invention can also be implemented without these specific details.

[0017] The present invention is aimed at a flexible joint collaborative robot with multiple degrees of freedom. Based on an improved robust estimation method of interactive force, the force in the interactive process is estimated, and the interactive force can be obtained in real time without adding additional sensors. The optimal impedance learning method based on an iterative strategy is used to learn the impedance model parameters in the interactive process, and the reference trajectory of the robot is corrected based on this impedance model. Finally, a robust control method suitable for the flexible joint collaborative robot is used to track the reference trajectory, and accurate and reliable active compliant interactive control is achieved. The present invention solves a series of problems of traditional collaborative robots, such as high hardware cost, poor interactive adaptability, and unstable control.

[0018] Example 1 The present invention provides a method for active compliant interaction control of a collaborative robot without force sensors, comprising the following steps: Step 1: Based on the robot state, the interaction force in the interaction process of physical contact between humans and collaborative robots is estimated through the interaction force estimation system, so that the flexible joint collaborative robot can obtain interaction information with humans without relying on additional force sensors when the interaction force varies in time, thereby reducing hardware costs; Step 2: The robot state and the interaction force information obtained in step 1 are passed to the impedance model optimization system, and the optimal impedance model is returned through the strategy iteration solution module, so as to adjust the dynamic characteristics of the robot to adapt to the uncertain interaction environment; Step 3: Substitute the initial reference trajectory of the robot and the interaction force obtained in step 1 into the optimal impedance model obtained in step 2 to obtain the actual reference trajectory of the robot. Through the active compliant interactive control system, the control input of the robot is solved so that it can track the reference trajectory, adjust its response according to human actions, and enhance the smoothness and compliance of the interaction.

[0019] As an implementation method, the sub-steps of step 1 include: Step 1.1, establish the interactive force observation system model of the collaborative robot through the dynamic equation of the flexible joint collaborative robot and the generalized momentum of the robot; The dynamic equation of the flexible joint collaborative robot is as follows: in = ∈ and = ∈ are the joint angle vector and the motor angle vector respectively, ∈ To control the torque. ∈ and ∈ is the inertia matrix and Coriolis force matrix of the flexible joint robot. ∈ is the gravity acting on the robot, ∈ is the human-machine interaction torque on the robot, and , For human-computer interaction, is the Jacobian matrix of the robot. ∈ and ∈ represents the inertia matrix of the motor and the stiffness matrix of the joint, represents the joint angular velocity vector, represents the joint angular acceleration vector, Represents the motor angular acceleration vector.

[0020] The generalized momentum of the robot is: Therefore, the interactive force observation system model of the flexible joint collaborative robot can be written as: in express The transpose of .

[0021] Step 1.2: Based on the interaction force observation system model, an improved interaction force robust estimation method is designed, the robot state is input, and the interaction force is estimated in real time.

[0022] The interaction force estimation error is defined as: ,in is the estimated value of the interaction torque, then the estimated value of the interaction torque can be calculated by the following formula: in represents the output of the generalized momentum observer, Indicates at time The robot system momentum at time , and are all positive definite diagonal matrices, and , represents the symbolic function, that is: As an implementation method, the sub-steps of step 1 include: Step 2.1, establish the target impedance equation to describe the state change relationship between the robot's position, velocity change, and interaction force with the human; The following target impedance equation is established to model human-computer interaction: in are the unknown mass, damping and stiffness matrices respectively, where represents the change in the robot's position, Indicates the speed change, represents the change in acceleration, Represents interaction force.

[0023] Step 2.2, based on the target impedance equation, combined with the robot's position change and the interaction force with the human, determine the performance index function to form a quadratic programming problem; The performance indicator function is set as follows: in They are all symmetric weight matrices. Set auxiliary variables satisfy, Express Seeking guidance, and is a known matrix, and the state quantity is defined as , then the target impedance equation in step 2.1 can be expressed by the state equation: in , .

[0024] in express The inverse matrix of express The identity matrix of The performance indicator function can also be re-expressed as: in Step 2.3: Solve the quadratic programming problem through the iterative update of the calculation factors and the iterative process of the impedance parameters of the strategy iteration solution module to obtain the optimal impedance model.

[0025] Based on the state equation of step 2.2 , design state feedback control input Make the performance indicator function of step 2.2 Minimize and find the optimal gain .

[0026] Find the optimal gain The following steps are involved: 2.3.a. Select the state equation that makes step 2.2 Stable feedback gain matrix , let the control input be , To meet the noise of continuous excitation, the calculation factor is obtained as follows , and Until satisfied : in Representation Matrix The rank of the matrix is ​​the number of linearly independent rows or columns. represents the dimension of the state variable, represents the dimension of the control input, Indicates the system status, express The square of express In time The value of 2.3.b. By Solution and ,in in The meaning of this is the matrix No. elements, express The identity matrix, vec is an operator that "stretches" a matrix into a vector, ; 2.3.c. Order And repeat 2.3.b until , Finally, the optimal gain is obtained .

[0027] As an implementation method, the sub-steps of step 3 include: Step 3.1, substitute the initial reference trajectory of the robot and the interaction force information obtained in step 1 into the optimal impedance model obtained in step 2.3, solve the trajectory correction value of the robot, correct the initial reference trajectory of the robot, and obtain the actual reference trajectory; The trajectory correction value is a subvector of the optimization variables: So the initial reference trajectory can be Make corrections to obtain the actual reference trajectory : Step 3.2: Use the joint space motion solution module to convert the actual reference trajectory of the robot into a numerical solution in the joint space to obtain the joint space reference trajectory. ; right The joint space reference trajectory can be obtained by integration ,in Represents the inverse of the Jacobian matrix.

[0028] Step 3.3: Based on the barrier Lyapunov function, the backstepping method is used to derive the control input of the flexible joint collaborative robot from the reference trajectory in the joint space so that it can track the reference trajectory.

[0029] First, define the error, sliding mode signal and auxiliary signal on the connecting rod side as follows: Here And the following are all positive definite diagonal constant coefficient matrices. Construct Lyapunov candidate function for: Where 𝜀>0 is a constant. Taking the derivative and substituting the semaphore into it, we get: Therefore, a virtual control input is designed in the backstepping process, namely Expected value for: The error and sliding mode signal of the motor rotation angle are defined as: Constructing Lyapunov functions : Likewise, yes Taking the derivative and substituting the semaphore and virtual control input, we get: The control input is thus designed as: in , is a positive definite matrix with diagonal constant coefficients, and Satisfies that its eigenvalue is greater than the joint stiffness matrix Substituting Can get Therefore, the human-computer interaction system is stable under the control rate.

[0030] See also Figure 1-4As shown, the system provided by the present invention includes an interactive force estimation system, an impedance model optimization system and an active and compliant interactive control system. The interactive force estimation system estimates the force of human-machine physical interaction between humans and collaborative robots, and the impedance model optimization system is used to learn the impedance model parameters during the interaction process, and the reference trajectory of the robot is corrected based on this impedance model. Finally, the control input of the robot is solved by the active and compliant interactive control system, so as to realize accurate and reliable human-machine active and compliant interactive control.

[0031] The interaction force estimation system first establishes an interaction force observation system model, and uses an improved interaction force estimation method based on generalized momentum observer to estimate the interaction force. Compared with the traditional estimation method, the improved interaction force estimation method based on generalized momentum observer adds a robust control term, solves the shortcoming that it cannot estimate time-varying interaction force, and improves the accuracy and robustness of interaction force estimation.

[0032] The impedance model optimization system first establishes the target impedance equation, then determines the performance indicator function, and finally returns the optimal impedance control gain through the strategy iteration solution module.

[0033] The active compliant interactive control system first obtains the reference trajectory through the impedance model, then uses the joint space motion solver module to obtain the numerical solution of the joint space from the task space trajectory, and finally derives the control input of the flexible joint collaborative robot from the expected output through the control rate update module based on the barrier Lyapunov function.

[0034] See also Figure 5 As shown, the system workflow provided by the present invention is as follows: at the beginning of human-machine interaction, the current position and speed of the robot are first obtained, and the interaction force is estimated by the interaction force estimation system. Then, the robot's state and interaction force information are passed to the target impedance equation and the performance index function, and the optimal impedance model is obtained through strategy iteration. Subsequently, the initial robot trajectory is corrected to obtain the robot's task space reference trajectory, and the corresponding joint space reference trajectory is solved. Finally, the control input of the robot is generated by the active compliant interaction control system so that it can track the reference trajectory. This process will be repeated until the robot completes the specified task. The above contents are merely examples and explanations of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the invention or exceed the scope defined by the claims, they shall all fall within the protection scope of the present invention.

Claims

1. A method for active compliant interaction control of a collaborative robot without force sensors, characterized in that: The following steps are involved: Step 1: Based on the robot state, the interaction force in the interaction process of physical contact between humans and collaborative robots is estimated through the interaction force estimation system to obtain the interaction force information; Step 2: The robot state and the interaction force information obtained in step 1 are passed to the impedance model optimization system, and the optimal impedance model is returned through the strategy iteration solution module to adjust the dynamic characteristics of the robot to adapt to the uncertain interaction environment; Step 3: Substitute the initial reference trajectory of the robot and the interaction force obtained in step 1 into the optimal impedance model obtained in step 2 to obtain the actual reference trajectory, and solve the control input of the robot through the active compliant interactive control system so that the collaborative robot can track the actual reference trajectory to achieve active compliant interactive control; The reference trajectories include: Task space reference trajectory: the expected motion path of the robot end effector in three-dimensional space; Joint space reference trajectory: defines how each joint moves over time to achieve the desired path in task space.

2. The method according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Establish the interactive force observation system model through the dynamic equation of the flexible joint collaborative robot and the generalized momentum of the robot. The dynamic equation of the flexible joint collaborative robot is as follows: represents the inertia matrix of the flexible joint manipulator, represents the Coriolis force matrix of the flexible joint manipulator, is the gravity acting on the robot, is the human-machine interaction torque on the robot, To control the torque, represents the inertia matrix of the motor, represents the stiffness matrix of the joint, represents the joint angle vector, represents the joint angular velocity vector, represents the joint angular acceleration vector, represents the motor angle vector, represents the motor angular acceleration vector, where "·" represents the first-order derivative and "··" represents the second-order derivative; The generalized momentum of the robot is: Therefore, the interactive force observation system model of the flexible joint collaborative robot is written as: in express The transpose of Step 1.2: Based on the interaction force observation system model, an improved interaction force robust estimation method is designed. The robot state is input and the interaction torque is estimated in real time. The details are as follows: The interaction force estimation error is defined as: ,in is the estimated value of the interaction moment, which is calculated by the following formula: in represents the output of the generalized momentum observer, Indicates at time The robot system momentum at time , and are all positive definite diagonal matrices, and , represents the robust term.

3. The method according to claim 2, characterized in that The step 2 comprises: Step 2.1: Establish the target impedance equation to describe the state change relationship between the robot's position, velocity change, and interaction force with the human. Specifically, establish the following target impedance equation to model human-machine interaction: in are the unknown mass, damping and stiffness matrices respectively, where represents the change in the robot's position, Indicates the speed change, represents the change in acceleration, represents the interaction force; Step 2.2: Based on the target impedance equation, combined with the robot's position change and the interaction force with the human, determine the performance index function to form a quadratic programming problem. The performance index function The settings are as follows: The state quantity The following state equation is satisfied: in express The inverse matrix of express The identity matrix of in are all symmetric weight matrices. and is a known matrix, is an auxiliary variable; Step 2.3: Solve the quadratic programming problem through the iterative update of the calculation factors and the iterative process of the impedance parameters of the strategy iteration solution module to obtain the optimal impedance model: Step 2.3.1: State equation based on step 2.2 , design state feedback control input Make the performance indicator function of step 2.2 Minimize: in represents the optimal gain.

4. The method according to claim 3, characterized in that The step 3 comprises: Step 3.1: Substitute the initial reference trajectory of the robot and the interaction force information obtained in step 1 into the optimal impedance model obtained in step 2, solve the trajectory correction value of the robot, correct the initial reference trajectory of the robot, and obtain the actual reference trajectory; The trajectory correction value is a subvector of the optimization variables: So the initial reference trajectory Make corrections to obtain the actual reference trajectory : ； Step 3.2: Convert the actual reference trajectory of the robot into a numerical solution in the joint space through the joint space motion solution module to obtain the joint space reference trajectory : right The integration gives the joint space reference trajectory ,in represents the inverse matrix of the Jacobian matrix; Step 3.3: Based on the barrier Lyapunov function, the backstepping method is used to derive the control input of the flexible joint collaborative robot from the joint space reference trajectory, so that the robot can track the actual reference trajectory.

5. The method according to claim 4, characterized in that The step 3.3 comprises: Step 3.3.1: Define the error on the connecting rod side as follows , Sliding mode signal and auxiliary semaphores : represents the desired joint angle vector, And the following are all positive definite matrices with diagonal constant coefficients; Step 3.3.2: Construct Lyapunov candidate function for: where 𝜀 > 0 is a constant, is the inertia matrix of the flexible joint manipulator; Step 3.3.3: Derivative the Lyapunov function and design the virtual control input. Take the derivative and substitute the sliding mode signal into the equation to obtain: Design a virtual control input , that is, the motor angle Expected value: is a positive definite diagonal constant coefficient matrix used to adjust the gain of the control input; Step 3.3.4: Define the error of the motor rotation angle and sliding mode semaphore for: Step 3.3.5: Construct Lyapunov function : Step 3.3.6: Derivative the Lyapunov function and design the control input: right Taking the derivative and substituting the semaphore and virtual control input, we get: The design control input is: , is a positive definite matrix with diagonal constant coefficients, and Satisfies that its eigenvalue is greater than the joint stiffness matrix The maximum eigenvalue of ; Step 3.3.7: Verify the stability of the system by using the above control inputs to ensure: Thereby ensuring the stability of the system.

6. A sensorless collaborative robot active compliance interactive control system, characterized in that: Including interactive force estimation system, impedance model optimization system, active compliant interactive control system; Interaction force estimation system: estimates the interaction force during the physical contact between humans and collaborative robots based on the robot state to obtain interaction force information; Impedance model optimization system: returns the optimal impedance model through the strategy iteration solution module according to the robot state and interaction force information; Active compliant interactive control system: Substitute the robot's initial reference trajectory and interactive force into the optimal impedance model to obtain the actual reference trajectory, solve the robot's control input, and enable the collaborative robot to track the actual reference trajectory to achieve accurate and reliable active compliant interactive control; The reference trajectories include: Task space reference trajectory: the expected motion path of its end effector in three-dimensional space; Joint space reference trajectory: defines how each joint moves over time to achieve the desired path in task space.

7. The system according to claim 6, characterized in that The interaction force estimation system includes: The interactive force observation system modeling module is used to establish an interactive force observation system model based on generalized momentum on the basis of the dynamics of the flexible joint collaborative robot. The dynamic equation of the flexible joint collaborative robot is as follows: represents the inertia matrix of the flexible joint manipulator, represents the Coriolis force matrix of the flexible joint manipulator, is the gravity acting on the robot, is the human-machine interaction torque on the robot, To control the torque, represents the inertia matrix of the motor, represents the stiffness matrix of the joint, represents the joint angle vector, represents the joint angular velocity vector, represents the joint angular acceleration vector, represents the motor angle vector, Represents the motor angular acceleration vector, where "·" represents the first-order derivative, and "··" represents the first-order derivative, where express The transpose of; The generalized momentum of the robot is: Therefore, the interactive force observation system model of the flexible joint collaborative robot is written as: in express The transpose of An interaction force observation module, used for estimating the interaction torque in real time based on the interaction force observation system model and the improved interaction force robust estimation method; The interaction force estimation error is defined as: ,in is the estimated value of the interaction moment, which is calculated by the following formula: in represents the output of the generalized momentum observer, Indicates at time The robot system momentum at time , and are all positive definite diagonal matrices, and , represents the robust term.

8. The system according to claim 7, characterized in that The impedance model optimization system comprises: The target impedance equation establishment module is used to establish the target impedance equation that describes the relationship between the robot's position, velocity, and interaction force. Specifically, the following target impedance equation is established to model human-machine interaction: in are the unknown mass, damping and stiffness matrices respectively, where represents the change in the robot's position, Indicates the speed change, represents the change in acceleration, represents the interaction force; The performance indicator function determination module is used to determine the performance indicator function based on the target impedance equation, combined with the position change and interaction force of the robot, to form a quadratic programming problem. The performance indicator function The setup is as follows: The state quantity The following state equation is satisfied: in express The inverse matrix of express The identity matrix of in are all symmetric weight matrices. and is a known matrix, is an auxiliary variable; The strategy iteration solution module is used to solve the quadratic programming problem and obtain the optimal impedance model by iteratively updating the calculation factors and iteratively updating the impedance parameters. Specifically: Based on the equation of state , design state feedback control input Make the performance indicator function of step 2.2 Minimize: in represents the optimal gain.

9. The system according to claim 8, characterized in that The active compliance interactive control system comprises: Reference trajectory acquisition module: used to acquire the actual reference trajectory of the robot based on the optimal impedance model and the initial reference trajectory of the robot, specifically: Substitute the robot's initial reference trajectory and interaction force information into the optimal impedance model, solve the robot's trajectory correction value, correct the robot's initial reference trajectory, and obtain the actual reference trajectory; The trajectory correction value is a subvector of the optimization variables: So the initial reference trajectory Make corrections to obtain the actual reference trajectory : ； Joint space motion solution module: used to convert the actual reference trajectory into a numerical solution in joint space to obtain the joint space reference trajectory : right The integration gives the joint space reference trajectory ,in represents the inverse matrix of the Jacobian matrix; The control rate update module, based on the barrier Lyapunov function, uses the backstepping recursion method to derive the control input of the flexible joint collaborative robot from the joint space reference trajectory, so that the robot can track the actual reference trajectory.

10. The system according to claim 9, characterized in that The active compliance interactive control system includes: the control rate update module is specifically implemented by the following steps: Step A: Define the error on the connecting rod side as follows , Sliding mode signal and auxiliary semaphores : represents the desired joint angle vector, And the following are all positive definite matrices with diagonal constant coefficients; Step B: Construct Lyapunov candidate function for: where 𝜀 > 0 is a constant, is the inertia matrix of the flexible joint manipulator; Step C: Derivate the Lyapunov function and design the virtual control input. Take the derivative and substitute the sliding mode signal into the equation to obtain: Design a virtual control input , that is, the motor angle Expected value: is a positive definite diagonal constant coefficient matrix used to adjust the gain of the control input; Step D: Define the error in the motor rotation angle and sliding mode semaphore for: express The derivative of Step E: Construct Lyapunov function : Step F: Derivative the Lyapunov function and design the control input: right Taking the derivative and substituting the semaphore and virtual control input, we get: The design control input is: , is a positive definite matrix with diagonal constant coefficients, and Satisfies that its eigenvalue is greater than the joint stiffness matrix The maximum eigenvalue of ; Step G: Verify the stability of the system, through the above control inputs, ensure that: Thereby ensuring the stability of the system.

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