An observer-based variable impedance machining method for robots

Abstract

The present invention belongs to the technical field related to robot control, and discloses a robot variable impedance processing method based on an observer. The method includes: S1, using the robot's end position, end velocity and end force in Cartesian space as state variables, and the impedance parameters of the workpiece to be processed and the robot's end disturbance parameters as observation variables, to construct a robot-workpiece state space equation; S2, constructing a rolling optimization observer, establishing constraints, and performing real-time observation of the impedance parameters of the workpiece to be processed and the robot's end disturbance; S3, constructing a robot variable impedance control model; using the robot's end disturbance compensator variable impedance control rate to obtain the robot's feedback torque, and using the feedback torque to control the robot to complete the robot processing task. The present invention solves the problem that the robot cannot be applied to scenarios where the workpiece impedance is constantly changing when processing low-impedance workpieces.

Description

Technical Field

[0001] The present invention belongs to the technical field related to robot control, and more specifically, relates to a robot variable impedance processing method based on an observer. Background Art

[0002] With the development of intelligent manufacturing, intelligent robots are widely used in industrial manufacturing to replace humans in tasks such as processing, handling, and assembly, thereby reducing human workload and improving processing efficiency and flexibility. When robots perform interactive tasks with their environment, due to their inherent low rigidity, contact between the robot and the environment can easily lead to system instability using traditional trajectory control methods. Researching appropriate compliant control strategies can improve the robot's adaptability to its environment. Robot impedance control is a compliant control method that uses a spring-mass-damper model to establish a response equation for the robot's end-point position and contact force. The force between the robot and the environment can be adjusted by changing the end-point position. Traditional robot impedance control strategies use fixed impedance parameters, which provide a certain degree of compliance. However, with the development of the aviation, transportation, and power industries, workpieces are becoming larger and thinner, resulting in low rigidity and incomplete clamping, which can easily cause deformation and vibration during processing. Using a fixed impedance strategy, controller performance deteriorates when the environmental impedance changes, and may even lead to instability. Therefore, it is necessary to study the variable impedance control strategy and adjust the impedance parameters of the robot in real time to respond to changes in the environmental impedance. However, the impedance parameters of the environment are unknown, so it is necessary to design an observer to estimate the stiffness of the environment in real time and design a variable impedance controller based on the observed environmental stiffness to ensure the stability of the system and improve the processing quality of the workpiece.

[0003] Patent CN202010650259.6 proposes an impedance control method, device, impedance controller and robot. This method has a compliant control characteristic and can achieve constant force processing. However, it is a fixed impedance control method. The impedance parameters of the robot are fixed. When the environmental impedance parameters change, the impedance parameters of the robot cannot be automatically adjusted. The stability of the robot and the contact effect with the environment are difficult to guarantee; Patent CN201911418791.9 proposes a robot adaptive variable damping impedance control method. This method compensates for the uncertainty factors in the dynamics and eliminates steady-state errors by changing the damping term in the impedance parameter. However, this method only changes the damping term in the impedance parameter without considering the stiffness term. The robot will produce a relatively large motion deviation and cannot respond quickly to changes in the external environment. The variable damping feedback term is only related to the tracking error and does not consider the stiffness characteristics of the environment; Patent CN201910485753.9 proposes a robot adaptive hybrid impedance / admittance control method based on environmental stiffness estimation. This method allows the controller to switch between impedance control and admittance control, so that impedance control is used when the environmental stiffness is high to improve compliance, and it switches to admittance control when the environmental stiffness is low to improve position accuracy. However, this method does not fundamentally improve the position tracking accuracy of impedance control. The effect of changing the robot operation by switching the controller is limited, and the impedance parameters of the robot itself are not changed to adapt to environmental changes.

[0004] The strategy for robot impedance control is to give the robot a dynamic response similar to that of a spring damper to achieve the desired impedance characteristics. Traditional robot impedance control suffers from model errors, resulting in low robot position tracking accuracy. Furthermore, due to the use of fixed impedance parameters, the robot's impedance performance degrades when the external environmental impedance conditions change, making it unsuitable for scenarios with constantly changing workpiece stiffness. Existing variable impedance control methods only consider the robot's trajectory and force tracking, without considering the environmental stiffness characteristics or the disturbance errors incurred by the robot under the influence of external forces. Therefore, existing robot impedance control strategies struggle to ensure stability and quality when machining variable-impedance workpieces. Summary of the Invention

[0005] In response to the above defects or improvement needs of the prior art, the present invention provides an observer-based robot variable impedance processing method to solve the problem that the robot cannot be applied to scenarios where the impedance of the workpiece is constantly changing when processing a workpiece with low impedance.

[0006] To achieve the above object, according to the present invention, a robot variable impedance machining method based on an observer is provided, the method comprising the following steps:

[0007] S1: When the end of the robot contacts the workpiece to be processed, the impedance model is used to model the workpiece to be processed, thereby obtaining the impedance model of the workpiece to be processed and simultaneously constructing the dynamic model of the robot; the end position, end velocity and end force of the robot in Cartesian space are used as state variables, the impedance parameters of the workpiece to be processed and the end disturbance parameters of the robot are used as observation variables, and the impedance model of the workpiece to be processed and the robot dynamic model are used to construct the state space equation of the robot-workpiece;

[0008] S2 collects data of the state variables in multiple control cycles of the robot-workpiece state space equation, constructs a rolling optimization observer using the collected data, and establishes constraint conditions to perform real-time observation of the impedance parameters of the workpiece to be processed and the end disturbance of the robot;

[0009] S3: Based on the characteristic that the robot impedance parameters change with the impedance of the workpiece being processed, the impedance parameters of the workpiece to be processed observed in step S2 are used to construct a robot variable impedance control model; the robot end disturbance observed in step S2 is used to compensate the robot dynamic model, thereby obtaining a compensated robot dynamic model; and the robot variable impedance control model and the compensated robot dynamic model are used to construct a robot variable impedance control rate in Cartesian space;

[0010] S4 converts the robot variable impedance control rate in the Cartesian space into the robot joint space to obtain the robot's feedback torque, and uses the feedback torque to control the robot to complete the robot processing task.

[0011] Further preferably, in step S1, the impedance model of the workpiece to be processed is carried out according to the following relationship:

[0012]

[0013] Among them, F represents the end force on the end of the robot, K e represents the stiffness parameter of the environment, P is the actual position of the workpiece surface, that is, the position of the robot end, and D e represents the damping parameter of the environment, P e Indicates the initial position of the workpiece surface.

[0014] Further preferably, in step S1, the state space equation of the robot-workpiece is performed according to the following relationship:

[0015]

[0016] in, are the derivatives of the state variables x1, x2, and x3, respectively. x1 = P represents the end position of the robot, x2 = V represents the end velocity of the robot, x3 = F represents the end force on the end of the robot, and M -1 (x1) represents the inverse matrix of the robot's inertia matrix, u represents the input term of the robot's Cartesian space, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the robot's gravity matrix, F represents the external force on the robot's end, η represents the robot's end disturbance term, and K e Denotes the stiffness matrix of the workpiece, D e Represents the damping matrix of the workpiece. The stiffness and damping parameters are collectively referred to as impedance parameters. Indicates the acceleration of the robot end.

[0017] Further preferably, in step S2, the observer is performed according to the following relationship:

[0018]

[0019] Among them, x(t k-N+1 ) represents t k-N+1 The value of the state variable at the moment; Indicates t k-N+1 Reference value of state variable x at the moment; z=[K e ,D e ,η] represents the observation matrix, which contains the environmental impedance parameters and the disturbance error of the robot; t k-N+1 The positive definite coefficient matrix at time y r (t i ) represents t i Time y(t i ) reference value; y(t i ) represents the robot system t i Output value at time e F (t i ) represents the external force error of the robot; R is the positive definite matrix of the output item, i is the number of the moment, and k represents the sequence number of the current moment.

[0020] More preferably, the x(t k-N+1 ) is carried out according to the following relationship:

[0021] x(t k-N+1 )=[x1(t k-N+1 ),x2(t k-N+1 ),x3(t k-N+1 )]

[0022] Where t represents time, k represents the sequence number of the current moment, and N represents that the observer's rolling time domain is N moments. The observer uses information from N moments before the current moment for calculation.

[0023] More preferably, the y(t i ) is carried out according to the following relationship:

[0024] y(t i )=[P(t i ),V(t i ),F(t i ),e F (t i ),η(t i )] T

[0025] Among them, t i Indicates the i-th moment, P(t i ) represents the end position of the robot corresponding to the i-th moment, V(t i ), represents the terminal velocity of the robot corresponding to the i-th moment, F(t i ) represents the external force on the end of the robot corresponding to the i-th moment, e F (t i ) represents the error between the force calculated by the workpiece impedance model at the i-th moment and the actual external force, η(t i ) represents the disturbance at the end of the robot corresponding to the i-th moment.

[0026] Further preferably, in step S1, the constraint conditions are as follows:

[0027]

[0028] y(t s )=h(x(t s ),u(t s ),v(t s ),z)

[0029] x(t s )∈χ,u(t s )∈μ,v(t s )∈υ,z∈ρ

[0030]

[0031] Among them, t s Indicates t i With t i+1 At any time in between, Represents the state variable x(t s ), f represents the state space equation of the robot-workpiece; y(ts ) represents the output variable, h represents the mapping equation from input variable to output variable; x(t s ) represents t s The state variables at the moment, χ represents the constraints of the state variables; u(t s ) represents t s The input variables at the moment, μ represents the constraints of the input variables; υ represents the physical constraints of the acceleration term; ρ represents the constraints of the observation data; m represents the dimension used in the Cartesian space, x r represents the reference value of the state variable; Δx max represents the maximum fluctuation of the state variable; represents the maximum fluctuation of the state variable derivative; u r Indicates the reference value of the input variable, J -T represents the inverse matrix of the Jacobian matrix transposed by the robot; Δτ max Indicates the maximum fluctuation value of the robot joint torque; v max represents the maximum constraint value of the acceleration term, z represents the parameter, z max represents the maximum constraint value of the observation variable, u represents the input item of the robot Cartesian space, represents the acceleration of the robot end, and x is the robot position, velocity, and force state variables.

[0032] Further preferably, in step S3, the robot variable impedance control model is performed according to the following relationship:

[0033]

[0034] Among them, M r Denotes the robot mass matrix, D r (t) represents the damping matrix of the robot at time t, K r (t) represents the stiffness matrix of the robot at time t, P d represents the ideal trajectory of the robot, P d =P e -F d / K e , P d The first derivative of P d The second derivative of is the first-order derivative of P, is the second-order derivative of P, F represents the end force on the end of the robot, F d is the ideal external force value of the robot.

[0035] Further preferably, in step S3, the robot variable impedance control rate in the Cartesian space is performed according to the following relationship:

[0036] u=M(x1)v+C(x1,x2)x2+G(x1)+η-x3

[0037] Where u represents the robot variable impedance control rate in Cartesian space, M(x1) represents the robot's inertia matrix, x1=P represents the robot's end position, v is an auxiliary variable, x2=V represents the robot's end velocity, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the robot's gravity matrix, x3=F represents the end force on the robot's end, and η represents the disturbance term at the robot's end.

[0038] Further preferably, in step S1, the auxiliary variable v is calculated according to the following relationship:

[0039]

[0040] in, represents the second-order derivative of the ideal value of the state variable, Denotes the inverse matrix of the mass matrix in the robot impedance model, D r (t k ) represents the robot t k The damping matrix at time , represents the robot terminal velocity, represents the ideal value of the robot's terminal velocity, K r (t k ) represents the robot t k The stiffness matrix at the moment, P represents the end position of the robot, P d represents the ideal value of the robot end position, F represents the external force on the robot end, and F d Indicates the ideal value of the external force acting on the end of the robot.

[0041] Further preferably, in step S4, the feedback torque τ of the robot is calculated according to the following relationship:

[0042]

[0043] Among them, J T represents the transpose of the robot Jacobian matrix, M represents the inertia matrix of the robot, represents the second-order derivative of the ideal value of the state variable, Denotes the inverse mass matrix in the robot impedance model, D r (t k ) represents the robot t k The damping matrix at the moment, x2=V represents the robot terminal velocity, represents the ideal value of the robot's terminal velocity, K r (t k ) represents the robot tk The stiffness matrix at the moment, x1 = P represents the end position of the robot, P d represents the ideal value of the robot end position, F represents the external force on the robot end, and F d represents the ideal value of the external force acting on the end of the robot, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the gravity matrix of the robot, η represents the disturbance term at the end of the robot, and x3=F represents the end force acting on the end of the robot.

[0044] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0045] 1. This paper proposes an observer-based robotic variable impedance machining method. The designed observer can simultaneously obtain the observed values of the environmental impedance and the robot disturbance error in a single optimization equation. This method can obtain parameters that cannot be directly measured in real time and has optimality.

[0046] 2. The variable impedance control strategy proposed in this paper can quickly respond to changes in environmental stiffness. By adjusting the robot's own impedance parameters, it improves the robot's dynamic response during force interaction tasks with the environment. Compared with fixed-parameter impedance control, it is more flexible. By compensating for the disturbance error at the robot's end, the controller's force and position tracking accuracy are improved.

[0047] 3. The method provided by the present invention is particularly suitable for situations where the contact environment impedance parameters are constantly changing, such as processing large weak-rigidity parts. It can ensure the stability of robot processing, enhance the compliance of the robot, improve the surface quality of the workpiece, and reduce the surface roughness of the workpiece. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 is a flow chart of observation-based robot variable impedance control constructed according to a preferred embodiment of the present invention;

[0049] Figure 2 This is a case study of a robot machining thin-walled workpieces constructed according to a preferred embodiment of the present invention;

[0050] Figure 3 is a stiffness map of a workpiece observed in actual machining constructed according to a preferred embodiment of the present invention;

[0051] Figure 4 is a damping map of a workpiece observed in actual machining constructed according to a preferred embodiment of the present invention;

[0052] Figure 5 It is the end disturbance of the robot observed in actual processing constructed according to the preferred embodiment of the present invention;

[0053] Figure 6 is a diagram showing the position tracking of a robot during actual processing constructed according to a preferred embodiment of the present invention;

[0054] Figure 7 This is a diagram showing the speed tracking of a robot during actual processing constructed according to a preferred embodiment of the present invention;

[0055] Figure 8 This is a diagram of the external force tracking of a robot during actual processing, constructed according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0056] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0057] like Figure 1 As shown in the figure, the present invention proposes an observer-based robot variable impedance machining method, which mainly consists of two parts: a rolling optimization observer and a variable impedance controller. The rolling optimization observer establishes an optimization equation based on the robot's historical state variable data, the environmental impedance model, and the robot's dynamic model, and predicts the current environmental impedance (stiffness and damping) parameters and the robot's disturbance parameters in real time. The variable impedance controller designs a variable impedance control rate, updates the robot's stiffness and damping parameters based on the observed environmental stiffness and damping parameters, updates the robot's trajectory based on the environmental stiffness parameters, supplements the robot's end-point interference term, and designs feedback torque input to the robot's joints to achieve the robot's machining task.

[0058] like Figure 2 As shown, this embodiment provides a case of robot processing thin-walled workpieces. The robot system and the environmental system are regarded as two mechanical impedance systems, and an impedance model is established. The robot grinds the thin-walled workpiece horizontally with constant force and speed. During the robot processing process, a state observer is designed to observe the stiffness and damping of the workpiece and the end disturbance parameters of the robot in real time. Then, a variable impedance controller is designed based on the observed parameters to improve the contact characteristics between the robot and the workpiece, enhance the flexibility of the robot processing, and improve the surface quality of the workpiece. The method mainly consists of the following steps:

[0059] Step 1: Establish the state space equation of the robot-environment system:

[0060]

[0061] in, They are the derivatives of the state variables x1, x2, and x3, respectively. x1 = P represents the end position of the robot, x2 = V represents the end velocity of the robot, and x3 = F represents the external force on the end of the robot. -1 (x1) represents the inverse matrix of the robot's inertia matrix, u represents the input term of the robot's Cartesian space, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the robot's gravity matrix, F represents the external force on the robot's end, η represents the robot's end disturbance term, and K e Denotes the stiffness matrix of the workpiece, D e Represents the damping matrix of the workpiece. The stiffness and damping parameters are collectively referred to as impedance parameters. Indicates the acceleration of the robot end.

[0062] Step 2: The control cycle is set to 1ms. Based on the historical data of 20 control cycles of the state-space equation and state variables, a rolling optimization observer is designed. This observer converts the observation problem of the unknown state into an optimization problem. By solving the optimal parameters in each cycle, the impedance parameters of the external environment and the end disturbance of the robot body can be obtained in real time.

[0063]

[0064] st

[0065]

[0066] where x(t k-n+1 )=[x1(t k-n+1 ),x2(t k-n+1 ),x3(t k-n+1 )] indicates t k-n+1 The value of the state variable at the moment; Indicates t k-n+1 Reference value of state variable x at the moment; z=[K e ,D e ,η] represents the observation matrix, which contains the environmental impedance parameters and the disturbance error of the robot; t k-n+1 The positive definite coefficient matrix at time, y r (t i ) represents t i Time y(t i ) reference value; y(t i ) represents the robot system t i Output value at time y(t i )=[P(t i ),V(t i ),F(t i ),eF (t i ),η(t i )] T ;e F (t i ) represents the external force error of the robot; R is the positive definite matrix of the output term R=diag(10 5 ,10 2 ,10 3 ,10 5 ,10 3 ); f represents the state space equation; h represents the mapping equation from input variables to output variables; the specific description of the optimization constraints is as follows:

[0067]

[0068] χ represents the constraints on state variables; μ represents the constraints on input variables; υ represents the physical constraints on acceleration terms; ρ represents the constraints on observation data; m is 1, x r represents the reference value of the state variable; Δx max The maximum fluctuation of the state variable is [1 mm, 5 mm / s, 1 N], where 1 mm is taken; The maximum fluctuation of the state variable derivative is [5mm / s, 10mm / s 2 ,10N / s];u r Indicates the reference value of the input variable, J -T represents the inverse matrix of the transposed Jacobian matrix of the robot; Δτ max Indicates the maximum fluctuation value of the robot joint torque, which is 1Nm; v max Indicates the maximum constraint value of the acceleration term, which is 1mm / s, z max represents the maximum constraint value of the observed variable, where The environmental stiffness parameters observed in real time are as follows Figure 3 As shown, the damping parameters are Figure 4 As shown, the robot end disturbance parameters are as follows Figure 5 shown.

[0069] Step 3: In Cartesian space, establish the robot variable impedance control model:

[0070] The variable impedance model of the robot is:

[0071]

[0072] Among them, M r Denotes the robot mass matrix, D r (t) represents the damping matrix of the robot at time t, K r (t) represents the stiffness matrix of the robot at time t. d The ideal trajectory P of the robot is represented byd =P e -F d / K e , P d The first derivative of P d The second derivative of is the first-order derivative of P, is the second-order derivative of P, F d is the ideal external force value of the robot.

[0073] The impedance model of the environment is:

[0074]

[0075] where K e represents the stiffness parameter of the environment, D e represents the damping parameter of the environment, P e Indicates the initial position of the environment surface.

[0076] Combining the above equations, we can get the system equation of the robot-environment system:

[0077]

[0078] The robot impedance parameter changes according to the observed environmental impedance parameter, where k The stiffness and damping parameters of the robot at this moment are selected as follows:

[0079]

[0080] Among them D * The setting is D r (t 20 )+D e (t 20 ).

[0081] The disturbance term of the robot is compensated into the dynamic model, the robot variable impedance model and the robot dynamic model are combined, and the robot variable impedance control rate in Cartesian space is designed.

[0082] The combined robot impedance model and robot dynamics model can be obtained:

[0083] u=M(x1)v+C(x1,x2)x2+G(x1)+η-F,

[0084] in

[0085]

[0086] Ideal participation speed Set to 20mm / s, ideal reference external force F d Set to 8N.

[0087] Step 4: Convert the robot control law in Cartesian space to the robot joint space to obtain the robot's feedback torque.

[0088]

[0089] The feedback torque is input into the joint controller of the robot to realize the control of the robot and complete the robot processing task. The robot completes the processing task through the above joint torque. The performance of its end theoretical reference position and actual position is as follows Figure 6 As shown, the theoretical reference speed and actual speed are as follows Figure 7 As shown, the theoretical reference external force and the actual external force value are as follows Figure 8 As shown in the figure, it can be seen that the robot's state errors gradually converge through the proposed observation-based variable impedance control rate. In actual processing, the position error can be controlled below 0.5mm, the speed error can be controlled below 0.5mm / s, and the force tracking error can be controlled below 1N.

[0090] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robot variable impedance machining method based on an observer, characterized in that: The method comprises the following steps: When the end of the robot contacts the workpiece, S1 uses the impedance model to model the workpiece, thereby obtaining the impedance model of the workpiece and constructing the dynamic model of the robot. The robot's end position, end velocity, and end force in Cartesian space are used as state variables, the impedance parameter of the workpiece to be processed and the robot's end disturbance parameter are used as observation variables, and the impedance model of the workpiece to be processed and the robot's dynamic model are used to construct the robot-workpiece state space equation; S2 collects data of the state variables in multiple control cycles of the robot-workpiece state space equation, constructs a rolling optimization observer using the collected data, and establishes constraint conditions to perform real-time observation of the impedance parameters of the workpiece to be processed and the end disturbance of the robot; S3: Based on the characteristic that the robot impedance parameters change with the impedance of the workpiece being processed, the impedance parameters of the workpiece to be processed observed in step S2 are used to construct a robot variable impedance control model; the robot end disturbance observed in step S2 is used to compensate the robot dynamic model, thereby obtaining a compensated robot dynamic model; and the robot variable impedance control model and the compensated robot dynamic model are used to construct a robot variable impedance control rate in Cartesian space; S4 converts the robot variable impedance control rate in the Cartesian space into the robot joint space to obtain the robot's feedback torque, and uses the feedback torque to control the robot to complete the robot processing task.

2. The observer-based robot variable impedance machining method according to claim 1, characterized in that: In step S1, the impedance model of the workpiece to be processed is carried out according to the following relationship: Among them, F represents the end force on the end of the robot, K e represents the stiffness parameter of the environment, P is the actual position of the workpiece surface, that is, the position of the robot end, and D e represents the damping parameter of the environment, P e Indicates the initial position of the workpiece surface.

3. The observer-based robot variable impedance machining method according to claim 2, characterized in that: In step S1, the robot-workpiece state space equation is calculated according to the following relationship: in, are the derivatives of the state variables x1, x2, and x3, respectively. x1 = P represents the end position of the robot, x2 = V represents the end velocity of the robot, x3 = F represents the end force on the end of the robot, and M -1 (x1) represents the inverse matrix of the robot's inertia matrix, u represents the input term of the robot's Cartesian space, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the robot's gravity matrix, F represents the external force on the robot's end, η represents the robot's end disturbance term, and K e Denotes the stiffness matrix of the workpiece, D e Represents the damping matrix of the workpiece. The stiffness and damping parameters are collectively referred to as impedance parameters. Indicates the acceleration of the robot end.

4. The observer-based robot variable impedance machining method according to claim 1, characterized in that: In step S2, the observer is operated according to the following relationship: Among them, x(t k-N+1 ) represents t k-N+1 The value of the state variable at the moment; Indicates t k-N+1 Reference value of state variable x at the moment; z=[K e ,D e ,η] represents the observation matrix, which contains the environmental impedance parameters and the disturbance error of the robot; t k-N+1 The positive definite coefficient matrix at time y r (t i ) represents t i Time y(t i ) reference value; y(t i ) represents the robot system t i The output value at the moment; R is the positive definite matrix of the output items, i is the number of the moment, and k represents the sequence number of the current moment; The x(t k-N+1 ) is carried out according to the following relationship: x(t k-N+1 )=[x1(t k-N+1 ),x2(t k-N+1 ),x3(t k-N+1 )] Where t represents time, k represents the sequence number of the current moment, and N represents that the observer's rolling time domain is N moments. The observer uses information from N moments before the current moment for calculation.

5. The observer-based robot variable impedance machining method according to claim 4, characterized in that: The y(t i ) is carried out according to the following relationship: y(t i )=[P(t i ),V(t i ),F(t i ),e F (t i ),η(t i )] T Among them, t i Indicates the i-th moment, P(t i ) represents the end position of the robot corresponding to the i-th moment, V(t i ) represents the terminal velocity of the robot corresponding to the i-th moment, F(t i ) represents the external force on the end of the robot corresponding to the i-th moment, e F (t i ) represents the error between the force calculated by the workpiece impedance model at the i-th moment and the actual external force, η(t i ) represents the disturbance at the end of the robot corresponding to the i-th moment.

6. The observer-based robot variable impedance machining method according to claim 2, characterized in that: In step S2, the constraints are as follows: =f(x(t s ),u(t s ),v(t s ),z) y(t s )=h(x(t s ),u(t s ),v(t s ),z) x(t s )∈χ,u(t s )∈μ,v(t s )∈υ,z∈ρ Among them, t s Indicates t i With t i+1 At any time in between, Represents the state variable x(t s ), f represents the state space equation of the robot-workpiece; y(t s ) represents the output variable, h represents the mapping equation from input variable to output variable; x(t s ) represents t s The state variables at the moment, χ represents the constraints of the state variables; u(t s ) represents t s The input variables at the moment, μ represents the constraints of the input variables; υ represents the physical constraints of the acceleration term; ρ represents the constraints of the observation data; m represents the dimension used in the Cartesian space, x r represents the reference value of the state variable; Δx max represents the maximum fluctuation of the state variable; represents the maximum fluctuation of the state variable derivative; u r Indicates the reference value of the input variable, J -T represents the inverse matrix of the Jacobian matrix transposed by the robot; Δτ max Indicates the maximum fluctuation value of the robot joint torque; v max represents the maximum constraint value of the acceleration term, z represents the parameter, z max represents the maximum constraint value of the observation variable, u represents the input item of the robot Cartesian space, represents the acceleration of the robot end, and x is the state variable of the robot's position, velocity, and force.

7. The observer-based robot variable impedance machining method according to claim 1, characterized in that: In step S3, the robot variable impedance control model is performed according to the following relationship: Among them, M r Denotes the robot mass matrix, D r (t) represents the damping matrix of the robot at time t, K r (t) represents the stiffness matrix of the robot at time t, P d represents the ideal trajectory of the robot, P d =P e -F d / K e , P d The first derivative of P d The second derivative of is the first-order derivative of P, is the second-order derivative of P, F represents the end force on the end of the robot, F d is the ideal external force value of the robot.

8. The observer-based robot variable impedance machining method according to claim 1, characterized in that: In step S3, the robot variable impedance control rate in the Cartesian space is performed according to the following relationship: u=M(x1)v+C(x1,x2)x2+G(x1)+η-x3 Where u represents the robot variable impedance control rate in Cartesian space, M(x1) represents the robot's inertia matrix, x1=P represents the robot's end position, v is an auxiliary variable, x2=V represents the robot's end velocity, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the robot's gravity matrix, x3=F represents the end force on the robot's end, and η represents the disturbance term at the robot's end.

9. The observer-based robot variable impedance machining method according to claim 8, characterized in that: In step S1, the auxiliary variable v is calculated according to the following relationship: in, represents the second-order derivative of the ideal value of the state variable, Denotes the inverse matrix of the mass matrix in the robot impedance model, D r (t k ) represents the robot t k The damping matrix at time , represents the robot terminal velocity, represents the ideal value of the robot's terminal velocity, K r (t k ) represents the robot t k The stiffness matrix at the moment, P represents the end position of the robot, P d represents the ideal value of the robot end position, F represents the external force on the robot end, and F d Indicates the ideal value of the external force acting on the end of the robot.

10. The observer-based robot variable impedance machining method according to claim 1, characterized in that: In step S4, the feedback torque τ of the robot is calculated according to the following relationship: Among them, J T represents the transpose of the robot Jacobian matrix, M represents the inertia matrix of the robot, represents the second-order derivative of the ideal value of the state variable, Denotes the inverse mass matrix in the robot impedance model, D r (t k ) represents the robot t k The damping matrix at the moment, x2=V represents the robot terminal velocity, represents the ideal value of the robot's terminal velocity, K r (t k ) represents the robot t k The stiffness matrix at the moment, x1 = P represents the end position of the robot, P d represents the ideal value of the robot end position, F represents the external force on the robot end, and F d represents the ideal value of the external force acting on the end of the robot, C(x1,x2) represents the Coriolis force matrix, G(x1) represents the gravity matrix of the robot, η represents the disturbance term at the end of the robot, and x3=F represents the end force acting on the end of the robot.

Images