A polishing control method and system for a robot arm based on adaptive impedance control

Abstract

The present application belongs to the technical field of mechanical arm polishing control, and provides a mechanical arm polishing control method and system based on adaptive impedance control, comprising establishing a Lagrange dynamics model of a mechanical arm; obtaining a desired trajectory of the end of the mechanical arm; based on the dynamics model, generating an adaptive impedance control method containing polishing workpiece environment uncertainty as a constraint; using the adaptive impedance control method, estimating unknown environment parameters, updating the reference trajectory in real time, adjusting the end position of the mechanical arm, and realizing the tracking of the end contact force. The present application solves the problem that it is difficult to complete the polishing task with high quality in the actual complex polishing process.

Description

Technical Field

[0001] This disclosure relates to the field of robotic arm grinding control technology, specifically to a robotic arm grinding control method and system based on adaptive impedance control. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] Grinding robot operations are generally divided into two stages: free movement and contact operation. Before grinding, the robot's end effector is often not in the target position. The first step is to control the robot's end effector to move to the target position; this is the free movement stage. In this stage, the robot needs to achieve motion control through a position control system. For grinding robots, trajectory tracking control is directly related to the accurate completion of both stages of the grinding operation. Currently, most grinding robots use multi-joint robotic arms, which are complex nonlinear mechanical systems with strong coupling relationships between joints. Furthermore, they are susceptible to interference from the external environment, resulting in parameter uncertainties. After the robot begins contact with the workpiece, forces are generated between the robot's end effector and the workpiece. If the end effector, tool, or workpiece has high rigidity, performing contact operations becomes quite difficult for the robot and may damage the robot or workpiece. This also leads to a reduction in processing accuracy, thus affecting the grinding quality of the workpiece surface. Therefore, it is essential to control the interaction force between the robot and the workpiece while ensuring the robot's positional accuracy, so that the robot can exhibit compliance with the environment. This is of great significance for improving the grinding accuracy and stability of the robotic arm. Summary of the Invention

[0004] To address the aforementioned shortcomings, this disclosure proposes a robotic arm grinding control method and system based on adaptive impedance control. Using the desired trajectory as a constraint, an adaptive impedance control method is generated that incorporates the environmental uncertainties of the workpiece being ground. Environmental parameters are estimated through real-time feedback of the robot's end-effector position and contact force, and the reference trajectory is adjusted online, enabling the robot's end-effector to quickly approach the desired position.

[0005] To achieve the above objectives, the present disclosure adopts the following technical solution:

[0006] The first aspect of this disclosure provides a robotic arm grinding control method based on adaptive impedance control, comprising the following steps:

[0007] Establish a Lagrangian dynamics model for the robotic arm;

[0008] Obtain the desired trajectory of the robotic arm's end effector;

[0009] Based on the dynamic model and with the desired trajectory as a constraint, an adaptive impedance control method is generated that incorporates the uncertainties of the workpiece grinding environment.

[0010] By using an adaptive impedance control method, unknown environmental parameters are estimated, the reference trajectory is updated in real time, and the position of the robotic arm's end effector is adjusted to achieve end-effector contact force tracking.

[0011] As a further implementation, a sensor is used to scan the workpiece to be polished to obtain point cloud data of its surface. The point cloud data of the workpiece to be polished is processed and analyzed to obtain the surface information of the workpiece, calculate the area of ​​the workpiece that needs to be polished, and obtain the workpiece polishing trajectory. The workpiece polishing trajectory is the expected trajectory of the end effector of the robotic arm.

[0012] As a further implementation, the Lagrangian dynamics model of the robotic arm is as follows:

[0013]

[0014] in, These represent the joint vector, joint velocity vector, and joint acceleration vector of the robotic arm, respectively, where H(q)∈R m×n The inertia matrix representing the robotic arm. The matrix representing the Coriolis force and centripetal force of the robotic arm, G(q)∈R n The gravity vector representing the robotic arm, τ∈R n This represents the driving torque vector of the robotic arm.

[0015] As a further implementation, based on the dynamic model and constrained by the desired trajectory, an adaptive impedance control method is generated that incorporates uncertainties in the workpiece grinding environment. Specifically:

[0016] The desired trajectory of the robotic arm end effector is abstracted into first-order and second-order forms of constraints. Assuming that the uncertainty of the system caused by external conditions has a boundary and the boundary is unknown, the system is divided into a nominal part and an uncertain part.

[0017] For the nominal part, nominal control based on UK theory is adopted, and the control input required to satisfy the constraint is obtained according to the Udwaidia-Kalaba equation;

[0018] A leakage-type adaptive law is designed for the uncertain part to estimate and effectively compensate for the disturbances and uncertainties caused by external factors in the system.

[0019] As a further implementation, the first-order formal expression of the constraint is:

[0020]

[0021] in, for The i-th element, A li c l C 1 Class function, t represents time, A li (q,t) represents the matrix related to system constraints, c l (q,t) represents a function related to the constraints;

[0022] The above constraints can be rearranged into matrix form:

[0023]

[0024] Among them, A=[A li ] m×n c = [c1, c2, ..., c m ] T ;

[0025] The second-order form of the constraint is:

[0026]

[0027] The above formula can be rewritten as:

[0028]

[0029] Written in matrix form:

[0030]

[0031] in, Represents a vector related to constraints;

[0032] The expression for the adaptive impedance control method is:

[0033]

[0034] Where, τ∈R n To control the input, t∈R is the independent variable, q∈R n For generalized coordinates, For generalized speed, These are adaptive parameters.

[0035] As a further implementation, the adaptive impedance control method estimates the unknown environmental parameters using the following expression:

[0036]

[0037] Among them, f, f r f represents the actual contact force and the expected contact force of the grinding robot, respectively.e This indicates the error value of the end contact force. x represents the estimated value of the actual contact force. r Represents the system reference trajectory, k e x e p1 and p2 represent environmental stiffness and environmental location, respectively. p1 and p2 are the diagonal elements of a constant diagonal matrix P, both of which are positive real constants, P∈R. 2×2 , where x represents the actual displacement of the robot's end effector.

[0038] As a further implementation method, the selection of impedance parameters satisfies the following rules:

[0039]

[0040] Where, m d b d k d Let represent the inertia matrix, damping matrix, and stiffness matrix in the desired impedance model, respectively; ξ represents the target damping ratio; and k represents the stiffness ratio.

[0041] The second aspect of this disclosure provides a robotic arm grinding control system based on adaptive impedance control, comprising:

[0042] The model building module is configured to: build a Lagrange dynamics model of the robotic arm;

[0043] The desired trajectory acquisition module is configured to acquire the desired trajectory of the robotic arm's end effector.

[0044] The control method generation module is configured to: generate an adaptive impedance control method that incorporates the uncertainties of the workpiece grinding environment, based on a dynamic model and constrained by the desired trajectory;

[0045] The control module is configured to use an adaptive impedance control method to estimate unknown environmental parameters, update the reference trajectory in real time, adjust the position of the robotic arm end effector, and achieve end-effector contact force tracking.

[0046] The third aspect of this disclosure provides a medium having a program stored thereon, which, when executed by a processor, implements the steps of the robotic arm grinding control method based on adaptive impedance control described in the first aspect of this disclosure.

[0047] The fourth aspect of this disclosure provides an electronic device including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the robotic arm grinding control method based on adaptive impedance control described in the first aspect of this disclosure.

[0048] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0049] (1) The adaptive impedance control method of the present invention assumes that the uncertainty of the system caused by external conditions has a boundary and the boundary is unknown. The system is divided into a nominal part and an uncertain part. For the nominal part, a nominal control based on UK theory is adopted. The control input required to satisfy the constraint is obtained according to the Udwaidia-Kalaba equation. The method is simple and clear, avoiding the calculation of complex parameters such as Lagrange multipliers. For the uncertain part, a leakage adaptive law is designed to estimate and effectively compensate for the disturbances and uncertainties that the system may be caused by external factors.

[0050] (2) Compared with traditional dynamic analysis methods, the UK method adopted in this invention does not require the introduction of additional auxiliary variables. Instead, it uses the desired trajectory as the performance constraint, and solves the constraint torque by analyzing the Udwadia-Kalaba equation. It can handle both complete and incomplete servo constraints. The designed adaptive law is leakage type, which can automatically adjust the adaptive parameters to compensate for the system uncertainty that changes rapidly over time.

[0051] (3) The present invention adopts an adaptive contact force tracking strategy based on impedance control, which can estimate environmental parameters through real-time feedback of robot end position and contact force, and adjust the reference trajectory online, so that the robot end can quickly approach the desired position. The improved impedance control model has adaptability to unknown environment and can improve the end contact force tracking accuracy and robustness of the system.

[0052] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0053] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0054] Figure 1 This is a flowchart of the framework of the robotic arm grinding control method based on adaptive impedance control disclosed herein.

[0055] Figure 2 This is a publicly disclosed schematic diagram of the grinding force breakdown. Detailed Implementation

[0056] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0057] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0058] Where there is no conflict, the embodiments and features described herein can be combined with each other.

[0059] Example 1

[0060] like Figure 1 As shown, Embodiment 1 of this disclosure provides a robotic arm grinding control method based on adaptive impedance control, including the following steps:

[0061] S1 establishes a Lagrangian dynamics model of the robotic arm;

[0062] S2 obtains the desired trajectory of the robotic arm's end effector;

[0063] S3 is based on a dynamic model and uses the desired trajectory as a constraint to generate an adaptive impedance control method that incorporates the uncertainties of the workpiece grinding environment.

[0064] S4 uses an adaptive impedance control method to estimate unknown environmental parameters, update the reference trajectory in real time, and adjust the position of the robotic arm's end effector to achieve end-effector contact force tracking.

[0065] First, S1 establishes the Lagrangian dynamics model of the robotic arm, specifically as follows:

[0066] The DH kinematic modeling method is used to establish joint coordinate systems for the robotic arm one by one, and the coordinate transformation matrix between adjacent joints is calculated.

[0067] Find the pose matrix of the end effector of the robotic arm in the base coordinate system to obtain the forward kinematics relationship of the robotic arm. Then solve the kinematic equations in the reverse direction to obtain the inverse kinematics solution.

[0068] Based on the Lagrange dynamics analysis method, the Lagrange dynamics model of the robotic arm is derived. The dynamics model is as follows:

[0069]

[0070] in, H(q)∈R represents the joint vector, joint velocity vector, and joint acceleration vector of the robotic arm, respectively. m×n The inertia matrix representing the robotic arm; The matrix representing the Coriolis force and centripetal force of the robotic arm; G(q)∈R n The gravity vector representing the robotic arm; τ∈R n This represents the driving torque vector of the robotic arm.

[0071] S2 obtains the desired trajectory of the robotic arm's end effector, specifically:

[0072] Point cloud acquisition: A 3D sensor is used to scan the workpiece to be polished and acquire point cloud data of its surface. This point cloud data represents the geometry and surface features of the workpiece.

[0073] Point cloud processing: The acquired point cloud data is processed and analyzed, including point cloud filtering, point cloud registration, and feature extraction steps, to obtain more accurate workpiece surface information, calculate the area of ​​the workpiece that needs to be polished, and obtain the workpiece polishing trajectory. The obtained workpiece polishing trajectory is the desired trajectory of the robotic arm's end effector.

[0074] S3, based on a dynamic model and constrained by the desired trajectory, generates an adaptive impedance control method that incorporates uncertainties in the workpiece grinding environment. Specifically:

[0075] (1) The desired trajectory of the end of the robotic arm is abstracted into the first-order and second-order forms of the constraint. Consider the uncertainty that the system may generate due to external conditions, and assume that this uncertainty has a boundary but the boundary is unknown. Divide the system into the nominal part and the uncertain part.

[0076] (2) For the nominal part, nominal control based on UK theory is adopted, and the control input required to satisfy the constraint is obtained according to the Udwaidia-Kalaba equation.

[0077] (3) Design a leakage adaptive law for the uncertain part to estimate and effectively compensate for the disturbances and uncertainties that the system may be caused by external factors.

[0078] The parameter estimation expression for the above adaptive impedance control method is as follows:

[0079]

[0080] Among them, f, f r f represents the actual contact force and the expected contact force of the grinding robot, respectively. e This indicates the error value of the end contact force. x represents the estimated value of the actual contact force. r Represents the system reference trajectory, k e x e p1 and p2 represent environmental stiffness and environmental location, respectively. p1 and p2 are the diagonal elements of a constant diagonal matrix P, both of which are positive real constants, P∈R. 2×2 , where x represents the actual displacement of the robot's end effector.

[0081] The first-order formal expression of the constraint is:

[0082]

[0083] in, for The i-th element, A li c l C 1 A class function, where t∈R is the independent variable, representing time, and A li (q,t) represents the matrix related to system constraints. In specific applications, A li The values ​​of the elements in (q,t) depend on the specific constraints of the system and the motion state of the robotic arm. It describes the motion velocities of each joint of the robotic arm. The relationship between constraints and... l (q,t) represents a constraint-related function. Its value also depends on the system's constraints and the robot's motion state, and is related to A. li (q,t) together constitute the expression of the first-order constraint. A li (q,t) and c l (q,t) plays a role in describing the relationship between the robot arm's motion and the desired trajectory or constraint in the first-order constraint formula. It is an important component in controller design for achieving trajectory tracking and satisfying constraints.

[0084] The above constraints can be rearranged into matrix form:

[0085]

[0086] Among them, A=[A li ] m×n c = [c1, c2, ..., c m ] T .

[0087] The second-order form of the constraint is:

[0088]

[0089] The above formula can be rewritten as:

[0090]

[0091] Written in matrix form:

[0092]

[0093] in, This represents a vector related to constraints. Its specific meaning is: based on the system's constraints and the robot arm's motion state (including position q, velocity, etc.) And time t), the quantities related to acceleration are calculated.

[0094] The value is obtained by differentiating the first-order constraint formula. It incorporates various factors related to acceleration in the system, such as force, torque, and external disturbances. In controller design, It is used to describe the acceleration characteristics that the end effector of the robotic arm should have under the condition of satisfying constraints, so as to provide a reference for the controller to control the control input and achieve precise control of the robotic arm.

[0095] The above adaptive impedance control method satisfies the following conditions:

[0096] (1) Constraints It is consistent, that is, the constraint equation has at least one solution vector.

[0097] (2) For each (q,t)∈R n ×R, A(q,t) is full rank, that is, A(q,t)A T (q,t) is invertible.

[0098] (3) Under the premise of condition (2), given a matrix Γ∈R m×m Γ>0, let:

[0099]

[0100] Then there exists a potentially unknown constant ω. E >-1, for all (q,t)∈R n ×R has all of the following:

[0101]

[0102] (4) There exists an unknown constant vector α∈(0,∞) h And a known function Θ(·):(0,∞) h ×R n ×R n ×R→R + ,

[0103] For each have:

[0104]

[0105] Here Γ, A(q,t), ΔS(q,δ,t), S(q,t), G(q,δ,t), These are all variables and functions defined in the controller design.

[0106] A(q,t) represents the matrix related to system constraints; ΔS(q,δ,t) and S(q,t) are related to the uncertainty and nominal part of the system. G(q,δ,t) represent centripetal force, Coriolis force, and gravity, respectively; and It is a component of the controller.

[0107] This expression means that by performing a certain operation on a combination of these variables and functions (the specific operation is given by the expression), the upper bound of the result can be determined by the function. To limit. ω E It is a system-related constant defined in Assumption 3, used to describe a certain characteristic of the system.

[0108] (5) For any It can be linearly decomposed into α, that is, there exists a function. make

[0109] make Representing the tracking error of the constraint, we obtain the first and second parts of the controller, let:

[0110]

[0111] here, It is a nominal control based on UK theory, used to suppress any tendency to deviate from the desired trajectory. Used to suppress the offset of initial conditions and make the system satisfy the given constraints; "+" indicates the Moore-Penrose (MP) generalized inverse matrix, for a matrix J, its MP generalized inverse matrix J0 is J0. + The following conditions must be met:

[0112] JJ + J = J, J + JJ + =J + JJ + =(JJ + ) T J + J = (J + J) T (14)

[0113] When the system has uncertainties and initial deviations, relying solely on Unable to achieve good robustness and tracking accuracy, a third part of the controller is introduced to address this issue. Let:

[0114]

[0115] in,

[0116]

[0117] parameter It follows the adaptive law:

[0118]

[0119] in Vector at time t0 The i-th element), ψ1, ψ2∈R + . It is an estimate of α, and the adaptive parameter is used when the system's tracking error is large. This will increase rapidly to effectively compensate for system uncertainties; when the system approaches the desired position and the tracking error is small, the parameters... It will gradually decrease.

[0120] The expression for the adaptive impedance control method is:

[0121]

[0122] Where, τ∈R n To control the input, t∈R is the independent variable, q∈R n For generalized coordinates, For generalized speed, These are adaptive parameters.

[0123] S4 utilizes an adaptive impedance control method to estimate unknown environmental parameters, update the reference trajectory in real time, and adjust the position of the robotic arm's end effector to achieve end-effector contact force tracking. Specifically:

[0124] The selection of impedance parameters shall satisfy the following rules:

[0125]

[0126] Where, m d b d k d Let represent the inertia matrix, damping matrix, and stiffness matrix in the desired impedance model, respectively; ξ represents the target damping ratio; and k represents the stiffness ratio.

[0127] By selecting appropriate three impedance parameters m d b d k d This allows the end effector of the grinding robot to exhibit good compliance, thereby achieving ideal grinding force tracking results.

[0128] pass Figure 2The grinding force is generally divided into three parts: axial force, tangential force in the tangential direction of the contact surface, and normal force in the normal direction of the contact surface. The axial force is usually very small and can be ignored in the analysis. The tangential force is mainly used to remove material from the workpiece surface, while the normal force is a pressure perpendicular to the contact surface, thus directly determining the magnitude of the frictional force at the contact surface. Its value is the largest of the three components, so the grinding normal force is taken as the controlled object. The mathematical form of its impedance control model is:

[0129]

[0130] In the frequency domain, it takes the form of:

[0131]

[0132] Where, x p =x d -x r f e =ff r m d b d k d Let f and f' represent the mass coefficient, damping coefficient, and stiffness coefficient of the impedance control model, respectively. r x represents the actual contact force and the expected contact force of the grinding robot, respectively. r x d Let x represent the system reference trajectory and the desired trajectory of the position control system, respectively. For equation (21) above, we only analyze the impedance control model and do not consider the position deviation of the robot position control system, i.e., the desired displacement x. d If the displacement x is equal to the actual displacement x of the robot's end effector, then x can be written as:

[0133]

[0134] Let G(s) = m d s 2 +b d s+k d Then the error value f of the end contact force e It can be derived in the following form:

[0135] f e =ff r (twenty three)

[0136] =k e (xx e )-f r

[0137] =k e xk e x e -fr

[0138] =k e (-f e / G+x r )-k e x e -f r

[0139] Where, k e x e These represent environmental stiffness and environmental location, respectively. Further transformation of equation (23) yields:

[0140] f e (G+k e )=G(k e x r -k e x e -f r )(twenty four)

[0141] Substituting the value of G(s) into the equation, we have:

[0142] f e (m d s 2 +b d s+k d +k e )

[0143] =(m d s 2 +b d s+k d (k) e x r -k e x e -f r (25)

[0144] Since the robot end effector reaches a steady state in the contact normal direction, the magnitudes of acceleration and velocity in that direction become zero. Consequently, the mass term related to acceleration characteristics and the damping term related to velocity characteristics in equation (25) are both zero. Therefore, the steady-state error value f of the end effector contact force is zero. ess Represented as:

[0145]

[0146] in, It represents the equivalent total stiffness of the environment and impedance model.

[0147] To make the steady-state error of the end contact force equal to zero, let both sides of equation (26) above equal to zero, then we have:

[0148]

[0149] When the reference trajectory x of the control system r Only when the condition of equation (27) above is satisfied can the actual contact force f at the end be in a steady state and match the desired contact force f. r The size remains the same, meaning that during the grinding process, the position x of the workpiece surface in the Cartesian coordinate system is known. e and the workpiece stiffness k e This allows for the offline calculation of the reference trajectory x of the control system. r Then, the displacement correction P is output in real time through the impedance model. x To continuously change the desired position command x of the robot's position control system d This allows for continuous adjustment of the end position, ensuring that the actual contact force f at the end accurately tracks the desired contact force f. r .

[0150] However, in actual grinding processes, ideal conditions with accurately known environmental parameters are practically nonexistent. This paper considers the uncertainty of environmental parameters and estimates their values, using the actual environmental position x... e Decomposed into estimated environmental location and error value Δx e The real-world stiffness is decomposed into estimated stiffness values. and error value Δk e The specific decomposition is as follows:

[0151]

[0152] According to equation (27), to make the steady-state contact force error zero, the reference trajectory needs to follow... To select the appropriate path, considering the uncertainty of the environment, we still decompose the environmental location and environmental stiffness according to the decomposition method in equation (28), and give the estimated value of the reference trajectory:

[0153]

[0154] Let parameter k x =k e x e The formula for calculating the actual contact force is:

[0155] f = k e (xx e )=k e xk x (30)

[0156] Similarly, an estimate of the actual contact force is given.

[0157]

[0158] Let ψ = [ψ1, ψ2] T ,in Subtracting equations (30) and (31), we get:

[0159]

[0160] Suppose that as t→∞, Substitute equation (29) into equation (31) to eliminate have to:

[0161]

[0162] Transforming the above equation, we get:

[0163]

[0164] Substituting equation (34) into the impedance control model equation (20), we get:

[0165]

[0166] The condition for equation (35) to hold is: f e →0 or And k d , The values ​​of all of them are greater than zero, therefore it can only be f. e →0, thus obtaining f→f r That is, as t→∞, Under the given assumptions, the actual contact force f at the end can track the expected contact force f. r If the value of parameter ψ is set appropriately so that as t→∞, If this holds true for all time, then we can obtain f→f as t→∞. r Here is a state equation for the vector ψ:

[0167]

[0168] Where P is a constant diagonal matrix, P∈R 2×2 Combining equations (32) and (36), let The equilibrium states of the system are: ψ1 = 0, ψ2 = 0. Choose a valid Lyapunov function:

[0169] V(ψ,t)=ψ T P-1ψ (37)

[0170] Taking the first derivative with respect to V(ψ,t), we get:

[0171]

[0172] From equation (38), we can see that The system then satisfies Lyapunov uniform asymptotic stability at equilibrium points ψ1=0 and ψ2=0. That is, as t→∞, ψ→0, and from equation (32) we can obtain... Therefore, we can deduce that when t→∞, f→f r Therefore, the conclusion is that when the parameter ψ satisfies the state equation (36), the actual end contact force f of the system in a steady state can accurately track the desired contact force f. r .

[0173] Will Substituting into equation (36), we can obtain the estimation laws for environmental location parameters and environmental stiffness parameters as follows:

[0174]

[0175] Where p l p1 and p2 are the diagonal elements of the diagonal matrix P, all of which are positive real constants.

[0176] Combining equations (39) and (29), we finally obtain the parameter estimation expression for the adaptive impedance control model:

[0177]

[0178]

[0179] The adaptive impedance control method is an improved version of the traditional impedance control model. It estimates environmental parameters through real-time feedback of the robot end position and contact force, and adjusts the reference trajectory online, so that the robot end can quickly approach the desired position.

[0180] Example 2

[0181] Embodiment 2 of this disclosure provides a robotic arm grinding control system based on adaptive impedance control, including:

[0182] The model building module is configured to: build a Lagrange dynamics model of the robotic arm;

[0183] The desired trajectory acquisition module is configured to acquire the desired trajectory of the robotic arm's end effector.

[0184] The control method generation module is configured to: generate an adaptive impedance control method that incorporates the uncertainties of the workpiece grinding environment, based on a dynamic model and constrained by the desired trajectory;

[0185] The control module is configured to use an adaptive impedance control method to estimate unknown environmental parameters, update the reference trajectory in real time, adjust the position of the robotic arm end effector, and achieve end-effector contact force tracking.

[0186] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0187] Example 3

[0188] Embodiment 3 of this disclosure provides a medium on which a program is stored, which, when executed by a processor, implements the steps in a robotic arm grinding control method based on adaptive impedance control as described in Embodiment 1 of this disclosure.

[0189] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0190] Example 4

[0191] Embodiment 4 of this disclosure provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the robotic arm grinding control method based on adaptive impedance control as described in Embodiment 1 of this disclosure.

[0192] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0193] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Various modifications and variations can be made to this disclosure by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A robotic arm grinding control method based on adaptive impedance control, characterized in that, Includes the following steps: Establish a Lagrangian dynamics model for the robotic arm; Obtain the desired trajectory of the robotic arm's end effector; Based on the dynamic model and with the desired trajectory as a constraint, an adaptive impedance control method is generated that incorporates the uncertainties of the workpiece grinding environment. By using an adaptive impedance control method, unknown environmental parameters are estimated, the reference trajectory is updated in real time, and the position of the robotic arm end effector is adjusted to achieve end-effector contact force tracking. The adaptive impedance control method estimates unknown environmental parameters using the following expression: in, , These represent the actual contact force and the expected contact force of the grinding robot, respectively. This indicates the error value of the end contact force. This represents an estimated value of the actual contact force. Indicates the system reference trajectory, These represent environmental stiffness and environmental location, respectively. A constant diagonal matrix The diagonal elements are all positive real constants. , This represents the actual displacement of the robot's end effector; The selection of impedance parameters shall satisfy the following rules: in, These represent the inertia matrix, damping matrix, and stiffness matrix in the desired impedance model, respectively. Indicates the target damping ratio. This indicates the stiffness ratio.

2. The robotic arm grinding control method based on adaptive impedance control as described in claim 1, characterized in that, The workpiece to be polished is scanned by a sensor to obtain point cloud data of its surface. The point cloud data of the workpiece to be polished is processed and analyzed to obtain the surface information of the workpiece, calculate the area of ​​the workpiece that needs to be polished, and obtain the workpiece polishing trajectory. The workpiece polishing trajectory is the expected trajectory of the end effector of the robotic arm.

3. The robotic arm grinding control method based on adaptive impedance control as described in claim 1, characterized in that, The Lagrange dynamics model of the robotic arm is as follows: in, These represent the joint vector, joint velocity vector, and joint acceleration vector of the robotic arm, respectively. The inertia matrix representing the robotic arm. The matrix representing the Coriolis force and centripetal force of the robotic arm. The gravity vector representing the robotic arm, This represents the driving torque vector of the robotic arm.

4. The robotic arm grinding control method based on adaptive impedance control as described in claim 1, characterized in that, Based on the dynamic model and constrained by the desired trajectory, an adaptive impedance control method is generated that incorporates uncertainties in the workpiece grinding environment. Specifically: The desired trajectory of the robotic arm end effector is abstracted into first-order and second-order forms of constraints. Assuming that the uncertainty of the system caused by external conditions has a boundary and the boundary is unknown, the system is divided into a nominal part and an uncertain part. For the nominal part, nominal control based on UK theory is adopted, and the control input required to satisfy the constraint is obtained according to the Udwaidia-Kalaba equation; A leakage-type adaptive law is designed for the uncertain part to estimate and effectively compensate for the disturbances and uncertainties caused by external factors in the system.

5. The robotic arm grinding control method based on adaptive impedance control as described in claim 4, characterized in that, The first-order form of the constraint is: in, for The One element, , for Class function, Indicates time, This represents a matrix related to system constraints. Represents functions related to constraints; The above constraints can be rearranged into matrix form: in, ; The second-order form of the constraint is: in, Represents a vector related to constraints; The expression for the adaptive impedance control method is: in, To control the input, As the independent variable, For generalized coordinates, For generalized speed, These are adaptive parameters.

6. A robotic arm grinding control system based on adaptive impedance control, characterized in that, The robotic arm grinding control method based on adaptive impedance control as described in any one of claims 1-5 includes: The model building module is configured to: build a Lagrange dynamics model of the robotic arm; The desired trajectory acquisition module is configured to acquire the desired trajectory of the robotic arm's end effector. The control method generation module is configured to: generate an adaptive impedance control method that incorporates the uncertainties of the workpiece grinding environment, based on a dynamic model and constrained by the desired trajectory; The control module is configured to use an adaptive impedance control method to estimate unknown environmental parameters, update the reference trajectory in real time, adjust the position of the robotic arm end effector, and achieve end-effector contact force tracking.

7. A medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the robotic arm grinding control method based on adaptive impedance control as described in any one of claims 1-5.

8. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the robotic arm grinding control method based on adaptive impedance control as described in any one of claims 1-5.

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