Self-adaptive impedance control method for robot to track unknown curved surface

Abstract

The invention relates to a self-adaptive impedance control method for a robot to track an unknown curved surface, and aims to solve the problems that traditional impedance control parameters are fixed and cannot adapt to sudden change of the curved surface, a solution integrating bimodal curved surface sensing and asymmetric impedance adjustment is provided, and the normal vector and curvature of the curved surface are identified online through an improved recursion method. The normal stiffness is dynamically adjusted based on curvature feedback, the tangential stiffness keeps flexible tracking, and a contact depth constraint mechanism is introduced to prevent overload. The parameter adaptive law is combined with geometric features, the inertia matrix is accelerated and updated in a high-curvature area, and a gravity item is preferentially corrected in the normal direction. Compared with a traditional method, the method has the advantages that the normal force overshoot can be reduced, the curvature sudden change response time is shortened, and the tangential tracking precision is improved.

Description

Technical Field

[0001] The present invention belongs to the field of robots (robotic arms), and particularly relates to an adaptive impedance control method for a robot to track an unknown surface. Background Art

[0002] In the field of robot compliant control, impedance control technology is widely applied to unknown environment interaction tasks. Traditional impedance control methods usually preset fixed parameters, which are difficult to adapt to sudden changes in surface geometry and changes in material properties, resulting in problems such as contact force overshoot and tracking accuracy degradation. Although existing improved schemes introduce a parameter adaptive mechanism, they have the following limitations: 1) The online identification of surface geometric parameters (such as normal vector, curvature) relies on the data fusion of a single sensor, which is vulnerable to noise interference during dynamic contact, leading to estimation lag and control instability; 2) The adjustment of impedance parameters mostly adopts an isotropic strategy, which cannot distinguish the characteristics of normal / tangential degrees of freedom, and rigid collisions or tangential slips are likely to occur in high-curvature regions; 3) Traditional adaptive laws do not fully combine surface geometric features, and parameter updates lack physical constraints, which are prone to estimation drift. In addition, although the disturbance rejection scheme based on sliding mode control can improve robustness, it is easy to introduce high-frequency chattering, which affects precision operation. Summary of the Invention

[0003] The present invention proposes a control method that combines high-precision surface perception, asymmetric impedance dynamic adjustment, and geometric-driven parameter adaptation to improve the tracking accuracy and interaction safety of a robot on an unstructured surface.

[0004] Specifically, the present invention proposes an adaptive impedance control method for a robot to track an unknown surface, which includes the following steps: (1) Online identify the geometric parameters of the unknown surface: Based on the contact force F ext at the end of the robot and the pose information x, recursively estimate the surface normal vector n, and dynamically identify the local curvature κ est ; (2) Asymmetric impedance dynamic control: Construct a time-varying impedance model with adaptive adjustment of the normal stiffness K n and flexible tracking of the tangential stiffness K t , and design a contact depth constraint mechanism; (3) Parameter adaptive update: Dynamically adjust the inertia matrix, Coriolis force term, and gravity term based on the surface geometric parameters, generate a control command, and drive the end of the robot to track the desired surface.

[0005] Specifically, the estimation method of the surface normal vector n in step (1) is:

[0006] Among them, Γ is the covariance matrix, λ is the forgetting factor, Φ is the force - pose coupling matrix, and β is the curvature feedback gain.

[0007] Specifically, the dynamic identification method of the local curvature in step (1) is as follows: Among them, w k is the weight coefficient, A is the gain coefficient, and N is the window size.

[0008] Specifically, the update law of the normal stiffness in step (2) is as follows: Among them, F err is the contact force error, δ n is the normal contact depth, δ max is the maximum normal contact depth, Γ K is the stiffness adjustment rate, σ K is the leakage factor, K n0 is the normal base stiffness, α n is the adjustment parameter, γ n is the attenuation rate, β n is the sensitivity coefficient.

[0009] Specifically, the adjustment method of the tangential stiffness in step (2) is: dynamically adjust the ratio of the tangential stiffness to the normal stiffness based on the curvature, and set a lower limit for the tangential stiffness to prevent the end - effector from slipping out of control.

[0010] Specifically, the adjustment method of the damping matrix of the impedance model in step (2) is: adaptively enhance the damping of the contact force amplitude according to the S - curve; additionally increase the normal damping in the high - curvature region.

[0011] Specifically, the dynamic adjustment of the inertia matrix in step (3) includes: adjusting the inertia matrix in the high - curvature region more quickly through curvature feedback; suppressing parameter drift through the leakage factor.

[0012] Specifically, the dynamic adjustment of the gravity term in step (3) includes: constraining the direction of the gravity correction in the normal vector direction.

[0013] Specifically, the estimation method of the surface normal vector in step (1) includes: updating the covariance matrix using the recursive least - squares method with a forgetting factor; correcting the estimated value through the combination of normal vector differential constraint and the principal curvature direction. Beneficial technical effects: By integrating and improving recursion and fractional-order differential geometry, the normal vector angle estimation error is reduced, the curvature identification accuracy is improved, and the dynamic modeling ability for unknown complex surfaces is significantly enhanced; the normal curvature-associated stiffness field combined with tangential flexible tracking ensures tangential tracking accuracy while guaranteeing stable contact force, breaking through the rigid collision and slip problems of traditional isotropic impedance strategies; by adopting contact depth constraint and asymmetric damping adjustment, the vibration amplitude in high-curvature regions is suppressed, and the working ability of the robot in unstructured scenarios such as aircraft skin grinding and medical surgical navigation can be improved. Description of the Drawings

[0014] Appendix Figure 1 This is a flowchart of the adaptive impedance control method for a robot to track an unknown surface according to the present invention.

[0015] Appendix Figure 2 This is a schematic diagram of the mechanical decomposition of the end effector of the robot in contact with an unknown surface. Detailed Implementation Manner

[0016] As Figure 1 shown, the present invention discloses an adaptive impedance control method for a robot to track an unknown surface, which includes: I. Online identification of the geometric parameters of the unknown surface First, perform system dynamics modeling and Cartesian space dynamics conversion to map the mechanical model in the joint space to the operation space of the robot end effector. The dynamics modeling is specifically as follows:

[0017] Among them, q is the joint angle vector, M is the inertia matrix, C is the Coriolis force matrix, G is the gravity term, τ is the joint driving torque, J is the Jacobian matrix, and F ext is the contact force vector, which is obtained by measuring the interaction force between the end and the surface through a six-axis force sensor and is fed back to the control system.

[0018] The Cartesian space dynamics conversion is specifically as follows:

[0019] Among them, x is the actual position of the contact point, Λ is the Cartesian inertia matrix, μ is the Cartesian Coriolis force term, p is the Cartesian gravity term, and F c is the command force vector.

[0020] After that, collect the joint angle q and the end contact force F ext , calculate the robot pose, and recursively estimate the normal vector of the unknown surface contacted by the robot end based on the contact force and pose information at the robot end, and dynamically identify the local curvature.

[0021] F extIt can be directly measured by a six-axis force sensor installed at the end, or inferred by joint torque.

[0022] The direction of the normal vector is determined by the surface geometry at the contact point position x and updated through online identification. In the recursive estimation of the normal vector of an unknown surface, a forgetting factor is used to give priority to the latest data and adapt to surface mutations; through curvature feedback correction, when the robot end operates in a high-curvature area, the estimation sensitivity is automatically increased and the lag error is reduced; through normal vector differential constraint, combined with the principal curvature direction, it is ensured that the change of the normal vector conforms to the laws of differential geometry.

[0023] Specifically, the method for estimating the normal vector of an unknown surface is as follows: 1. Set the initial covariance matrix Γ(0) and the estimated value of the initial normal vector n(0) 2. Based on the normal vector estimation at the previous moment, calculate the current force-pose coupling matrix Φ(t): , where x is the current end position, and x s is the initial position of the contact point, which is a measured or estimated value and is different from the real-time change of x. x s is the reference point, K q is the stiffness coefficient, and θ is the regularization factor.

[0024] 3. Use the current force-pose coupling matrix Φ(t) and the covariance matrix Γ(t - 1) at the previous moment to update the current covariance matrix Γ(t):

[0025] where λ is the forgetting factor, λ is preferably 0.98, β is the curvature feedback gain, preferably 0.3, and κ est (t - 1) is the curvature estimation value at the previous moment.

[0026] 4. Based on the current force-pose coupling matrix Φ(t) and the contact force F ext (t), recursively calculate the current normal vector estimated value:

[0027] 5. According to the principal curvatures κ1(t - 1), κ2(t - 1) and the end velocity at the previous moment, apply the normal vector differential constraint to correct the normal vector change rate:

[0028] where κ1 and κ2 are the principal curvature components, e1 and e2 are the tangent space basis vectors, e1 is the unit tangent vector along the motion direction, and e2 is the unit vector in the direction of the cross product of the normal vector and e1. .

[0029] 6. Fusion of recursive estimation and differential constraint results, update normal vector estimate: .

[0030] In the process of curvature dynamic identification, the synthetic curvature estimate κ est The basic curvature term and the fractional differential term are integrated to calculate the local curvature based on the cross product amplitude of the normal vector change rate and the terminal velocity. The historical motion data is introduced through the fractional term to enhance the sensitivity to small curvature changes. Specifically, the synthetic curvature estimate κ est for:

[0031] Among them, A is the gain coefficient, preferably 1.2, N is the window size, and the weight coefficient w is k Calculated according to the fractional order α, α is preferably 0.7, specifically: , .

[0032] In the process of curvature dynamic identification, contact force derivative feedback can be introduced to correct the curvature estimation, specifically: , where ζ is the correction gain, which is preferably 0.5.

[0033] Through dual-modal surface perception, the normal vector and curvature estimation are verified against each other, so that it can adapt to sudden changes in complex surfaces, such as the transition from a plane to a groove, and the curvature feedback adjusts subsequent control parameters in real time to improve the tracking accuracy of highly curved areas.

[0034] 2. Asymmetric impedance dynamic control like Figure 2 As shown in the figure, the contact force exerted by the robot end on the surface can be decomposed into normal force and tangential force, so an asymmetric time-varying impedance model can be constructed. The normal degree of freedom adopts the curvature-related stiffness field adaptive adjustment, the tangential degree of freedom maintains low stiffness flexible tracking, and a contact depth constraint mechanism is designed. The inertia, damping and gravity compensation items are dynamically updated based on the surface geometric parameters. The stiffness field of impedance control is designed to have high stiffness in the normal direction and low stiffness in the tangential direction, that is, to maintain high stiffness in the direction perpendicular to the surface, such as 800N / m, to ensure stable contact force, and reduce stiffness along the tangent direction of the surface, such as 200N / m, to allow smooth sliding of the end. At the same time, a safety constraint mechanism is set to set the maximum allowable contact force, such as 50N, and the maximum penetration depth, such as 2mm, to prevent mechanical damage. The deeper the contact, the nonlinear increase in stiffness to avoid excessive deformation.

[0035] Impedance control is as follows: , where F d is the expected contact force, M dis the inertia matrix, K d is the stiffness, B d is the damping, and e is the tracking error.

[0036] The stiffness K d is decomposed into the normal stiffness K n and the tangential stiffness K t , and their dynamic relationship is defined as K d = diag([K n , K n , K n , K t , K t , K t ), where the normal stiffness K n is perpendicular to the surface direction and is responsible for maintaining the contact force stability, and the tangential stiffness K t is along the surface tangent direction and allows smooth sliding.

[0037] The normal stiffness includes a limiting term and a depth protection term. The tanh function in the limiting term smoothly constrains the normal stiffness within the interval [K n0 , 3K n0 . When K n →3K n0 , the tanh term approaches 1, causing the term in the brackets to approach 0 and suppressing the stiffness growth. In the depth protection term, when the contact depth δ n > δ max , the exponential term is quickly activated, forcing the stiffness to decay exponentially.

[0038] The update rate of the normal stiffness is specifically , where F err is the contact force error, that is, the difference between F ext and F d , δ n is the normal contact depth, representing the normal distance between the actual position and the contact point, Γ K is the stiffness adjustment rate, σ K is the leakage factor to prevent stiffness drift, K n0 is the normal base stiffness, α n is the adjustment parameter, which is preferably 5 and is used to control the boundary transition speed, γ n is the decay rate, which is preferably 10, and β n is the sensitivity coefficient, which is preferably 20.

[0039] The update rate of the tangential stiffness includes a safety constraint, that is, a lower limit protection term is set. When K t →K t0 , the tanh term approaches 0, suppressing the further decrease of the stiffness. The update rate of the tangential stiffness is specifically

[0040] Among them, δ t is the tangential displacement increment, , representing the tiny displacement of the end in the tangential direction, and K t0 is the tangential base stiffness, and the transition coefficient α t is preferably 5, used to control the transition steepness of the lower limit boundary, and β(κ) is the dynamic proportional coefficient of the normal stiffness to the tangential stiffness, , where β0 is preferably 0.25, γ is preferably 1.5, and Γ K is the stiffness adjustment rate, and σ K is the leakage factor. Here, Γ K and σ K can be the same as or different from the values in the normal stiffness.

[0041] The damping can be adaptively adjusted. The greater the contact force, the damping increases according to the S curve, suppressing high-frequency vibrations, and additionally increasing the normal damping in high-curvature regions to prevent the end from jittering. The specific dynamic adjustment of the damping matrix is , where B0 is the base damping, set according to experience, and η is the damping gain.

[0042] The damping control system is associated with the surface parameters and the contact depth, realizing the "soft contact - hard tracking" characteristic.

[0043] III. Parameter Adaptive Update and Generation of Control Commands Adjust the parameters, output the control torque, and drive the end to move along the surface. Embed the surface geometric features (normal vector direction, curvature amplitude) into the parameter adaptive process, breaking through the limitations of traditional isotropic updates. For the inertia matrix, accelerate the adjustment of the inertia matrix in high-curvature regions to improve the dynamic response speed. For the gravity term, mainly correct the gravity estimation along the normal vector direction to reduce tangential interference. The higher the confidence of the normal vector, the greater the gravity compensation weight.

[0044] Λ, μ, p are defined the same as in Cartesian dynamics, but here they are estimated values . Specifically:

[0045] Among them, Γ Λ , Γ μ , Γ p are the adaptive gain matrices of each parameter. It is a positive definite matrix, which determines the parameter update speed. It needs to be positive definite and match the system dynamics. Its structure can be determined through Lyapunov stability analysis, and the numerical values are debugged through experiments. σ Λ , σ μ , σ pis the attenuation parameter of each parameter, which prevents the estimated value from deviating from the physically reasonable range. It can be set according to experience, usually 0.01 - 0.1, or optimized based on the system robustness analysis, γ p is the normal gravity gain, which is used to control the correction intensity in the normal vector direction, and is preferably 5, β Λ is the curvature inertia gain, which is used to adjust the influence weight of curvature on the inertial parameter adjustment. It is preferably 0.3, Λ0 is the nominal value or initial estimated value of the inertia matrix, μ0 is the nominal value or initial estimated value of the Coriolis force term, and p0 is the nominal value or initial estimated value of the gravity term.

[0046] Finally, according to the updated parameters, the command force vector F c is generated to drive the end effector to track the desired motion, F c Specifically: , where K p is the proportional gain, K i is the integral gain.

[0047] The method of the present invention realizes high-precision surface tracking through the curvature-stiffness coupling, normal vector constraint damping, and geometric parameter-driven adaptive law. The curvature feedback improves the adaptability to complex surfaces, and the asymmetric stiffness field avoids excessive contact force, ensuring the global convergence of the control.

Claims

1. An adaptive impedance control method for a robot to track an unknown surface, characterized in that, It includes the following steps: (1) Online identification of geometric parameters of unknown surfaces: Based on the contact force F at the end of the robot ext and the pose information x, recursively estimate the surface normal vector n and dynamically identify the local curvature κ est ; (2) Asymmetric impedance dynamic control: construct the normal stiffness K n Adaptive adjustment, tangential stiffness K t Time-varying impedance model for flexible tracking, and design a contact depth constraint mechanism; (3) Parameter adaptive update: Dynamically adjust the inertia matrix, Coriolis force term, and gravity term based on the surface geometric parameters to generate control commands and drive the end of the robot to track the desired trajectory.

2. The method according to claim 1, wherein The estimation method of the surface normal vector n described in step (1) is as follows: , where Γ is the covariance matrix, λ is the forgetting factor, Φ is the force-position coupling matrix, and β is the curvature feedback gain.

3. The method according to claim 1, characterized in that, The dynamic identification method of the local curvature described in step (1) is as follows: , where w k is the weight coefficient, A is the gain coefficient, and N is the window size.

4. The method according to claim 1, wherein The update law of the normal stiffness described in step (2) is as follows: Among them, F err is the contact force error, δ n is the normal contact depth, δ max is the maximum normal contact depth, Γ K is the stiffness adjustment rate, σ K is the leakage factor, K n0 is the normal base stiffness, α n is the adjustment parameter, γ n is the attenuation rate, β n is the sensitivity coefficient.

5. The method according to claim 1, wherein The adjustment method of the tangential stiffness described in step (2) is: Dynamically adjust the ratio of the tangential stiffness to the normal stiffness based on the curvature, and set the lower limit of the tangential stiffness to prevent out-of-control sliding at the end.

6. The method according to claim 1, wherein The adjustment method of the damping matrix of the impedance model in step (2) is: The contact force amplitude adaptively enhances the damping according to the S curve; additionally increases the normal damping in the high-curvature region.

7. The method according to claim 1, wherein The dynamic adjustment of the inertia matrix described in step (3) includes: Curvature feedback accelerates the adjustment of the inertia matrix in the high-curvature region; suppresses parameter drift through the leakage factor.

8. The method according to claim 1, wherein The dynamic adjustment of the gravity term described in step (3) includes: The direction of the normal vector constrains the correction direction of the gravity.

9. The method according to claim 1, characterized in that The estimation method of the surface normal vector described in step (1) includes: Update the covariance matrix using the recursive least squares method with a forgetting factor; correct the estimated value through the combination of normal vector differential constraint and the principal curvature direction.

10. A robot system, characterized in that, It is used to execute any one of the control methods described in claims 1-9.

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