Adaptive impedance control method for robot tracking unknown surfaces

Abstract

The present invention relates to an adaptive impedance control method for a robot to track an unknown surface. This method addresses the problem that traditional impedance control parameters are fixed and cannot adapt to surface mutations. It proposes a solution that integrates dual-modal surface perception and asymmetric impedance adjustment. The surface normal vector and curvature are identified online through an improved recursive method. The normal stiffness is dynamically adjusted based on curvature feedback, the tangential stiffness maintains flexible tracking, and a contact depth constraint mechanism is introduced to prevent overload. The parameter adaptation law is combined with geometric features, the inertia matrix is ​​updated at an accelerated rate in high curvature areas, and the gravity term is corrected preferentially along the normal direction. Compared with traditional methods, the method of the present invention can reduce normal force overshoot, shorten the curvature mutation response time, and improve tangential tracking accuracy.

Description

Technical Field

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

[0002] In the field of compliant robot control, impedance control technology is widely used for interactive tasks in unknown environments. Traditional impedance control methods typically pre-set fixed parameters and are difficult to adapt to sudden changes in surface geometry and changes in material properties, leading to problems such as contact force overshoot and reduced tracking accuracy. Although existing improvement schemes have introduced parameter adaptation mechanisms, they have the following limitations: 1) Online identification of surface geometric parameters (such as normal vectors and curvature) relies on single sensor data fusion, which is easily affected by noise interference during dynamic contact, resulting in estimation lag and control instability; 2) Impedance parameter adjustment often uses an isotropic strategy, which cannot distinguish between normal and tangential degrees of freedom characteristics, and high curvature areas are prone to rigid collisions or tangential slip; 3) Traditional adaptive laws do not fully incorporate surface geometric characteristics, and parameter updates lack physical constraints, which can easily lead to estimation drift. In addition, while anti-disturbance schemes based on sliding mode control can improve robustness, they are prone to introducing high-frequency chattering, which affects precision operation. Summary of the Invention

[0003] The present invention proposes a control method that integrates high-precision surface perception, dynamic adjustment of asymmetric impedance and adaptive geometry drive parameters to improve the tracking accuracy and interactive safety of the robot on unstructured surfaces.

[0004] Specifically, the present invention proposes an adaptive impedance control method for a robot tracking an unknown surface, which includes the following steps:

[0005] (1) Online identification of geometric parameters of unknown surfaces: based on the contact force F at the end of the robot ext With the pose information x, recursively estimate the surface normal vector n and dynamically identify the local curvature κ est ;

[0006] (2) Asymmetric impedance dynamic control: constructing normal stiffness K n Adaptive adjustment, tangential stiffness K t Time-varying impedance model for flexible tracking and design of contact depth constraint mechanism;

[0007] (3) Parameter adaptive update: Dynamically adjust the inertia matrix, Coriolis force term, and gravity term based on the surface geometric parameters to generate control instructions to drive the robot end to track the desired surface.

[0008] Specifically, the method for estimating the surface normal vector n in step (1) is:

[0009]

[0010] Where Γ is the covariance matrix, λ is the forgetting factor, Φ is the force-pose coupling matrix, and β is the curvature feedback gain.

[0011] Specifically, the dynamic identification method of the local curvature in step (1) is:

[0012] Among them, w k is the weight coefficient, A is the gain coefficient, and N is the window size.

[0013] Specifically, the update law of the normal stiffness in step (2) is:

[0014] 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 foundation stiffness, α n is the adjustment parameter, γ n is the decay rate, β n is the sensitivity coefficient.

[0015] Specifically, the tangential stiffness in step (2) is adjusted by dynamically adjusting the proportional relationship between the tangential stiffness and the normal stiffness based on the curvature, and setting a lower limit of the tangential stiffness to prevent the end from sliding out of control.

[0016] Specifically, the damping matrix of the impedance model in step (2) is adjusted as follows: the contact force amplitude is adaptively enhanced by damping according to the S curve; and the normal damping is additionally increased in the high curvature area.

[0017] Specifically, the dynamic adjustment of the inertia matrix in step (3) includes: curvature feedback to accelerate the adjustment of the inertia matrix in high curvature areas; and suppression of parameter drift through leakage factors.

[0018] Specifically, the dynamic adjustment of the gravity term in step (3) includes: constraining the gravity correction direction in the normal vector direction.

[0019] Specifically, the method for estimating 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 by combining the normal vector differential constraint with the principal curvature direction.

[0020] Beneficial technical effects: By integrating improved recursion and fractional differential geometry, the normal vector angle estimation error is reduced, the curvature identification accuracy is improved, and the dynamic modeling capability for unknown complex surfaces is significantly improved; the normal curvature-associated stiffness field is combined with tangential flexible tracking to ensure tangential tracking accuracy while ensuring contact force stability, breaking through the rigid collision and slip problems of traditional isotropic impedance strategies; using contact depth constraints and asymmetric damping adjustment to suppress vibration amplitude in high curvature areas, the robot's ability to work in unstructured scenarios such as aviation skin polishing and medical surgical navigation can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Attachment Figure 1 This is a flow chart of the adaptive impedance control method for a robot tracking an unknown surface according to the present invention.

[0022] Attachment Figure 2 Schematic diagram of the mechanical decomposition of the robot's end effector contacting an unknown surface. DETAILED DESCRIPTION

[0023] like Figure 1 As shown, the present invention discloses an adaptive impedance control method for a robot to track an unknown surface, which includes:

[0024] 1. Online identification of geometric parameters of unknown surfaces

[0025] First, the system dynamics modeling is performed, and Cartesian space dynamics transformation is performed to map the mechanical model of the joint space to the operation space of the robot end effector. The dynamics modeling is specifically as follows:

[0026]

[0027] Where 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-dimensional force sensor and fed back to the control system.

[0028] The Cartesian space dynamic transformation is specifically:

[0029]

[0030] Where 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.

[0031] Afterwards, the joint angle q and the end contact force F are collected. ext, calculate the robot pose, based on the contact force and pose information of the robot end, recursively estimate the normal vector of the unknown surface that the robot end contacts, and dynamically identify the local curvature.

[0032] F ext It can be directly measured by a six-axis force sensor installed at the end, or inferred through joint torque.

[0033] The direction of the normal vector is determined by the surface geometry at the contact point x and is updated through online identification. A forgetting factor is used in the recursive estimation of the normal vector for unknown surfaces to prioritize the most recent data and adapt to sudden surface changes. Curvature feedback correction automatically improves estimation sensitivity and reduces hysteresis errors when the robot end-user operates in areas of high curvature. Normal vector differential constraints, combined with the principal curvature directions, ensure that normal vector changes conform to differential geometry.

[0034] Specifically, the estimation method of the unknown surface normal vector is:

[0035] 1. Set the estimated values ​​of the initial covariance matrix Γ(0) and the initial normal vector n(0)

[0036] 2. Based on the normal vector estimate at the previous moment, calculate the current force-pose coupling matrix Φ(t):

[0037] , where x is the current end position, x s is the initial position of the contact point, which is a measured or estimated value. Different from the real-time change of x, x s As the reference point, K q is the stiffness coefficient and θ is the regularization factor.

[0038] 3. Update the current covariance matrix Γ(t) using the current force-pose coupling matrix Φ(t) and the previous moment covariance matrix Γ(t-1):

[0039]

[0040] Where λ is the forgetting factor, which is preferably 0.98, β is the curvature feedback gain, which is preferably 0.3, and κ est (t-1) is the curvature estimate at the previous moment.

[0041] 4. Based on the current force-pose coupling matrix Φ(t) and contact force F ext (t), recursively calculate the current normal vector estimate:

[0042]

[0043] 5. According to the principal curvatures κ1(t-1), κ2(t-1) and the terminal velocity at the previous moment, apply the normal vector differential constraint to correct the normal vector change rate:

[0044]

[0045] Among them, 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 direction of motion, and e2 is the unit vector in the direction of the cross product of the normal vector and e1. .

[0046] 6. Fuse the recursive estimation and differential constraint results to update the normal vector estimate:

[0047] .

[0048] 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:

[0049]

[0050] 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:

[0051] , .

[0052] During the dynamic identification of curvature, contact force derivative feedback can be introduced to correct the curvature estimation, specifically: , where ζ is the correction gain, which is preferably 0.5.

[0053] 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. The curvature feedback adjusts subsequent control parameters in real time to improve the tracking accuracy of highly curved areas.

[0054] 2. Asymmetric Impedance Dynamic Control

[0055] 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, and the tangential degree of freedom maintains low stiffness flexible tracking. A contact depth constraint mechanism is designed, and the inertia, damping and gravity compensation terms are dynamically updated based on the surface geometric parameters.

[0056] The impedance-controlled stiffness field is designed to have high stiffness in the normal direction and low stiffness in the tangential direction. Specifically, the stiffness is maintained high in the direction perpendicular to the surface, such as 800 N / m, to ensure stable contact force, while the stiffness is reduced along the tangent direction, such as 200 N / m, to allow smooth end-to-end sliding. A safety constraint mechanism is also implemented, setting a maximum allowable contact force, such as 50 N, and a maximum penetration depth, such as 2 mm, to prevent mechanical damage. The deeper the contact, the more nonlinear the stiffness increases, preventing excessive deformation.

[0057] Impedance control is specifically:

[0058] , where F d is the expected contact force, M d is the inertia matrix, K d is the stiffness, B d is the damping, and e is the tracking error.

[0059] Stiffness K d Decomposed into normal stiffness K n and tangential stiffness K t , and define its dynamic relationship as K d =diag([K n ,K n ,K n ,K t ,K t ,K t ]), where the normal stiffness K n Perpendicular to the surface direction, responsible for maintaining the stability of the contact force, tangential stiffness K t Allows smooth sliding along the surface tangent direction.

[0060] The normal stiffness includes the clipping term and the depth protection term. The tanh function in the clipping term smoothly constrains the normal stiffness in [K n0 ,3K n0 ] interval, when K n →3K n0 When the tanh term approaches 1, the value in the bracket approaches 0, which suppresses the stiffness growth. In the depth protection term, when the contact depth δ n >δ max When , the exponential term is activated quickly, forcing the stiffness to decay exponentially.

[0061] The normal stiffness update rate is specifically

[0062] , where F err is the contact force error, that is, F ext With F d The difference, δ n is the normal contact depth, which represents the normal distance between the actual position and the contact point, Γ K is the stiffness adjustment rate, σK is the leakage factor to prevent stiffness drift, K n0 is the normal foundation stiffness, α n is an adjustment parameter, preferably 5, used to control the boundary transition speed, γ n is the decay rate, which is preferably 10, β n is the sensitivity coefficient, which is preferably 20.

[0063] The tangential stiffness update rate includes a safety constraint, that is, a lower limit protection item is set. When K t →K t0 When , the tanh term approaches 0, which inhibits the stiffness from further decreasing. The tangential stiffness update rate is specifically

[0064]

[0065] Among them, δ t is the tangential displacement increment, , represents the small displacement of the end in the tangential direction, K t0 is the tangential foundation stiffness, transition coefficient α t The preferred value is 5, which is used to control the transition steepness of the lower boundary. β(κ) is the dynamic proportional coefficient between the normal stiffness and the tangential stiffness. , where β0 is preferably 0.25, γ is preferably 1.5, Γ K is the stiffness adjustment rate, σ K is the leakage factor, where Γ K , σ K Can be the same as or different from the value in Normal Stiffness.

[0066] The damping can be adjusted adaptively. The greater the contact force, the damping increases according to the S curve to suppress high-frequency vibration. In the high curvature area, the normal damping is increased to prevent end vibration. The dynamic adjustment of the damping matrix is ​​as follows: , where B0 is the basic damping, set according to experience, and η is the damping gain.

[0067] The damping control system is associated with the surface parameters and contact depth to achieve the "soft contact-hard tracking" characteristic.

[0068] 3. Parameter adaptive update and generation of control instructions

[0069] Adjust parameters, output control torque, and drive the end point along the surface. Surface geometric features (normal vector direction, curvature amplitude) are embedded in the parameter adaptation process, overcoming the limitations of traditional isotropic updates. For the inertia matrix, high-curvature areas accelerate inertia matrix adjustments, improving dynamic response. For the gravity term, gravity estimation is primarily corrected along the normal vector direction to reduce tangential interference. Higher normal vector confidence increases gravity compensation weight.

[0070] Λ,μ,p are consistent with the definitions in Cartesian dynamics, but are estimated here. . Specifically:

[0071]

[0072] where Γ Λ ,Γ μ ,Γ p is the adaptive gain matrix of each parameter, which is a positive definite matrix that determines the parameter update speed. It needs to be positive and match the system dynamics. The structure can be determined by Lyapunov stability analysis. The value is debugged by experiment. Λ ,σ μ ,σ p It is the attenuation parameter of each parameter to prevent the estimated value from deviating from the physical reasonable range. It can be set according to experience, usually 0.01~0.1, or optimized based on system robustness analysis. p is the normal gravity gain, which is used to control the correction strength in the normal vector direction, preferably 5, β Λ is the curvature inertia gain, which is used to adjust the influence weight of curvature on the inertia parameter adjustment, preferably 0.3, Λ0 is the nominal value or initial estimate of the inertia matrix, μ0 is the nominal value or initial estimate of the Coriolis force term, and p0 is the nominal value or initial estimate of the gravity term.

[0073] Finally, according to the updated parameters, the command force vector F is generated c , used to drive the end to track the desired motion, F c Specifically:

[0074] , where K p is the proportional gain, K i is the integral gain.

[0075] The method of the present invention achieves high-precision surface tracking through curvature-stiffness coupling, normal vector constrained damping and geometric parameter-driven adaptive laws. Curvature feedback improves the adaptability of complex surfaces, and the asymmetric stiffness field avoids excessive contact force, ensuring the global convergence of control.

Claims

1. An adaptive impedance control method for a robot tracking an unknown surface, characterized in that: The following steps are involved: (1) Online identification of geometric parameters of unknown surfaces: based on the contact force F at the end of the robot ext With the pose information x, recursively estimate the surface normal vector n and dynamically identify the local curvature κ est ; (2) Asymmetric impedance dynamic control: constructing normal stiffness K n Adaptive adjustment, tangential stiffness K t A time-varying impedance model for flexible tracking is developed, and a contact depth constraint mechanism is designed. The damping matrix of the impedance model is adjusted by adaptively enhancing damping along an S-curve for the contact force amplitude and increasing normal damping in high-curvature regions. (3) Parameter adaptive update: Dynamically adjust the inertia matrix, Coriolis force term, and gravity term based on the surface geometry parameters to generate control instructions to drive the robot end to track the desired trajectory.

2. The method according to claim 1, characterized in that The estimation method of the surface normal vector n in step (1) is: , where Γ is the covariance matrix, λ is the forgetting factor, Φ is the force-pose 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 in step (1) is: , 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 in step (2) is: 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 n is the normal stiffness, K n0 is the normal foundation stiffness, α n is the adjustment parameter, γ n is the decay rate, β n is the sensitivity coefficient.

5. The method according to claim 1, wherein The tangential stiffness in step (2) is adjusted by dynamically adjusting the proportional relationship between the tangential stiffness and the normal stiffness based on the curvature, and setting a lower limit for the tangential stiffness to prevent the end from sliding out of control.

6. The method according to claim 1, characterized in that The dynamic adjustment of the inertia matrix in step (3) includes: curvature feedback to accelerate the adjustment of the inertia matrix in high curvature areas; and suppression of parameter drift through leakage factors.

7. The method according to claim 1, characterized in that The dynamic adjustment of the gravity term in step (3) includes: constraining the gravity correction direction in the normal vector direction.

8. The method according to claim 1, characterized in that The method for estimating the surface normal vector in step (1) includes: updating the covariance matrix using a recursive least squares method with a forgetting factor; and correcting the estimated value by combining the normal vector differential constraint with the principal curvature direction.

9. A robot system, characterized in that: Used to execute the control method described in any one of claims 1-8.

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