Sliding Mode Control Method for a Robot to Track an Unknown Surface

Abstract

The present invention relates to a sliding mode control method for a robot to track an unknown surface, which includes: establishing a Cartesian space dynamics model in the initialization stage; in the online operation stage, through the feedback of a six-axis force sensor, recursively estimating the normal vector of the unknown surface and dynamically identifying the local curvature, combining the recurrence factor to preferentially update data, curvature feedback correction and differential geometry constraints to achieve robust estimation of the normal vector and curvature; designing a geometry-sensitive sliding mode controller, decomposing the tracking error into normal and curvature-weighted tangential components, suppressing noise through fractional-order differentiation and adaptively adjusting the control weights to enhance the tracking accuracy in the curvature mutation region; introducing a parameter adaptive mechanism, embedding the normal vector direction and curvature amplitude into the dynamics parameter update law to improve the dynamic adaptability to complex surfaces; and finally generating a command force to drive the end effector to move along the surface.

Description

Technical Field

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

[0002] Existing robotic surface tracking control methods are mostly based on fixed models or offline calibration, making them difficult to adapt to sudden geometric changes on unknown surfaces (such as curvature jumps and rapid changes in normal vectors). This leads to problems such as insufficient tracking accuracy and excessive contact forces. Traditional sliding mode control on complex surfaces is prone to tangential error accumulation due to isotropic gains. Parameter updates lack geometric sensitivity, making it impossible to dynamically adjust normal and tangential control weights. Furthermore, online estimation of normal vectors and curvature often suffers from hysteresis errors due to sensor noise or motion coupling, compromising control stability. Summary of the Invention

[0003] The present invention discloses a sliding mode control method for a robot to track an unknown surface, which comprises:

[0004] Establish a Cartesian space dynamics model;

[0005] Online recursive estimation of surface normal vectors, combining recursive factors, curvature feedback corrections, and differential geometry constraints to update normal vectors;

[0006] Dynamically identify local curvature and fuse the fundamental curvature term with the fractional differential term to enhance the sensitivity to small curvature changes;

[0007] A geometry-sensitive sliding mode controller is designed to decompose the tracking error into a normal component and a curvature-weighted tangential component. The noise is suppressed by fractional differentiation and the control weights are adaptively adjusted.

[0008] The dynamic parameters are updated based on the normal vector direction and curvature amplitude, and a command force vector is generated to drive the robot end to move along the surface.

[0009] Specifically, the sliding surface of the sliding mode controller includes a normal error term, a curvature-weighted tangential error term, a fractional differential term, and an integral term, wherein the fractional differential term is used to suppress high-frequency noise, and the integral term is used to eliminate steady-state errors.

[0010] Specifically, the sliding surface is:

[0011]

[0012] Where n is the normal vector, κ est is the synthetic curvature, e is the tracking error, δ is the fractional order of the sliding surface, α1 is the fractional order gain, and α2 is the integral term gain.

[0013] Specifically, the fractional order δ of the sliding surface satisfies 0.6 < δ < 0.9, and the gain α1 of the fractional order term is positively correlated with the tracking speed, and the gain α2 of the integral term is inversely correlated with the system damping.

[0014] Specifically, the reaching law of the sliding mode controller includes a geometric adaptive gain term and a curvature damping term.

[0015] Specifically, the reaching law of the sliding mode controller is specifically:

[0016] , where k1 0 is the basic gain coefficient.

[0017] Specifically, the update of the dynamic parameters includes the online adjustment of the inertia matrix, the Coriolis force term, and the gravity term. Among them, the inertia matrix is updated by the curvature weighted normal acceleration component, the Coriolis force term fuses the normal vector change rate and the end velocity, and the gravity term is compensated by quadratic projection based on the normal component of the sliding surface.

[0018] Specifically, the update of the dynamic parameters is specifically:

[0019]

[0020] where Λ is the Cartesian inertia matrix, μ is the Cartesian Coriolis force term, p is the Cartesian gravity term, Γ Λ , Γ μ , Γ p is the adaptive gain matrix of each parameter, and σ Λ , σ μ , σ p is the decay parameter of each parameter.

[0021] Specifically, the command force vector is specifically:

[0022] where K p is the curvature adaptive proportional gain, and K d is the normal damping gain.

[0023] Beneficial technical effects: Through recursive estimation of the normal vector and dynamic curvature identification, it can adapt to sudden changes in surface geometry in real time and reduce the tracking lag error; Design a geometry-sensitive sliding mode control, combined with fractional order differentiation and curvature weighted error decomposition, automatically enhance the tangential control weight in the curvature mutation area, taking into account noise suppression and tracking accuracy; The parameter update law deeply integrates surface geometric features (normal vector direction, curvature amplitude), improving the adaptability of the dynamic model to complex surfaces; Introduce a recurrence factor and a curvature feedback correction mechanism to enhance the robustness of online estimation and avoid estimation errors caused by sensor noise or motion coupling; Through the multi-component synthesis of the command force vector, smooth motion and stable contact of the end effector are achieved. Description of the Drawings

[0024] Appendix Figure 1 It is the flowchart of the sliding mode control method for a robot to track an unknown surface according to the present invention.

[0025] Appendix Figure 2 It is the schematic diagram of the normal vector and curvature of the unknown surface tracked by the robot. Specific Embodiment

[0026] The present invention discloses a sliding mode control method for a robot to track an unknown surface. As Figure 1 shown, it includes:

[0027] I. Initialization Stage

[0028] Perform system dynamics modeling and carry out Cartesian space dynamics conversion to map the mechanical model in the joint space to the operation space of the robot end effector. Specifically:

[0029]

[0030] 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 - dimensional force sensor and is fed back to the control system. 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 commanded force vector.

[0031] II. Online Operation Stage

[0032] 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. F ext can be directly measured by a six - dimensional force sensor installed at the end or deduced by joint torques.

[0033] As Figure 2 shown, the direction n of the normal vector is determined by the surface geometry at the contact point position x and is updated through online identification. In the recursive estimation of the normal vector of the 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 differential geometry law.

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

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

[0036] 2. Calculate the current force - pose coupling matrix Φ(t) based on the normal vector estimation at the previous moment:

[0037] , where x is the current end - effector position, 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.

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

[0039] .

[0040] 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.

[0041] 4. Recursively calculate the current normal vector estimation value based on the current force - pose coupling matrix Φ(t) and the contact force F ext (t):

[0042] .

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

[0044] .

[0045] where κ₁, κ₂ are the principal curvature components, e₁, 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, .

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

[0047] .

[0048] During the curvature dynamic identification process, synthesize the curvature estimation value κ estFuse the basic curvature term and the fractional derivative term. Based on the magnitude of the cross product of the normal vector change rate and the end velocity, calculate the local curvature. Through the fractional term, introduce historical motion data to enhance the sensitivity to small curvature changes. Specifically, synthesize the curvature estimate value κ est is:

[0049]

[0050] where A is the gain coefficient, preferably 1.2, N is the window size, and the weight coefficient w k is calculated according to the fractional order α, and α is preferably 0.7. Specifically:

[0051] , .

[0052] In the process of curvature dynamic identification, the contact force derivative feedback can be introduced to correct the curvature estimate. Specifically: , where ζ is the correction gain, and it is preferably 0.5.

[0053] Through bimodal surface perception, the normal vector and the curvature estimate are mutually verified, so as to adapt to the complex surface with mutations, such as transitioning from a plane to a groove, and the curvature feedback adjusts the subsequent control parameters in real time to improve the tracking accuracy in the high-curvature area.

[0054] III. Geometrically sensitive sliding mode control

[0055] The sliding mode control of the present invention decomposes the tracking error into a normal component and a tangential component weighted by curvature. The tangential error term considers the real-time curvature estimate value. The greater the curvature, the higher the requirement for tangential tracking accuracy. At the same time, through fractional differentiation, the noise suppression characteristics of the sliding mode control are retained. Therefore, in the area with a large curvature, such as a protrusion / depression, the tangential control weight is automatically enhanced, and in the flat area, it tends to a pure normal tracking mode to reduce energy consumption. The sliding mode surface is specifically:

[0056]

[0057] where e is the tracking error, δ is the fractional order of the sliding mode surface, which is used to control the attenuation rate of the historical error, 0.6 < δ < 0.9, preferably 0.7, α1 is the fractional term gain, which is used to adjust the contribution of the fractional integral to the sliding mode surface, α1 is positively correlated with the tracking speed, 10 ≤ α1 ≤ 20; α2 is the integral term gain, which is used to eliminate the steady-state error and is inversely correlated with the system damping, 3 ≤ α2 ≤ 8.

[0058] The reaching law includes a geometric adaptive term and a curvature damping term. The geometric adaptive term includes a gain strengthening mechanism, which can combine the normal vector change rate, and the gain can be adaptively adjusted. The curvature damping term is used to prevent overcompensation during high-speed motion, and the control quantity overflow is avoided through curvature limiting. The reaching law is specifically:

[0059] , where k1 0 is the base gain coefficient, 5 ≤ k1 0 ≤ 15.

[0060] IV. Execution

[0061] Adjust the parameters, output the control torque, and drive the end of the robot to move along the curved surface. Embed the geometric features of the curved surface, including the normal vector direction, curvature amplitude, etc., into the parameter adaptation process, breaking through the limitations of traditional isotropic updates. The parameters Λ, μ, p are consistent with the definitions in Cartesian dynamics, but here they are estimated values .

[0062] For the Cartesian inertia matrix Λ, by weighting the normal acceleration component with curvature, the parameter learning is concentrated in the normal direction. The Cartesian Coriolis force term μ introduces the coupling of the normal vector change rate and velocity, which can reflect the influence of the curved surface geometric dynamics on the Coriolis force and enhance the parameter sensitivity of the tangential motion. The Cartesian gravity term p extracts the component of the sliding mode surface in the normal direction and realizes the specific compensation of the contact force through quadratic projection, suppressing the interference of the tangential error on the gravity estimation. Specifically:

[0063] , where Γ Λ , Γ μ , Γ p is the adaptive gain matrix of each parameter, which is a positive definite matrix, determines the parameter update speed, needs to be positive definite and match the system dynamics, and its structure can be determined through Lyapunov stability analysis, and the numerical value is debugged by experiments. σ Λ , σ μ , σ p is the decay parameter of each parameter, which prevents the estimated value from deviating from the physically reasonable range, can be set according to experience, usually 0.01~0.1, or optimized based on the system robustness analysis.

[0064] Generate the command force vector F c , which is used to drive the end to track the desired motion. F c Specifically:

[0065] , where K p is the curvature adaptive proportional gain, and K d is the normal damping gain.

[0066] This scheme deeply couples the geometric features of the curved surface with the parameter learning process, significantly improving the adaptability of the system to complex curved surfaces while ensuring stability, providing a new solution for the precise curved surface operation of robots.

Claims

1. A sliding mode control method for a robot to track an unknown surface, characterized in that, include: Establish a Cartesian space dynamics model; Online recursive estimation of surface normal vectors, combining recursive factors, curvature feedback corrections, and differential geometry constraints to update normal vectors; Dynamically identify local curvature and fuse the fundamental curvature term with the fractional differential term to enhance the sensitivity to small curvature changes; A geometry-sensitive sliding mode controller is designed to decompose the tracking error into a normal component and a curvature-weighted tangential component. The noise is suppressed by fractional differentiation and the control weights are adaptively adjusted. The dynamic parameters are updated based on the normal vector direction and curvature amplitude, and a command force vector is generated to drive the robot end to move along the surface.

2. The method according to claim 1, wherein The sliding mode surface of the sliding mode controller includes a normal error term, a curvature-weighted tangential error term, a fractional differential term, and an integral term.

3. The method according to claim 1, characterized in that, The sliding surface is as follows: , where n is the normal vector, κ est is the synthetic curvature, e is the tracking error, δ is the fractional order of the sliding mode surface, α1 is the fractional order term gain, and α2 is the integral term gain.

4. The method according to claim 3, wherein The fractional order δ of the sliding surface satisfies 0.6<δ<0.9, and the fractional order gain α1 is positively correlated with the tracking speed, and the integral term gain α2 is inversely correlated with the system damping.

5. The method according to claim 1, wherein The reaching law of the sliding mode controller includes a geometric adaptive gain term and a curvature damping term.

6. The method according to claim 1, wherein The reaching law of the sliding mode controller is specifically: , where k1 0 is the base gain coefficient.

7. The method according to claim 1, characterized in that The dynamic parameter update includes online adjustment of the inertia matrix, Coriolis force term and gravity term, wherein the inertia matrix is updated by the curvature-weighted normal acceleration component, the Coriolis force term integrates the normal vector change rate and the terminal velocity, and the gravity term is compensated by secondary projection based on the normal component of the sliding surface.

8. The method according to claim 1, characterized in that, The dynamic parameter update is specifically as follows: , where Λ is the Cartesian inertia matrix, μ is the Cartesian Coriolis force term, p is the Cartesian gravity term, Γ Λ , Γ μ , Γ p is the adaptive gain matrix of each parameter, σ Λ , σ μ , σ p is the decay parameter of each parameter.

9. The method according to claim 1, characterized in that, The command force vector is specifically: where K p is the curvature adaptive proportional gain, and K d is the normal damping gain.

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

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