Sliding mode control method for robot to track unknown curved surface

Abstract

The invention relates to a sliding-mode control method for a robot to track an unknown curved surface. The sliding-mode control method comprises the following steps: establishing a Cartesian space dynamic model in an initialization stage; in the online operation stage, through feedback of a six-dimensional force sensor, recursively estimating a normal vector of an unknown curved surface and dynamically identifying a local curvature, and realizing robust estimation of the normal vector and the curvature in combination with recursion factor preferential data updating, curvature feedback correction and differential geometric constraint; a geometric sensitive sliding mode controller is designed, tracking errors are decomposed into normal and curvature weighted tangential components, noise is suppressed through fractional order differential, the control weight is adjusted in a self-adaptive mode, and the tracking precision is enhanced in a curvature sudden change area; a parameter adaptive mechanism is introduced, a normal vector direction and a curvature amplitude are embedded into a kinetic parameter updating law, and the dynamic adaptability to a complex curved surface is improved; and finally generating instruction force to drive the end effector to move along the curved surface.

Description

Technical Field

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

[0002] Existing robot surface tracking control methods are mostly based on fixed models or offline calibration, which are difficult to adapt to the geometric mutations of unknown surfaces (such as curvature jumps and rapid changes in normal vectors), resulting in problems such as insufficient tracking accuracy and excessive contact force. Traditional sliding mode control is prone to tangential error accumulation due to isotropic gain on complex surfaces, and parameter updates lack geometric sensitivity, making it impossible to dynamically adjust the normal and tangential control weights. In addition, online estimation of normal vectors and curvature often produces hysteresis errors due to sensor noise or motion coupling, affecting control stability. Summary of the invention

[0003] The present invention discloses a sliding mode control method for a robot to track an unknown curved surface, which comprises: 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 basic 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, suppress noise through fractional differentials, and adaptively adjust the control weights. The dynamic parameters are updated based on the normal vector direction and curvature amplitude, and the command force vector is generated to drive the robot end to move along the surface.

[0004] Specifically, the sliding surface of the sliding mode controller includes a normal error term, a curvature-weighted tangential error term, a fractional-order differential term and an integral term, wherein the fractional-order differential term is used to suppress high-frequency noise, and the integral term is used to eliminate steady-state errors.

[0005] Specifically, the sliding surface is:

[0006] 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 gain.

[0007] Specifically, 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 negatively correlated with the system damping.

[0008] Specifically, the reaching law of the sliding mode controller includes a geometric adaptive gain term and a curvature damping term.

[0009] Specifically, the reaching law of the sliding mode controller is: , where k1 0 is the basic gain factor.

[0010] Specifically, 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.

[0011] Specifically, the dynamic parameter update is as follows:

[0012] 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 attenuation parameter of each parameter.

[0013] Specifically, the command force vector is: Where K p is the curvature adaptive proportional gain, K d is the normal damping gain.

[0014] Beneficial technical effects: Through recursive estimation of normal vector and dynamic curvature identification, it can adapt to surface geometric mutations in real time and reduce tracking lag errors; design geometry-sensitive sliding mode control, combine fractional-order differentials with curvature weighted error decomposition, and automatically enhance the tangential control weight in the curvature mutation area, taking into account both noise suppression and tracking accuracy; the parameter update law deeply integrates surface geometric features (normal vector direction, curvature amplitude) to improve the adaptability of the dynamic model to complex surfaces; introduce recursive factors and curvature feedback correction mechanisms to enhance the robustness of online estimation and avoid estimation deviations caused by sensor noise or motion coupling; through multi-component synthesis of the command force vector, smooth motion and stable contact of the end effector are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Attached Figure 1 The present invention is a flow chart of the sliding mode control method for a robot to track an unknown surface.

[0016] Attached Figure 2Schematic diagram of the normal vector and curvature of an unknown surface tracked by a robot. Detailed implementation manners

[0017] The present invention discloses a sliding mode control method for a robot to track an unknown surface, as Figure 1 shown, which includes: I. Initialization stage Perform system dynamics modeling and conduct Cartesian space dynamics conversion to map the mechanical model in the joint space to the operation space of the robot end effector. Specifically:

[0018] 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, 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 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, F c is the commanded force vector.

[0019] II. Online operation stage 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-axis force sensor installed at the end or deduced by joint torques.

[0020] 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 and combined with the principal curvature direction, it is ensured that the change of the normal vector conforms to the differential geometry law.

[0021] Specifically, the estimation method of the normal vector of the unknown surface is: 1. Set the initial covariance matrix Γ(0) and the estimated value of the initial normal vector n(0) 2. Calculate the current force-pose coupling matrix Φ(t) based on the normal vector estimation at the previous moment: , where x is the current end 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, xs is the reference point, and K q is the stiffness coefficient, and θ is the regularization factor.

[0022] 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: .

[0023] Among them, 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 estimate at the previous moment.

[0024] 4. Based on the current force - pose coupling matrix Φ(t) and the contact force F ext (t), recursively calculate the current normal vector estimate: .

[0025] 5. According to the principal curvatures κ1(t - 1), κ2(t - 1) and the end - effector velocity at the previous moment, apply the normal vector differential constraint to correct the normal vector change rate: .

[0026] Among them, 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, .

[0027] 6. Fusion of the recursive estimation and the differential constraint results to update the normal vector estimate: .

[0028] During the curvature dynamic identification process, the synthetic curvature estimate κ est Fuses the basic curvature term and the fractional - order differential term. Based on the magnitude of the cross - product of the normal vector change rate and the end - effector velocity, calculate the local curvature. Through the fractional - order term, introduce historical motion data to enhance the sensitivity to small curvature changes. Specifically, the synthetic curvature estimate κ est is:

[0029] Among them, 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: , .

[0030] During the curvature dynamic identification process, the contact force derivative feedback can be introduced to correct the curvature estimate, specifically: , where ζ is the correction gain, preferably 0.5.

[0031] Through bimodal surface perception, the normal vector and curvature estimation are mutually verified, so as to adapt to complex surfaces with mutations, such as transitioning from a plane to a groove, and the curvature feedback adjusts subsequent control parameters in real time, improving the tracking accuracy in highly curved regions.

[0032] III. Geometrically sensitive sliding mode control The sliding mode control of the present invention decomposes the tracking error into a normal component and a curvature-weighted tangential component. The tangential error term considers the real-time curvature estimation value. The higher the curvature, the higher the requirement for tangential tracking accuracy. At the same time, through fractional-order differentiation, the noise suppression characteristics of the sliding mode control are retained, so that in regions with large curvature, such as protrusions / depressions, the tangential control weight is automatically enhanced, and in flat regions, it tends to a pure normal tracking mode, reducing energy consumption. The sliding mode surface is specifically:

[0033] where e is the tracking error, δ is the fractional-order order of the sliding mode surface, used to control the attenuation rate of historical errors, 0.6 < δ < 0.9, preferably 0.7, α1 is the fractional-order term gain, used to adjust the contribution of the fractional-order integral to the sliding mode surface, α1 is positively correlated with the tracking speed, 10 ≤ α1 ≤ 20; α2 is the integral term gain, used to eliminate the steady-state error, and is inversely correlated with the system damping, 3 ≤ α2 ≤ 8.

[0034] 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 rate of change of the normal vector, and the gain can be adaptively adjusted. The curvature damping term is used to prevent overcompensation during high-speed movement, and the control quantity overflow is avoided through curvature limiting. The reaching law is specifically: , where k1 0 is the basic gain coefficient, 5 ≤ k1 0 ≤ 15.

[0035] IV. Execution Adjust the parameters, output the control torque, and drive the end of the robot to move along the surface. Embed the surface geometric features, including the normal vector direction, curvature amplitude, etc., into the parameter adaptive process, breaking through the limitations of traditional isotropic updates. The parameters Λ, μ, p are consistent with the definitions in Cartesian dynamics, but are estimated values here .

[0036] The Cartesian inertia matrix Λ focuses the parameter learning on the normal direction by means of the curvature-weighted normal acceleration component. The Cartesian Coriolis force term μ introduces the coupling of the rate of change of the normal vector and the velocity, which can reflect the influence of the 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: , where Γ Λ , Γ μ , Γ p is the adaptive gain matrix of each parameter. It is a positive definite matrix that 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 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. It can be set according to experience, usually 0.01~0.1, or optimized based on the system robustness analysis.

[0037] Generate the command force vector F c , which is used to drive the end effector to track the desired motion. F c Specifically: , where K p is the curvature adaptive proportional gain, and K d is the normal damping gain.

[0038] This scheme deeply couples the surface geometric features with the parameter learning process, significantly improving the system's adaptability to complex surfaces while ensuring stability, providing a new solution for the precise surface operation of robots.

Claims

1. A sliding mode control method for a robot to track an unknown surface, characterized in that, Including: Establish a Cartesian space dynamics model; Online recursively estimate the surface normal vector, and update the normal vector by combining the recurrence factor, curvature feedback correction, and differential geometry constraints; Dynamically identify the local curvature, and fuse the basic curvature term and the fractional order differential term to enhance the sensitivity to small curvature changes; Design a geometry-sensitive sliding mode controller, decompose the tracking error into a normal component and a curvature-weighted tangential component, suppress noise through fractional order differentiation, and adaptively adjust the control weight; Update the dynamic parameters based on the normal vector direction and curvature amplitude, and generate a command force vector to drive the end of the robot to move along the surface; 2. The method according to claim 1, characterized in that, The sliding surface of the sliding mode controller includes a normal error term, a curvature-weighted tangential error term, a fractional order differential term, and an integral term; 3. The method according to claim 1, wherein The sliding surface is specifically: , where n is the normal vector, κ est is the composite curvature, e is the tracking error, δ is the fractional order of the sliding surface, α1 is the fractional order term gain, and α2 is the integral term gain.

4. The method according to claim 3, characterized in that, The fractional order order δ of the sliding surface satisfies 0.6 < δ < 0.9, and the fractional order term 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, characterized in that The reaching law of the sliding mode controller is specifically: , where k1 0 is the basic gain coefficient.

7. The method according to claim 1, wherein The update of the dynamic parameters includes the online adjustment of the inertia matrix, Coriolis force term, and gravity term, where 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; 8. The method according to claim 1, wherein The update of the dynamic parameters is specifically: , 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, For implementing the control method described in any one of claims 1-9.

Images