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Singularity-Avoidance Control of Robotic Systems with Model Mismatch and Actuator Constraints

Mingkun Wu, Alisa Rupenyan, Burkhard Corves

TL;DR

This paper proposes a learning-based control strategy to prevent robots entering singularity regions by leveraging Gaussian process (GP) regression to learn the unknown model mismatch, where the prediction error is restricted by a deterministic bound.

Abstract

Singularities, manifesting as special configuration states, deteriorate robot performance and may even lead to a loss of control over the system. This paper addresses the kinematic singularity concerns in robotic systems with model mismatch and actuator constraints through control barrier functions (CBFs). We propose a learning-based control strategy to prevent robots entering singularity regions. More precisely, we leverage Gaussian process (GP) regression to learn the unknown model mismatch, where the prediction error is restricted by a deterministic bound. Moreover, we offer the criteria for parameter selection to ensure the feasibility of CBFs subject to actuator constraints. The proposed approach is validated by high-fidelity simulations on a 2 degrees-of-freedom (DoFs) planar robot.

Singularity-Avoidance Control of Robotic Systems with Model Mismatch and Actuator Constraints

TL;DR

This paper proposes a learning-based control strategy to prevent robots entering singularity regions by leveraging Gaussian process (GP) regression to learn the unknown model mismatch, where the prediction error is restricted by a deterministic bound.

Abstract

Singularities, manifesting as special configuration states, deteriorate robot performance and may even lead to a loss of control over the system. This paper addresses the kinematic singularity concerns in robotic systems with model mismatch and actuator constraints through control barrier functions (CBFs). We propose a learning-based control strategy to prevent robots entering singularity regions. More precisely, we leverage Gaussian process (GP) regression to learn the unknown model mismatch, where the prediction error is restricted by a deterministic bound. Moreover, we offer the criteria for parameter selection to ensure the feasibility of CBFs subject to actuator constraints. The proposed approach is validated by high-fidelity simulations on a 2 degrees-of-freedom (DoFs) planar robot.

Paper Structure

This paper contains 10 sections, 6 theorems, 40 equations, 4 figures.

Table of Contents

  1. INTRODUCTION
  2. Preliminaries
  3. Problem Formulation
  4. Control Barrier Function approach for singularity avoidance
  5. Singularity constraints
  6. Velocity constraints
  7. Main results
  8. NUMERICAL VERIFICATION
  9. CONCLUSION
  10. Appendix A

Key Result

Lemma 1

Suppose that Assumption 1 holds, and a training data $\mathcal{D}:=\{(x_i,y_i)\}_{i=1}^M$ is given. Then, for all $x\in\mathcal{X}$, the prediction error of GP regression is bounded by where $\omega_i=y_{\mathcal{D},i}^T\left( K_{\mathcal{D},i}+\sigma^2_vI_M \right)^{-1}y_{\mathcal{D},i}$.

Figures (4)

  • Figure 1: Singularities occur when these two robots are in configuration 2. (a) 2 DoFs manipulator. (b) 5 DoFs robot.
  • Figure 2: The impact of $\gamma$ and $\delta$ on the singularity constraint $z_{min}(q)$
  • Figure 3: Comparison of trajectory tracking results. (a) with GP regression. (b) without GP regression.
  • Figure 4: Comparison of singularity constraints. (a) with GP regression. (b) without GP regression.

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Lemma 1: hashimoto2022learning
  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 2
  • ...and 3 more