Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metrics

Abstract

This paper presents an approach towards guaranteed trajectory tracking for nonlinear control-affine systems subject to external disturbances based on robust control contraction metrics (CCM) that aims to minimize the ${\mathcal{L}}_{\infty }$ gain from the disturbances to nominal-actual trajectory deviations. The guarantee is in the form of invariant tubes, computed offline and valid for any nominal trajectories, in which the actual states and inputs of the system are guaranteed to stay despite disturbances. Under mild assumptions, we prove that the proposed robust CCM (RCCM) approach yields tighter tubes than an existing approach based on CCM and input-to-state stability analysis. We show how the RCCM-based tracking controller together with tubes can be incorporated into a feedback motion planning framework to plan safe trajectories for robotic systems. Simulation results illustrate the effectiveness of the proposed method and empirically demonstrate reduced conservatism compared to the CCM-based approach.

Extended version of a paper published in IEEE Robotics and Automation Letters (2022). 13 pages, 6 figures

References in corpus (3)

• Neural Contraction Metrics for Robust Estimation and Control: A Convex Optimization Approach
• Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization
• Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metrics

Cited by in corpus (9)

• Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview
• Robust adaptive MPC using control contraction metrics
• Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metrics
• Perspectives on Contractivity in Control, Optimization, and Learning
• Predictive control for nonlinear stochastic systems: Closed-loop guarantees with unbounded noise
• Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation
• Dynamic Constraint Tightening for Nonlinear MPC for Autonomous Racing via Contraction Analysis
• Improving the Robustness of Reinforcement Learning Policies with ${\mathcal{L}}_1$ Adaptive Control
• A robust and adaptive MPC formulation for Gaussian process models