Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach

TL;DR

This paper introduces LAG-ROS, a learning-based motion planning method that guarantees robustness and stability using contraction theory, neural networks, and convex optimization, ensuring exponential tracking error bounds under disturbances.

Contribution

It develops a novel framework combining contraction theory with neural network-based control to provide formal robustness and stability guarantees in learning-based motion planning.

Findings

Demonstrates exponential bounds on tracking error under disturbances

Shows superior robustness and stability in simulations

Retains computational efficiency of existing methods

Abstract

This paper presents Learning-based Autonomous Guidance with RObustness and Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear motion planners with formal robustness and stability guarantees, by designing a differential Lyapunov function using contraction theory. LAG-ROS utilizes a neural network to model a robust tracking controller independently of a target trajectory, for which we show that the Euclidean distance between the target and controlled trajectories is exponentially bounded linearly in the learning error, even under the existence of bounded external disturbances. We also present a convex optimization approach that minimizes the steady-state bound of the tracking error to construct the robust control law for neural network training. In numerical simulations, it is demonstrated that the proposed method indeed possesses superior properties of robustness and nonlinear stability resulting from contraction theory, whilst retaining the computational efficiency of existing learning-based motion planners.