Robust-RRT: Probabilistically-Complete Motion Planning for Uncertain Nonlinear Systems

TL;DR

Robust-RRT is a probabilistically complete sampling-based motion planning algorithm that guarantees safe plans under all uncertainties for nonlinear systems, including unstable and hybrid dynamics, by integrating reachability analysis.

Contribution

This paper introduces Robust-RRT, the first probabilistically complete algorithm for robust motion planning that handles general nonlinear, unstable, and hybrid systems with bounded uncertainties.

Findings

Proves probabilistic completeness for a broad class of systems.

Demonstrates robustness on nonlinear, underactuated, and hybrid systems.

Incorporates sampling-based reachability analysis for practical implementation.

Abstract

Robust motion planning entails computing a global motion plan that is safe under all possible uncertainty realizations, be it in the system dynamics, the robot's initial position, or with respect to external disturbances. Current approaches for robust motion planning either lack theoretical guarantees, or make restrictive assumptions on the system dynamics and uncertainty distributions. In this paper, we address these limitations by proposing the robust rapidly-exploring random-tree (Robust-RRT) algorithm, which integrates forward reachability analysis directly into sampling-based control trajectory synthesis. We prove that Robust-RRT is probabilistically complete (PC) for nonlinear Lipschitz continuous dynamical systems with bounded uncertainty. In other words, Robust-RRT eventually finds a robust motion plan that is feasible under all possible uncertainty realizations assuming such a plan exists. Our analysis applies even to unstable systems that admit only short-horizon feasible plans; this is because we explicitly consider the time evolution of reachable sets along control trajectories. Thanks to the explicit consideration of time dependency in our analysis, PC applies to unstabilizable systems. To the best of our knowledge, this is the most general PC proof for robust sampling-based motion planning, in terms of the types of uncertainties and dynamical systems it can handle. Considering that an exact computation of reachable sets can be computationally expensive for some dynamical systems, we incorporate sampling-based reachability analysis into Robust-RRT and demonstrate our robust planner on nonlinear, underactuated, and hybrid systems.