Wasserstein Distributionally Robust Chance Constrained Trajectory Optimization for Mobile Robots within Uncertain Safe Corridor

TL;DR

This paper introduces a distributionally robust approach to safe corridor-based trajectory optimization for autonomous robots, effectively handling perception uncertainty to improve navigation safety.

Contribution

It proposes DRSCCs integrated with Bernstein basis polynomials, resulting in a convex quadratic program that accounts for corridor uncertainty in trajectory planning.

Findings

Reduces infeasible motions under uncertainty

Enhances navigation safety in uncertain environments

Validated on UAV and quadruped robot applications

Abstract

Safe corridor-based Trajectory Optimization (TO) presents an appealing approach for collision-free path planning of autonomous robots, offering global optimality through its convex formulation. The safe corridor is constructed based on the perceived map, however, the non-ideal perception induces uncertainty, which is rarely considered in trajectory generation. In this paper, we propose Distributionally Robust Safe Corridor Constraints (DRSCCs) to consider the uncertainty of the safe corridor. Then, we integrate DRSCCs into the trajectory optimization framework using Bernstein basis polynomials. Theoretically, we rigorously prove that the trajectory optimization problem incorporating DRSCCs is equivalent to a computationally efficient, convex quadratic program. Compared to the nominal TO, our method enhances navigation safety by significantly reducing the infeasible motions in presence of uncertainty. Moreover, the proposed approach is validated through two robotic applications, a micro Unmanned Aerial Vehicle (UAV) and a quadruped robot Unitree A1.