Chance-Constrained Motion Planning using Modeled Distance-to-Collision Functions

TL;DR

This paper presents a novel motion planning algorithm that models distance-to-collision uncertainties with Gaussian Processes, enabling guaranteed chance-constraint satisfaction under motion and state estimate uncertainties.

Contribution

It introduces CCGP-MP, a new approach combining Gaussian Process modeling with global optimization to ensure safe, optimal trajectories under uncertainty.

Findings

Reduces collision risk in uncertain environments

Guarantees chance-constraint satisfaction along planned paths

Demonstrates effectiveness through robotic experiments

Abstract

This paper introduces Chance Constrained Gaussian Process-Motion Planning (CCGP-MP), a motion planning algorithm for robotic systems under motion and state estimate uncertainties. The paper's key idea is to capture the variations in the distance-to-collision measurements caused by the uncertainty in state estimation techniques using a Gaussian Process (GP) model. We formulate the planning problem as a chance constraint problem and propose a deterministic constraint that uses the modeled distance function to verify the chance-constraints. We apply Simplicial Homology Global Optimization (SHGO) approach to find the global minimum of the deterministic constraint function along the trajectory and use the minimum value to verify the chance-constraints. Under this formulation, we can show that the optimization function is smooth under certain conditions and that SHGO converges to the global minimum. Therefore, CCGP-MP will always guarantee that all points on a planned trajectory satisfy the given chance-constraints. The experiments in this paper show that CCGP-MP can generate paths that reduce collisions and meet optimality criteria under motion and state uncertainties. The implementation of our robot models and path planning algorithm can be found on GitHub.