Trajectory Planning Under Environmental Uncertainty With Finite-Sample Safety Guarantees

TL;DR

This paper develops a trajectory planning method for environments with uncertain, time-varying obstacles, using finite samples to estimate distribution moments and providing safety guarantees despite limited data.

Contribution

It introduces a novel approach that estimates distribution moments from finite samples and derives concentration bounds to ensure safety guarantees in uncertain environments.

Findings

Provides tight concentration bounds on moment estimation errors.

Offers provable safety guarantees for trajectory planning under uncertainty.

Demonstrates effectiveness through autonomous vehicle case studies.

Abstract

We tackle the problem of trajectory planning in an environment comprised of a set of obstacles with uncertain time-varying locations. The uncertainties are modeled using widely accepted Gaussian distributions, resulting in a chance-constrained program. Contrary to previous approaches however, we do not assume perfect knowledge of the moments of the distribution, and instead estimate them through finite samples available from either sensors or past data. We derive tight concentration bounds on the error of these estimates to sufficiently tighten the chance-constraint program. As such, we provide provable guarantees on satisfaction of the chance-constraints corresponding to the nominal yet unknown moments. We illustrate our results with two autonomous vehicle trajectory planning case studies.