Trajectory planning under environmental uncertainty with finite-sample safety guarantees

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. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study focuses on trajectory planning in an environment with a set of obstacles whose locations vary with uncertain time. Uncertainties are modeled using Gaussian distributions, and estimates are made through finite samples to tighten the chance-constraint program. Provable guarantees are provided on satisfaction of the chance-constraints corresponding to nominal but unknown moments.