Risk-Averse Trajectory Optimization via Sample Average Approximation

TL;DR

This paper introduces a risk-averse trajectory optimization method that handles complex uncertainties and nonlinear dynamics, providing an efficient, theoretically sound approach with proven asymptotic optimality and finite-sample guarantees.

Contribution

It presents a novel continuous-time planning formulation with an average-value-at-risk constraint and a sample-based approximation algorithm for risk-averse trajectory optimization.

Findings

High speed and reliability demonstrated in simulations

Handles stochasticity in nonlinear dynamics and terrain

Proven asymptotic optimality with finite-sample error bounds

Abstract

Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations, nonlinear dynamics, and non-convex constraints. In this work, we first introduce a continuous-time planning formulation with an average-value-at-risk constraint over the entire planning horizon. Then, we propose a sample-based approximation that unlocks an efficient and general-purpose algorithm for risk-averse trajectory optimization. We prove that the method is asymptotically optimal and derive finite-sample error bounds. Simulations demonstrate the high speed and reliability of the approach on problems with stochasticity in nonlinear dynamics, obstacle fields, interactions, and terrain parameters.