Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy

TL;DR

This paper introduces a risk-aware trajectory optimization method that reduces the number of required rollouts by distilling statistical information using RKHS and MMD, leading to safer trajectories with fewer samples.

Contribution

It develops an algorithm to distill statistical information from many rollouts into a smaller set and introduces a novel MMD-based surrogate for collision risk estimation.

Findings

Achieves safer trajectories with fewer rollouts in low-sample regimes.

Outperforms CVaR-based methods in risk estimation accuracy.

Demonstrates effectiveness through extensive benchmarking.

Abstract

This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the collision risk associated with a sequence of control commands. We consider a setting where it is expensive to estimate risk using perturbed rollouts, for example, due to expensive collision-checks. We put forward two key contributions. First, we develop an algorithm that distills the statistical information from a larger set of rollouts to a reduced-set with sample size $N<<\tilde{N}$. Consequently, we estimate collision risk using just $N$ rollouts instead of $\tilde{N}$. Second, we formulate a novel surrogate for the collision risk that can leverage the distilled statistical information contained in the reduced-set. We formalize both algorithmic contributions using distribution embedding in Reproducing Kernel Hilbert Space (RKHS) and Maximum Mean Discrepancy (MMD). We perform extensive benchmarking to demonstrate that our MMD-based approach leads to safer trajectories at low sample regime than existing baselines using Conditional Value-at Risk (CVaR) based collision risk estimate.