Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy
Year: 2025
Type: article
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 areduced-setwith 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 thereduced-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.
Authors: Basant Sharma, Arun Kumar Singh
Institution: University of Tartu
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,645
Funder: Eesti Teadusagentuur
OpenAlex ID: W4409917115