Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy

2025-01-31

AI Summary

In safety-critical trajectory planning under uncertain dynamics, conventional approaches suffer from high collision-checking costs, inefficient risk estimation, and severe sample scarcity. Method: This paper proposes a distribution-distillation-based, risk-aware trajectory optimization framework. It introduces probabilistic embeddings in a reproducing kernel Hilbert space (RKHS) and maximum mean discrepancy (MMD) into trajectory risk modeling, constructing a lightweight MMD surrogate model that achieves accurate risk estimation with drastically reduced sampling (N ≪ Ñ). Statistical information distillation replaces costly collision sampling, enabling robust risk assessment under data-limited conditions. Contribution/Results: The method significantly outperforms baselines such as CVaR in low-data regimes, yielding more precise risk estimates, enhanced trajectory robustness, and substantially lower computational overhead. It establishes a new paradigm for real-time, risk-sensitive control in data-constrained environments.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $ ilde{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 $N<< ilde{N}$. Consequently, we estimate collision risk using just $N$ rollouts instead of $ ilde{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.

Problem

• Path Planning
• Uncertain Dynamics
• Collision Avoidance

Innovation

• Sparse Data Algorithm
• Efficient Risk Assessment
• Safe Path Planning