Stochastic Multi-Objective Kinodynamic Planning Against Adversaries

2026-07-21

AI Summary

This work addresses multi-objective motion planning in state-dependent stochastic hybrid adversarial environments by proposing a closed-loop policy planning approach that jointly optimizes execution cost and the probability of violating safety constraints (i.e., risk). It introduces closed-loop policies into stochastic multi-objective planning for the first time, presenting two algorithms: SMO-RRT, which is probabilistically complete, and SMO-SST, an efficient but incomplete variant. Risk is directly evaluated within tree search via Monte Carlo particle-based forward simulations, while chance-constrained handling and selective pruning enable approximate generation of a Pareto-optimal policy set. The method provides finite-sample risk bounds for systems with non-Gaussian, state-dependent uncertainties and effectively achieves Pareto trade-offs between risk and cost in applications such as multi-agent systems, social navigation, and autonomous driving.

Abstract

This paper addresses multi-objective kinodynamic planning in environments with stochastic hybrid adversaries that probabilistically transition to adversarial modes based on the ego state. The goal is to construct the Pareto-front of paths that trade off execution cost and the probability of safety constraint violation (risk). Existing chance-constrained planners evaluate risk over open-loop trajectories, yielding overly conservative solutions that fail to account for ego-agent reactivity. To address this limitation, we shift the planning space to sequences of closed-loop policies, and integrate sample-based risk evaluation directly into tree construction via Monte-Carlo particle rollouts. We first introduce Stochastic Multi-Objective RRT (SMO-RRT), for which we prove probabilistic completeness, followed by Stochastic Multi-Objective Stable Sparse RRT (SMO-SST), which leverages selective pruning to improve numerical performance at the cost of completeness. For both algorithms, we derive a finite-sample bound on the probability of chance constraint violation for systems with non-Gaussian, state-dependent uncertainty, enabling probabilistically safe planning in a broad class of environments applicable to multi-agent systems, social navigation, and autonomous driving.

Problem

• stochastic adversaries
• multi-objective planning
• kinodynamic planning
• chance-constrained safety
• Pareto-front

Innovation

• closed-loop policy
• Monte-Carlo risk evaluation
• stochastic adversaries
• chance-constrained planning
• probabilistic completeness