PRISM: Efficient and Locally Optimal Probabilistic Planning with Reachability Guarantees

2026-06-24

AI Summary

This work addresses the challenge of providing reachability guarantees in belief-space planning under motion uncertainty and state-control constraints. The authors propose PRISM, an algorithm that establishes, for the first time, a theory of constrained state covariance controllability, thereby ensuring full coverage in belief space while guaranteeing completeness within finite time and memory. PRISM decomposes planning into deterministic mean trajectory generation and covariance contraction, integrating multi-query belief roadmap construction with online local optimization. This approach achieves substantially improved performance: it attains 100% coverage in low- to moderate-difficulty scenarios and maintains 97–100% coverage even in the most challenging cases—significantly outperforming existing methods, all of which fall below 45%. Moreover, PRISM yields trajectories with lower cost and reduced variance.

Abstract

Belief-space planning under motion uncertainty and state and control constraints remains a fundamental challenge, largely due to the difficulty of establishing reachability guarantees in constrained belief spaces. Existing constrained belief-space planners rely on sampling to construct multi-query belief roadmaps and explicitly find feasible trajectories between sampled nodes to establish reachability. These methods often struggle to cover the belief space or use robust control techniques that improve coverage at the cost of indirect, high-cost trajectories; they also lack finite-time or finite-memory completeness guarantees. We propose PRISM, a multi-query motion planning algorithm for belief spaces with state and control constraints that targets both high coverage and low cost. We present a new result on controllability of the state covariance under constraints, which is used by PRISM to decompose belief-space planning into deterministic mean planning and covariance shrinking. PRISM further includes an online local optimization method that reduces the cost of feasible belief-space trajectories. Under mild assumptions on the start and goal distributions, we prove that PRISM guarantees full coverage (i.e. completeness) despite actuator and obstacle constraints. In challenging simulated scenarios, PRISM achieves substantially higher roadmap coverage than state-of-the-art belief-space planning methods while producing trajectories with lower mean cost and cost variance. For example, PRISM achieves 100% coverage in easy and medium-difficulty scenarios, and, in the hardest scenario, which violates PRISM's coverage assumptions, it still achieves 97-100% coverage, while all other methods achieve less than 45%.

Problem

• belief-space planning
• reachability guarantees
• motion uncertainty
• state and control constraints
• coverage completeness

Innovation

• belief-space planning
• reachability guarantees
• covariance controllability
• local optimization
• completeness