Provably Safe Stein Variational Clarity-Aware Informative Planning

TL;DR

The paper addresses planning informative and safe robot trajectories in stochastic spatiotemporal environments where information decays at spatially varying rates. It introduces clarity as a normalized, entropy-based uncertainty measure and embeds clarity dynamics into a Stein variational trajectory optimization framework to learn a posterior over informative paths. Safety is guaranteed through a gatekeeper safety filter that concatenates nominal Stein trajectories with backups and verifies safety prior to execution. Hardware experiments and simulations demonstrate provable safety, reduced information deficits, and computational efficiency over baselines, enabling robust information gathering in dynamic and obstacle-rich environments.

Abstract

Autonomous robots are increasingly deployed for information-gathering tasks in environments that vary across space and time. Planning informative and safe trajectories in such settings is challenging because information decays when regions are not revisited. Most existing planners model information as static or uniformly decaying, ignoring environments where the decay rate varies spatially; those that model non-uniform decay often overlook how it evolves along the robot's motion, and almost all treat safety as a soft penalty. In this paper, we address these challenges. We model uncertainty in the environment using clarity, a normalized representation of differential entropy from our earlier work that captures how information improves through new measurements and decays over time when regions are not revisited. Building on this, we present Stein Variational Clarity-Aware Informative Planning, a framework that embeds clarity dynamics within trajectory optimization and enforces safety through a low-level filtering mechanism based on our earlier gatekeeper framework for safety verification. The planner performs Bayesian inference-based learning via Stein variational inference, refining a distribution over informative trajectories while filtering each nominal Stein informative trajectory to ensure safety. Hardware experiments and simulations across environments with varying decay rates and obstacles demonstrate consistent safety and reduced information deficits.

Figures (8)

• Figure 1: The baseline derives a TISD from the clarity model and uses it as an ergodic metric, whereas the proposed framework directly optimizes the clarity model via a Stein variational approach, producing multiple informative and provably safe trajectories.
• Figure 2: Safety filtering through the gatekeeper framework. Candidate trajectories (shown in yellow) are generated in parallel for each nominal Stein trajectory. Unsafe candidate trajectories are rejected, and the least-cost safe candidate is executed.
• Figure 3: Planner behavior across representative environments. The planner maintains low clarity deficits and safe motion.
• Figure 4: Hardware Experiments
• Figure 5:

Theorems & Definitions (12)

• definition 1: Trajectory
• definition 2
• definition 3
• definition 4: Nominal Trajectory
• definition 5: Backup Set
• definition 6: Valid Backup Trajectory
• definition 7: Candidate Trajectory
• definition 8: Safe Candidate Trajectory
• definition 9: Committed Trajectory
• theorem 1