Provably-Safe Stein Variational Clarity-Aware Informative Planning

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 challeng- ing because information decays when regions are not revisited. Most existing planners model infor- mation 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 uncer- tainty 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 frame- work for safety verification. The planner performs Bayesian inference-based learning via Stein variational inference, refining a distribution over informative trajectories while filtering each nom- inal Stein informative trajectory to ensure safety. Simulations across environments with varying decay rates and obstacles demonstrate consistent safety and reduced information deficits.