Risk-Aware Belief Control Barrier Functions over Random Finite Sets
TL;DR
This work addresses safe control under the induced multi-object state uncertainty with a risk-aware belief control barrier function (BCBF) framework and establishes forward invariance of the safe set under continuous prediction, and derives an explicit condition under which discrete updates preserve safety.
Abstract
Ensuring robot safety in unknown, dynamic environments is a fundamental requirement. It involves inferring the states of an unknown and time-varying number of moving objects from noisy, incomplete measurements. We address safe control under the induced multi-object state uncertainty with a risk-aware belief control barrier function (BCBF) framework. The uncertainty is captured by a random finite set (RFS) belief, estimated by a sequential Monte Carlo probability hypothesis density (SMC-PHD) filter that represents it with a set of particles. Building directly on these particles, we construct a nonsmooth BCBF, establish forward invariance of the safe set under continuous prediction, and derive an explicit condition under which discrete updates preserve safety. Simulation and real-world underwater experiments demonstrate the effectiveness and efficiency of the proposed approach.