Risk-Aware Belief Control Barrier Functions over Random Finite Sets

• URL: http://arxiv.org/abs/2607.15016v1
• Date: Thu, 16 Jul 2026 14:04:12 GMT
• Title: Risk-Aware Belief Control Barrier Functions over Random Finite Sets
• Abstract summary: We address safe control under the induced multi-object state uncertainty with a risk-aware belief control barrier function (BCBF) framework.<n>The uncertainty is captured by a random finite set (RFS) belief, estimated by a sequential Monte Carlo probability hypothesis density filter.<n>We derive an explicit condition under which discrete updates preserve safety.
• Score: 24.17957184198205
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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