Risk-Aware Belief Control Barrier Functions over Random Finite Sets

2026-07-16

AI Summary

This work addresses the challenge of safe robot control under state uncertainty of multiple targets in unknown dynamic environments. The authors propose a novel approach that integrates random finite set (RFS)-based belief representation with risk-aware control barrier functions. Specifically, they employ a sequential Monte Carlo PHD filter to construct a particle-based environmental belief and, for the first time, directly formulate a nonsmooth, risk-aware belief control barrier function (BCBF) at the particle level. This formulation rigorously guarantees forward invariance of the safe set in hybrid discrete–continuous systems and ensures safety preservation during discrete belief updates. Theoretical analysis and underwater robotic experiments demonstrate that the proposed method achieves both high efficiency and strong safety guarantees in complex dynamic scenarios.

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.

Problem

• robot safety
• multi-object state uncertainty
• random finite sets
• dynamic environments
• noisy measurements

Innovation

• Risk-Aware Belief Control Barrier Functions
• Random Finite Sets
• SMC-PHD Filter
• Forward Invariance
• Safe Control