Continuous-Time Belief Trees Certify Robot Safety in Narrow Passages

Planning safe motion for robots under process and measurement noise is traditionally handled with discrete-time checks at sampled nodes. However, these node-based checks can miss dangerous constraint violations between time steps. Mazouz et al. address this by deriving a hybrid belief propagation model that evolves continuously via ordinary differential equations (ODEs) and only updates with discrete Kalman filter jumps at measurement times. This continuous-time treatment captures the full trajectory-level uncertainty, enabling a more principled safety verification.

To enforce safety, the authors introduce a belief-barrier-function (BBF) safety checker that verifies probabilistic chance constraints over entire continuous trajectory segments, not just at isolated points. They integrate this framework into sampling-based planners like RRT and SST. Benchmarks across multiple environments, including narrow passages, show high success rates and robust constraint enforcement. The BBF checker reliably detects inter-sample violations that cause discrete-time planners to fail, offering a new level of safety for autonomous systems operating under real-world uncertainty.