Continuous-Time Gaussian Belief Trees for Motion Planning
This paper addresses sampling-based motion planning for continuous-time stochastic systems under process and measurement uncertainty, with probabilistic guarantees on safety and performance. It models robot dynamics as a continuous-time linear stochastic differential equation and uses discrete-time sensor measurements. A hybrid belief propagation model is derived, where belief evolves via continuous-time ODEs between measurements and undergoes discrete Kalman filter updates at measurement times. A belief-barrier-function-based safety checker enables segment-level probabilistic verification, detecting inter-sample chance-constraint violations missed by conventional node-based checks. The method is integrated with RRT and SST planners and evaluated on benchmark environments, showing high success rates and robust chance constraint enforcement, especially in narrow passages where discrete-time methods fail.
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[Submitted on 3 Jul 2026]
Title:Continuous-Time Gaussian Belief Trees for Motion Planning
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Abstract:We address sampling-based motion planning for continuous-time stochastic systems under process and measurement uncertainty, with probabilistic guarantees on safety and performance. The robot dynamics are modeled as a continuous-time linear stochastic differential equation, while sensor measurements arrive at discrete time instants. We derive an offline hybrid belief propagation model in which the belief evolves according to continuous-time ODEs between measurements and undergoes discrete Kalman filter update jumps at measurement times. To ensure safety, we introduce a belief-barrier-function-based safety checker for segment-level probabilistic verification. This enables the planner to certify safety over entire continuous trajectory segments and detect inter-sample chance-constraint violations that are missed by conventional node-based checks. Together, these components provide a principled framework for sampling-based belief planning that accounts for both continuous-time uncertainty propagation and continuous-time safety requirements. We integrate the method with RRT and SST planners and evaluate it across multiple benchmark environments. The results show that the proposed method achieves high success rates and robust enforcement of chance constraints, including in narrow-passage scenarios where discrete-time counterparts fail due to missed inter-sample unsafe behavior.
Subjects:
Robotics (cs.RO)
Cite as: arXiv:2607.02884 [cs.RO]
(or arXiv:2607.02884v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2607.02884
arXiv-issued DOI via DataCite
Submission history
From: Rayan Mazouz [view email] [v1] Fri, 3 Jul 2026 02:29:42 UTC (407 KB)
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