Continuous-Time Gaussian Belief Trees for Motion Planning
2026-07-03 • Robotics
Robotics
AI summaryⓘ
The authors study how to plan safe paths for robots when there is randomness in both their movement and sensor readings. They create a model that continuously tracks the robot's estimated position, updating it smoothly over time and correcting it discretely when new sensor data arrives. To make sure the robot stays safe, they develop a method that checks safety not just at specific moments but over entire path segments, catching potential risks that earlier methods might miss. They test their approach with popular planners and find it works well even in tricky spaces where older methods can fail.
sampling-based motion planningstochastic differential equationKalman filterbelief propagationchance constraintbelief barrier functionRRT (Rapidly-exploring Random Tree)SST (Stable Sparse RRT)continuous-time uncertaintyrobot safety verification
Authors
Rayan Mazouz, Qi Heng Ho, Zachary N. Sunberg, Morteza Lahijanian
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.