Safe Polytope-in-Polytope Motion Planning and Control with Control Barrier Functions

• URL: http://arxiv.org/abs/2606.09719v1
• Date: Mon, 08 Jun 2026 16:44:28 GMT
• Title: Safe Polytope-in-Polytope Motion Planning and Control with Control Barrier Functions
• Abstract summary: This work proposes a safe local motion planning and control method that guarantees that a polytopic robot footprint stays inside a convex free-space region.<n>The proposed free-space formulation does not need any obstacle detection or segmentation.<n>The approach is validated in simulation with an autonomous surface vehicle and on hardware with a non-holonomic mobile robot.
• Score: 45.68209588239261
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Autonomous mobile robots operating in tight environments require motion planning frameworks that account for the physical footprint of the robot. Simplifying the geometry to a point or a circle is conservative and discards information needed to successfully and safely traverse narrow passages. This work proposes a safe local motion planning and control method that guarantees that a polytopic robot footprint stays inside a continuously updated convex free-space region. The containment condition is formulated as a set of discrete-time control barrier function constraints within a model predictive controller. The number of safety constraints depends on the complexity of the local free-space geometry and the robot shape, instead of the number of obstacles. The proposed free-space formulation does not need any obstacle detection or segmentation. A comparative analysis against a polytope-based obstacle avoidance formulation confirms favorable scaling up to a reduction of 91$\times$ in computation time as the number of obstacles increases. The approach is validated in simulation with an autonomous surface vehicle and on hardware with a non-holonomic mobile robot, using both occupancy grids and LiDAR sensing. The experiments demonstrate safe real-time motion planning and control at 10~Hz on an onboard embedded computer, including reactive avoidance of dynamic obstacles.

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