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

2026-06-08

AI Summary

This work addresses the conservatism of conventional motion planning approaches that model robots as points or circles, which often hinder efficient navigation in narrow environments. To overcome this limitation, the authors propose a safe local motion planning method based on discrete-time control barrier functions, unifying the representation of polyhedral robots and dynamically updated convex free space as polyhedra. This formulation ensures that the number of safety constraints scales only with local geometric complexity, substantially improving scalability. Notably, the approach eliminates the need for explicit obstacle detection by directly integrating occupancy grids and LiDAR measurements into a model predictive controller for real-time collision avoidance. Extensive simulations and hardware experiments demonstrate up to a 91-fold reduction in computation time, enabling real-time 10 Hz control on embedded platforms.

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.

Problem

• motion planning
• polytope-in-polytope
• robot footprint
• narrow passages
• safe navigation

Innovation

• Control Barrier Functions
• Polytope-in-Polytope Containment
• Model Predictive Control
• Free-Space Representation
• Real-Time Motion Planning