Safe Polytope-in-Polytope Motion Planning and Control with Control Barrier Functions
2026-06-08 • Robotics
Robotics
AI summaryⓘ
The authors developed a new way for robots to move safely in tight spaces by keeping the robot's exact shape inside a safe area that constantly updates. Instead of treating the robot as just a point or circle, their method uses a polygon shape and controls its movement to stay within free space. This method doesn't need to detect specific obstacles, making it faster and more efficient, especially when there are many obstacles. They tested it in simulations and real robots, showing it works safely in real time, even when obstacles move around.
motion planningrobot footprintconvex free-spacecontrol barrier functionmodel predictive controlpolytopic robotnon-holonomic robotoccupancy gridLiDAR sensingreal-time control
Authors
Alejandro Gonzalez-Garcia, Dries Dirckx, Jan Swevers, Wilm Decré
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.