DC-CAPT: Concurrent Assignment and Planning of Trajectories for Dubins Cars

Abstract

We present an algorithm for the concurrent assignment and planning of collision-free trajectories (DC-CAPT) for robots whose kinematics can be modeled as Dubins cars, i.e., robots constrained in terms of their initial orientation and their minimum turning radius. Coupling the assignment and trajectory planning subproblems allows for a computationally tractable solution. This solution is guaranteed to be collision- free through the use of a single constraint: the start and goal locations have separation distance greater than some threshold. We derive this separation distance by extending a prior work that assumed holonomic robots. We demonstrate the validity of our approach, and show its efficacy through simulations and experiments where groups of robots executing Dubins curves travel to their assigned goal locations without collisions.