CAPT: Concurrent assignment and planning of trajectories for multiple robots

In this paper, we consider the problem of concurrent assignment and planning of trajectories (which we denote Capt) for a team of robots. This problem involves simultaneously addressing two challenges: (1) the combinatorially complex problem of finding a suitable assignment of robots to goal locations, and (2) the generation of collision-free, time parameterized trajectories for every robot. We consider the Capt problem for unlabeled (interchangeable) robots and propose algorithmic solutions to two variations of the Capt problem. The first algorithm, c-Capt, is a provably correct, complete, centralized algorithm which guarantees collision-free optimal solutions to the Capt problem in an obstacle-free environment. To achieve these strong claims, c-Capt exploits the synergy obtained by combining the two subproblems of assignment and trajectory generation to provide computationally tractable solutions for large numbers of robots. We then propose a decentralized solution to the Capt problem through d-Capt, a decentralized algorithm that provides suboptimal results compared to c-Capt . We illustrate the algorithms and resulting performance through simulation and experimentation.