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 throughd-Capt, a decentralized algorithm that provides suboptimal results compared toc-Capt. We illustrate the algorithms and resulting performance through simulation and experimentation.

In this work we consider the problem of controlling a team of micro-aerial vehicles moving quickly through a three-dimensional environment while maintaining a tight formation. The formation is specified by shape vectors which prescribe the relative separations and bearings between the robots. To maintain the desired shape, each robot plans its trajectory independently based on its local information of other robot plans and estimates of states of other robots in the team. We explore the interaction between nonlinear decentralized controllers, the fourth-order dynamics of the individual robots, time delays in the network, and the effects of communication failures on system performance. Simulations as well as an experimental evaluation of our approach on a team of quadrotors suggests that suitable performance is maintained as the formation motions become increasingly aggressive and as communication degrades.

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