  This paper proposes a decentralized approach for solving the problem of
moving a swarm of agents into a desired formation. We propose a decentralized
assignment algorithm which prescribes goals to each agent using only local
information. The assignment results are then used to generate energy-optimal
trajectories for each agent which have guaranteed collision avoidance through
safety constraints. We present the conditions for optimality and discuss the
robustness of the solution. The efficacy of the proposed approach is validated
through a numerical case study to characterize the framework's performance on a
set of dynamic goals.
