  In this paper, we present an approach for solving the problem of moving $N$
homogeneous agents into $M \geq N$ goal locations along energy-minimizing
trajectories. We propose a decentralized framework that only requires knowledge
of the goal locations and partial observations of the global state by each
agent. The framework includes guarantees on safety through dynamic constraints,
and a method to impose a dynamic, global priority ordering on the agents. A
solution to the goal assignment and trajectory generation problems are derived
in the form of a binary program and a nonlinear system of equations. Then, we
present the conditions for optimality and characterize the conditions under
which our algorithm is guaranteed to converge to a unique assignment of agents
to goals. We also solve the fully constrained decentralized trajectory
generation problem considering the state, control, and safety constraints.
Finally, we validate the efficacy of our approach through a numerical
simulation in MATLAB.
