  We present a scalable and effective multi-agent safe motion planner that
enables a group of agents to move to their desired locations while avoiding
collisions with obstacles and other agents, with the presence of rich
obstacles, high-dimensional, nonlinear, nonholonomic dynamics, actuation
limits, and disturbances. We address this problem by finding a piecewise linear
path for each agent such that the actual trajectories following these paths are
guaranteed to satisfy the reach-and-avoid requirement. We show that the spatial
tracking error of the actual trajectories of the controlled agents can be
pre-computed for any qualified path that considers the minimum duration of each
path segment due to actuation limits. Using these bounds, we find a
collision-free path for each agent by solving Mixed Integer-Linear Programs and
coordinate agents by using the priority-based search. We demonstrate our method
by benchmarking in 2D and 3D scenarios with ground vehicles and quadrotors,
respectively, and show improvements over the solving time and the solution
quality compared to two state-of-the-art multi-agent motion planners.
