  State-of-the-art motion planners cannot scale to a large number of systems.
Motion planning for multiple agents is an NP (non-deterministic
polynomial-time) hard problem, so the computation time increases exponentially
with each addition of agents. This computational demand is a major stumbling
block to the motion planner's application to future NASA missions involving the
swarm of space vehicles. We applied a deep neural network to transform
computationally demanding mathematical motion planning problems into deep
learning-based numerical problems. We showed optimal motion trajectories can be
accurately replicated using deep learning-based numerical models in several 2D
and 3D systems with multiple agents. The deep learning-based numerical model
demonstrates superior computational efficiency with plans generated 1000 times
faster than the mathematical model counterpart.
