Multi-agent Path Planning with Heterogenous Interactions in Tight Spaces

By starting with the assumption that motion is fundamentally a decision making problem, we use the world-line concept from Special Relativity as the inspiration for a novel multi-agent path planning method. We have identified a particular set of problems that have so far been overlooked by previous works. We present our solution for the global path planning problem for each agent and ensure smooth local collision avoidance for each pair of agents in the scene. We accomplish this by modelling the collision-free trajectories of the agents through 2D space and time as rods in 3D. We obtain smooth trajectories by solving a non-linear optimization problem with a quasi-Newton interior point solver, initializing the solver with a non-intersecting configuration from a modified Dijkstra's algorithm. This space-time formulation allows us to simulate previously ignored phenomena such as highly heterogeneous interactions in very constrained environments. It also provides a solution for scenes with unnaturally symmetric agent alignments without the need for jittering agent positions or velocities.