Potential Games on Cubic Splines for Self-Interested Multi-Agent Motion Planning

Existing multi-agent motion planners face scalability challenges with the number of agents and route plans that span long time horizons. We tackle these issues by introducing additional abstraction by interpolating agent trajectories with natural cubic splines and leveraging existing results that under some natural assumptions, the resulting game has the structure of a potential game. We prove a simultaneous gradient descent method using independent per-agent step sizes is guaranteed to converge to a local Nash equilibrium. Compared with recent iLQR-based potential game solvers, our method solves for local Nash equilibrium trajectories faster in games with up to 52 agents, and we demonstrate scalability to long horizons.