Path Planning Games

Path planning is a fundamental and extensively explored problem in robotic control. We present a novel economic perspective on path planning. Specifically, we investigate strategic interactions among path planning agents using a game theoretic path planning framework. Our focus is on economic tension between two important objectives: efficiency in the agents' achieving their goals, and safety in navigating towards these. We begin by developing a novel mathematical formulation for path planning that trades off these objectives, when behavior of other agents is fixed. We then use this formulation for approximating Nash equilibria in path planning games, as well as to develop a multi-agent cooperative path planning formulation. Through several case studies, we show that in a path planning game, safety is often significantly compromised compared to a cooperative solution.