  In this work, we consider the problem of autonomous racing with multiple
agents where agents must interact closely and influence each other to compete.
We model interactions among agents through a game-theoretical framework and
propose an efficient algorithm for tractably solving the resulting game in real
time. More specifically, we capture interactions among multiple agents through
a constrained dynamic game. We show that the resulting dynamic game is an
instance of a simple-to-analyze class of games. Namely, we show that our racing
game is an instance of a constrained dynamic potential game. An important and
appealing property of dynamic potential games is that a generalized Nash
equilibrium of the underlying game can be computed by solving a single
constrained optimal control problem instead of multiple coupled constrained
optimal control problems. Leveraging this property, we show that the problem of
autonomous racing is greatly simplified and develop RAPID (autonomous
multi-agent RAcing using constrained PotentIal Dynamic games), a racing
algorithm that can be solved tractably in real-time. Through simulation
studies, we demonstrate that our algorithm outperforms the state-of-the-art
approach. We further show the real-time capabilities of our algorithm in
hardware experiments.
