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Many problems in robotics involve multiple decision making agents. To operateefficiently in such settings, a robot must reason about the impact of itsdecisions on the behavior of other agents. Differential games offer anexpressive theoretical framework for formulating these types of multi-agentproblems. Unfortunately, most numerical solution techniques scale poorly withstate dimension and are rarely used in real-time applications. For this reason,it is common to predict the future decisions of other agents and solve theresulting decoupled, i.e., single-agent, optimal control problem. Thisdecoupling neglects the underlying interactive nature of the problem; however,efficient solution techniques do exist for broad classes of optimal controlproblems. We take inspiration from one such technique, the iterativelinear-quadratic regulator (ILQR), which solves repeated approximations withlinear dynamics and quadratic costs. Similarly, our proposed algorithm solvesrepeated linear-quadratic games. We experimentally benchmark our algorithm inseveral examples with a variety of initial conditions and show that theresulting strategies exhibit complex interactive behavior. Our results indicatethat our algorithm converges reliably and runs in real-time. In a three-player,14-state simulated intersection problem, our algorithm initially converges in <0.25s. Receding horizon invocations converge in < 50 ms in a hardwarecollision-avoidance test.

Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games