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The aim of this work is to present a sampling-based algorithm designed to solve various classes of stochastic differential games. The foundation of the proposed approach lies in the formulation of the game solution in terms of a decoupled pair of forward and backward stochastic differential equations (FBSDEs). In light of the nonlinear version of the Feynman–Kac lemma, probabilistic representations of solutions to the nonlinear Hamilton–Jacobi–Isaacs equations that arise for each class are obtained. These representations are in form of decoupled systems of FBSDEs, which may be solved numerically.more » « less
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We introduce an algorithm for autonomous control of multiple fast ground vehicles operating in close proximity to each other. The algorithm is based on a combination of the game theoretic notion of iterated best response, and an information theoretic model predictive control algorithm designed for non-linear stochastic systems. We test the algorithm on two one-fifth scale AutoRally platforms traveling at speeds upwards of 8 meters per second, while maintaining a following distance of under two meters from bumper-to-bumper.more » « less
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