Random Forests for Time Optimal Feedback Control and Pursuit Evasion Games

In this paper, the suitability of decision tree/random forest classifiers for learning the feedback solutions to time-optimal control problems and pursuit evasion games involving Dubins vehicles, is investigated through several numerical experiments. Recent results [1] have shown that feedback solutions to the game of two cars are bang-bang with the pursuer and evader controls switching between extreme values based on the relative geometry of the players. However no explicit formula for the feedback laws exist. This article demonstrates that this geometry based logic can be learnt by decision trees/forests quite efficiently, resulting in relatively simple implementations of the feedback laws. The laws thus learned matches with analytical solutions for the variants of the game where these are known. For the cases where such closed form solutions are unknown, the decision tree/forest based laws match with optimal trajectories computed according to other available numerical methods.