Study of Multiple Target Defense Differential Games Using Receding Horizon-Based Switching Strategies
Sharad Kumar Singh, Puduru Viswanadha Reddy, Bhaskar Vundurthy
Abstract
In this article, we study a variation of the active target-attacker-defender (ATAD) differential game involving multiple targets, an attacker, and a defender. Our model allows for 1) a capability of the defender to switch roles from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rescuer</i> (rendezvous with all the targets) to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interceptor</i> (intercepts the attacker) and vice versa and 2) the attacker to continuously pursue the closest target (which can change during the course of the game). We assume that the mode of the defender (rescue or interception) defines the mode of the game itself. Using the framework of Games of a Degree, we first analyze the game within each mode. More specifically, the objectives of the players are taken as a combination of weighted Euclidean distances and penalties on their control efforts. We model the interaction of the players within each mode as a linear quadratic differential game (LQDG) and obtain the open-loop Nash equilibrium strategies. We then use the receding horizon approach to enable switching between the modes to obtain switching strategies for the players. By partitioning the matrices associated with the Riccati differential equations we obtain geometric characterization of the trajectories of the players. Furthermore, under mild restrictions on the problem parameters and for a particular choice of the defender’s switching function we show that interception mode is invariant. We illustrate our results with numerical simulations. Experimental results involving multiple autonomous differential drive mobile robots are presented.