Analysing interactions between a trio of differential drive robots via a differential game formulation

Interactions involving two friendly agents (termed prey and protector) working in the presence of a predatory (third) agent are considered in this paper. The three agents are modelled as differential drive mobile robots (DDMR). The task of the protector is to operate either in rescue mode or in interception mode to save the prey from the predator. To this end, we first perform feedback linearization on each robot model and then using a linear quadratic differential game (LQDG) approach, we design control strategies for each robot that achieve open-loop Nash equilibria. To facilitate switching (of the role of the protector) between rescue and interception while the game is in progress, we synthesize a receding horizon control policy. Simulations are presented to study the tradeoffs involved in feedback linearization of the robot models and to study the effectiveness of the synthesis strategy for switching between the modes. The simulations also illustrate a scenario where mere application of the open-loop Nash equilibrium strategy leads to capture of a prey while the protector mode switching (via the receding horizon policy) results in escape of the prey.