A visibility-based pursuit-evasion game between two nonholonomic robots in environments with obstacles

In this paper, a visibility-based pursuit-evasion game in an environment with obstacles is addressed. A pursuer wants to maintain the visibility of an evader at all times. Both players are nonholonomic robots shaped like discs. To determine the players’ motion policies and their trajectories–subject to differential constraints–, an RRT* approach that minimizes the time traveled is utilized. The proposed formulation presents an alternative for computing a strategy of persistent surveillance of the evader, difficult to model from a classical differential games perspective given that there is no clear termination condition when the pursuer can maintain the evader’s visibility forever. A sufficient condition to keep evader surveillance is also provided. Additionally, the proposed approach is general because it can be adapted to address a variety of scenarios. To illustrate such flexibility, we address different aspects of the problem: (1) Knowledge of the environment (availability of a global map vs. a local representation). (2) Strategies of the players (execution of optimal strategies vs. deviations from the optimal ones to deceive the opponent). (3) Sensor capabilities (limited vs. unlimited sensor range).