Time-Optimal Motion Strategies for Capturing an Omnidirectional Evader Using a Differential Drive Robot

Abstract

In this paper, we consider the problem of capturing an omnidirectional evader using a differential drive robot in an obstacle-free environment. At the beginning of this game, the evader is at a distance L > l (the capture distance) from the pursuer. The goal of the evader is to keep the pursuer farther than this capture distance for as long as possible. The goal of the pursuer is to capture the evader as soon as possible. In this paper, we make the following contributions. We present closed-form representations of the motion primitives and time-optimal strategies for each player; these strategies are in Nash equilibrium, meaning that any unilateral deviation of each player from these strategies does not provide to such player benefit toward the goal of winning the game. We propose a partition of the playing space into mutually disjoint regions where the strategies of the players are well established. This partition is represented as a graph, which exhibits properties that guarantee global optimality. We also analyze the decision problem of the game and we present the conditions defining the winner.

Pursuit-evasion with fixed beams

“…In the lion and man game, a lion tries to capture a man who is trying to escape [20], [30]. In game theory, the homicidal chauffeur is a pursuit evasion problem which pits a slowly moving but highly maneuverable runner against the driver of a vehicle, which is faster but less maneuverable, who is attempting to run him over [7], [28]. Capture bounds for a pursuit-evasion problem that require the pursuer to physically capture the evader suggests the number or pursuers required to satisfy this capture condition exceeds that needed for the visibilitybased pursuit-evasion problem [10].…”

A sampling-based algorithm for multi-robot visibility-based pursuit-evasion

“…In the lion and man game, a lion tries to capture a man who is trying to escape [15], [21]. In game theory, the homicidal chauffeur is a pursuit-evasion problem which pits a slowly moving but highly maneuverable runner against the driver of a vehicle, which is faster but less maneuverable, who is attempting to run him over [7], [19].…”

Tracking an omnidirectional evader with a differential drive robot at a bounded variable distance

“…Note that the change in the mechanical model for the pursuer (if this role is taken by the DDR, which can rotate in place) has as distinctive consequences that both the condition defining the winner and the motion strategies of the two players also change with respect to the homicidal chauffeur solution. Ruiz and Murrieta-Cid (2012) as well as Ruiz et al (2013) presented time-optimal strategies for the game of capturing an omnidirectional evader with a differential drive robot. The results presented here, although not time-optimal, have the advantage over those of Ruiz and Murrieta-Cid (2012) as well as Ruiz et al (2013) of allowing solution of two problems: capturing an OA evader with a DDR pursuer and maintaining surveillance at a bounded variable distance of an OA with a DDR.…”

“…Ruiz and Murrieta-Cid (2012) as well as Ruiz et al (2013) presented time-optimal strategies for the game of capturing an omnidirectional evader with a differential drive robot. The results presented here, although not time-optimal, have the advantage over those of Ruiz and Murrieta-Cid (2012) as well as Ruiz et al (2013) of allowing solution of two problems: capturing an OA evader with a DDR pursuer and maintaining surveillance at a bounded variable distance of an OA with a DDR.…”