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Tracking an Omnidirectional Evader with a Differential Drive Robot

We consider the surveillance problem of tracking a moving evader by a nonholonomic mobile pursuer. We deal specifically with the situation in which the only constraint on the evader's velocity is a bound on speed (i.e., the evader is able to move omnidirectionally), and the pursuer is a nonholonomic, differential drive system having bounded speed. We formulate our problem as a game. Given the evader's maximum speed, we determine a lower bound for the required pursuer speed to track the evader. This bound allows us to determine at the beginning of the game whether or not the pursuer can follow the evader based on the initial system configuration. We then develop the system model, and obtain optimal motion strategies for both players, which allow us to establish the long term solution for the game. We present an implementation of the system model, and motion strategies, and also present simulation results of the pursuit-evasion game.
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Tracking an Omnidirectional Evader with a Differential Drive Robot
R. Murrieta-Cid, U. Ruiz, J.L. Marroquin, J.-P. Laumond and S. Hutchinson
Journal Autonomous Robot, special issue on Search and Pursuit/Evasion with Mobile Robots, Vol 31, No. 4, pages 345-366, 2011.
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A Homicidal Differential Drive Robot

We consider the problem of capturing an omnidirectional evader using a Differential Drive Robot in an obstacle free environment. At the beginning of the game the evader is at a distance L > l from the pursuer. The pursuer goal is to get closer from the evader than the capture distance l. The goal of the evader is to keep the pursuer at all time farther from it than this capture distance. In this work, we found 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 also present the condition defining the winner of the game and we construct a solution over the entire reduced space.

A Homicidal Differential Drive Robot
U. Ruiz and R. Murrieta-Cid
To appear in IEEE International Conference on Robotics and Automation, Saint Paul MN, USA, ICRA 2012.
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