In this work, we analyze approximations of capture sets  for a visibility based pursuit-evasion game. In contrast to the capture problem, the pursuer tries to maintain a line-of-sight with the evader in free space in our problem. We extend the concept of U set initially proposed in  for holonomic players to the scenario in which the pursuer is holonomic. The problem of computing the U set is reduced to that of computing time-optimal paths for the non-holonomic vehicles to an arbitrary line. We characterize the primitives for time-optimal paths for the Dubin’s vehicle, Reed-shepps car and a Differential Drive robot. Based on these primitives, we construct the optimal paths and provide an algorithm to compute the U set.
- Dynamic Systems and Control Division
Approximation of Capture Sets in Visibility-Based Target-Tracking Games for Non-Holonomic Players
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Zou, R, & Bhattacharya, S. "Approximation of Capture Sets in Visibility-Based Target-Tracking Games for Non-Holonomic Players." Proceedings of the ASME 2017 Dynamic Systems and Control Conference. Volume 2: Mechatronics; Estimation and Identification; Uncertain Systems and Robustness; Path Planning and Motion Control; Tracking Control Systems; Multi-Agent and Networked Systems; Manufacturing; Intelligent Transportation and Vehicles; Sensors and Actuators; Diagnostics and Detection; Unmanned, Ground and Surface Robotics; Motion and Vibration Control Applications. Tysons, Virginia, USA. October 11–13, 2017. V002T07A004. ASME. https://doi.org/10.1115/DSCC2017-5379
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