A dynamic boundary guarding problem with translating targets

Abstract— We introduce a problem in which a service vehicle seeks to defend a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when th...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Stephen L. Smith, Shaunak Dattaprasad Bopardikar, Francesco Bullo
• Keywords: Capture Fraction, CDC 2009, Control Systems, Mobile Targets, Service Vehicle