We address optimal placement of vehicles with simple motion, to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the target. With a single vehicle, we assume that the target either moves with fixed speed and in a fixed direction or moves to maximize the vertical height or intercept time. We show that each of the corresponding cost functions is convex, has smooth gradient and has a unique minimizing location, and so the optimal vehicle placement is obtained by any standard gradient-based optimization technique. With multiple vehicles, we assume that the target moves with fixed speed and in fixed direction. We present a discrete time partitioning and gradient-based algorithm, and characterize conditions under which the algorithm asymptotically leads the vehicles to a set of critical configurations of the cost function.
Vehicle Placement to Intercept Moving Targets (Preprint)
2010
9 pages
Report
Keine Angabe
Englisch
Algebra, Analysis, Geometry, & Mathematical Logic , Operations Research , Computers, Control & Information Theory , Detection & Countermeasures , Interception , Algorithms , Functions(Mathematics) , Moving targets , Motion , Orientation(Direction) , Probability density functions , Lines(Geometry) , Costs , Convergence , Autonomous navigation , Evasion , Continuity , Invariance , Height , Gradients , Circles , Optimization , Robotics , Simulation , Velocity , Time , Coverage control , Pursuit evasion games , Autonomous systems , Multi agent systems , Placement , Cost functions , Gradient based optimization techniques , Time partitioning , Continuous weber function , Continuous multimedian function , Line segments , Constrained travel time , Vertical height , Intercept time , Single vehicle scenarios , Multiple vehicle scenarios , Appolonius circles , Wall pursuit games , Pairwise dominance region , Lloyd descent , La salle invariance principle , Disconnected partitions
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