A sequential pursuer-target assignment problem under external disturbances

In this paper we deal with the problem of a team of pursuers distributed in the plane subject to an environmental disturbance (e.g., wind). The objective of the pursuers is to intercept a moving target which is not affected by the presence of the disturbance. We solve this problem by assigning only one pursuer to chase the target at every instant of time, based on a Voronoi-like partition of the plane. During the pursuit, the pursuer assignment changes dynamically based on this partition. We present an algorithm to efficiently update this Voronoi-like partition on-line. Simulations are included to illustrate the theoretical results.

[1]  Efstathios Bakolas,et al.  Minimum-Time Paths for a Small Aircraft in the Presence of Regionally-Varying Strong Winds , 2010 .

[2]  Efstathios Bakolas,et al.  The Zermelo-Voronoi Diagram: a dynamic partition problem , 2010, ACC.

[3]  A. I. Blagodatskikh.  Group pursuit in Pontryagin’s nonstationary example , 2008 .

[4]  Olivier Devillers.  On Deletion in Delaunay Triangulations , 2002, Int. J. Comput. Geom. Appl..

[5]  Leonidas J. Guibas,et al.  Voronoi Diagrams of Moving Points in the Plane , 1991, WG.

[6]  Efstathios Bakolas,et al.  Optimal pursuer and moving target assignment using dynamic Voronoi diagrams , 2011, Proceedings of the 2011 American Control Conference.

[7]  David M. Mount,et al.  Dynamic maintenance of Delaunay triangulations , 1991 .

[8]  Thomas Roos,et al.  Voronoi Diagrams over Dynamic Scenes , 1993, Discret. Appl. Math..

[9]  A. A. Chikrii,et al.  On a group pursuit problem , 1982 .

[10]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  J.P. Hespanha,et al.  Multiple-agent probabilistic pursuit-evasion games , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Leonidas J. Guibas,et al.  An empirical comparison of techniques for updating Delaunay triangulations , 2004, SCG '04.

[13]  A. I. Blagodatskikh.  Simultaneous multiple capture in a simple pursuit problem , 2009 .

[14]  Olivier Devillers,et al.  Dog Bites Postman: Point Location in the Moving Voronoi Diagram and Related Problems , 1993, Int. J. Comput. Geom. Appl..

[15]  Efstathios Bakolas,et al.  Feedback Navigation in an Uncertain Flowfield and Connections with Pursuit Strategies , 2012 .

[16]  Olivier Devillers,et al.  Queries on Voronoi Diagrams of Moving Points , 1996, Comput. Geom..

[17]  Richard C. T. Lee,et al.  Voronoi Diagrams of Moving Points in the Plane , 1990, FSTTCS.

[18]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[19]  Otomar Hájek,et al.  Pursuit Games: An Introduction to the Theory and Applications of Differential Games of Pursuit and Evasion , 2008 .

[20]  S. Shankar Sastry,et al.  Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation , 2002, IEEE Trans. Robotics Autom..

[21]  Efstathios Bakolas,et al.  The Zermelo-Voronoi Diagram: a dynamic partition problem , 2010, Proceedings of the 2010 American Control Conference.

[22]  Efstathios Bakolas,et al.  Relay pursuit of a maneuvering target using dynamic Voronoi diagrams , 2012, Autom..

[23]  Pierre Alliez,et al.  Filtering Relocations on a Delaunay Triangulation , 2009, Comput. Graph. Forum.

[24]  Olivier Devillers,et al.  The Delaunay Hierarchy , 2002, Int. J. Found. Comput. Sci..

[25]  Ickjai Lee,et al.  Interactive Analysis Using Voronoi Diagrams: Algorithms to Support Dynamic Update from a Generic Triangle‐based Data Structure , 2002, Trans. GIS.