Pursuit and evasion in non-convex domains of arbitrary dimension

Robotics: Science and Systems

Volumn 2, Issue , 2006, Pages 113-120

  Alexander, Stephanie ^a   Bishop, Richard ^a   Ghrist, Robert ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84959285804     PISSN: None     EISSN: 2330765X     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. S. Alexander, I. Berg, R. Bishop, Geometric curvature bounds in Riemannian manifolds with boundary, Transactions Amer. Math. Soc., 339 (1993), 703-716.
2. S. Alexander, R. Bishop, The Fary-Milnor theorem in Hadamard spaces, Proc. Amer. Math. Soc. 126 (1998), 3427-3436.
3. A. Alexandrov, Y. Reshetnyak, General Theory of Irregular Curves, Kluwer Academic Publishers, Dodrecht, Boston, London, 1989.
4. M. Bridson, A. Haefliger, Metric Spaces of Non-positive Curvature, Springer-Verlag, 1999.
5. D. Burago, Y. Burago, S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics, Vol. 33, Amer. Math. Soc., Providence, RI, 2001.
6. J. Canny and J. Reif. Lower bounds for shortest path and related problems. Proc. 28th Ann. IEEE Symp. Found. Comp. Sci., (1987) 49-60.
7. B. Dekster, The length of a curve in a space of curvature ? K, Proc. Amer. Math. Soc. 79 (1980), 271-278.
8. L. Dubins. On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. American Journal of Mathematics 79, (1957) 497-516.
9. R. Ghrist, J. O'Kane, and S. LaValle, Pareto optimal coordination on roadmaps, Proc. Workshop Alg. Foundations of Robotics, 2004.
10. L. Guibas, J.-C. Latombe, S. LaValle, D. Lin, and R. Motwani, A visibility-based pursuit-evasion problem, Inter. J. Comput. Geom. & Applications 9:4-5 (1999), 471-.
11. N. Hovakimyan and A. Melikyan, Geometry of pursuit-evasion on second order rotation surfaces, Dynamics & Control 10(3) (2000), 297-312.
12. R. Isaacs, Differential Games. Wiley Press, NY, 1965.
13. V. Isler, S. Kannan, and S. Khanna, Locating and capturing an evader in a polygonal environment, in Proc. Workshop Alg. Foundations of Robotics, 2004.
14. V. Isler, D. Sun. and S. Sastry, Roadmap based pursuitevasion and collision avoidance, in Proc. Robotics, Systems, & Science, 2005.
15. S. Kopparty and C. Ravishankar, A framework for pursuitevasion games in Rn, Information Proc. Letters, 96 (2005), 114-122.
16. A. Kovshov, The simple pursuit by a few objects on the multidimensional sphere, Game Theory & Applications II, L. Petrosjan and V. Mazalov, eds., Nova Science Publ., (1996) 27-36.
17. C. Maneesawarng and Y. Lenbury, Total curvature and length estimate for curves in CAT(K) spaces. Differential Geom. Appl. 19:2 (2003), 211-222.
18. A. Melikyan, Generalized Characteristics of First Order PDEs, Birkhauser, 1998.
19. J. Mitchell and M. Sharir, New results on shortest paths in three dimensions, Proc. 20th Annual ACM Symposium on Computational Geometry, (2004), 124-133.
20. T. Parsons, Pursuit evasion in a graph, in Theory & Application of Graphs, Y. Alavi and D. Lick, eds., Springer Verlag, (1976), 426-441.
21. Y. Reshetnyak, Nonexpanding maps in a space of curvature no greater than K, Sibirskii Mat. Zh. 9 (1968), 918-928 (Russian).
22. English translation: Inextensible mappings in a space of curvature no greater than K, Siberian Math. Jour. 9 (1968), 683-689.
23. J. Sgall, Solution of David Gale's lion and man problem, Theor. Comp. Sc. 259 (2001), 663-670
24. I. Suzuki and M. Yamashita, Searching for a mobile intruder in a polygonal region. SIAM J. Comput. 21:5 (1992) 863-888.
25. R. Vidalm O. Shakernia, H. Kim, D. Shim, and S. Sastry, Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation. IEEE Trans. Robotics & Aut. 18 (2002), 662-669.