Abstract
Pursuit games have application to robotics: the pursuer models a moving obstacle and the evader models a robot that tries to reach a goal region without colliding with the moving obstacle, at each moment the robot does not know the future trajectory of the obstacle. The motion of the pursuer and the evader is controlled by their sets of permissible velocities, called indicatrices. We allow indicatrices that are more general than the simple motion (i.e., velocities are bounded by an L 2-norm circle). We provide sufficient condition for a pursuit game to “have value”, in this case we give optimal strategies for the pursuer and the evader. We prove that the pursuit game in which the pursuer and the evader are convex objects moving with simple motion “has value”.
This work was partly supported by Deutsche Forschungsgemeinschaft grant Kl 655/2-2.
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References
P. Agarwal, M. Sharir and P. Shor: Sharp upper and lower bounds for the length of general Davenport-Schinzel sequences. J. Combin. Theory, Ser. A 52(1989), pp. 228–274.
N. M. Amato: Determining the Separation of Simple Polygons. To appear in Internat. J. Comp. Geom. Appl.
F. Aurenhammer: Voronoi Diagrams—A Survey of a Fundamental Data Structure. ACM Computer Surveys 23(3), 1991.
C. Bajaj and M.-S. Kim: Generation of Configuration Space Obstacles: The Case of Moving Algebraic Curves. Algorithmica 4(1989), pp. 157–172.
C. Bajaj and M.-S. Kim: Convex Hulls of Objects Bounded by Algebraic Curves. Algorithmica 6(1991), pp. 533–553.
D. B. Dobkin, D. L. Souvaine, and C. J. Van Wyk: Decomposition and Intersection of Simple Splinegons. Algorithmica 3(1988), pp. 473–485.
D. B. Dobkin and D. L. Souvaine: Computational Geometry in a Curved World. Algorithmica 5(1990), pp. 421–457.
A. Friedman: Differential Games. Wiley-Interscience, New York, 1971.
L. J. Guibas and R. Seidel: Computing Convolutions by Reciprocal Search. Discrete Comput. Geom. 2(1987), pp. 175–193.
J. Hershberger: Finding the upper envelope of n line segments in O(n log n) time. Information Processing Letters 33(1989), pp. 169–174.
R. Isaacs: Differential Games. Wiley, New York, 1965.
N.-M. LÊ: On Determining Optimal Strategies in Pursuit Games in the Plane. Technical Report 172, Dep. of Comp. Science, FernUniversitÄt Hagen, Germany.
T. Lozano-Pérez: Spatial planning: A configuration space approach. IEEE Trans. Computers 32(2), pp. 108–120, 1983.
F. P. Preparata and M. I. Shamos: Computational Geometry. Springer-Verlag, New York, 1985.
J. H. Reif and S. R. Tate: Continuous Alternation: The Complexity of Pursuit in Continuous Domains. Algorithmica 10(1993), pp. 156–181.
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© 1995 Springer-Verlag Berlin Heidelberg
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LÊ, NM. (1995). On determining optimal strategies in pursuit games in the plane. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_100
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DOI: https://doi.org/10.1007/3-540-60084-1_100
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