Abstract
Planning corridors among obstacles has arisen as a central problem in game design. Instead of devising a one-dimensional motion path for a moving entity, it is possible to let it move in a corridor, where the exact motion path is determined by a local planner. In this paper we introduce a quantitative measure for the quality of such corridors. We analyze the structure of optimal corridors amidst point obstacles and polygonal obstacles in the plane, and propose an algorithm to compute approximations for optimal corridors according to our measure.
This work has been supported in part by the IST Programme of the EU as Shared-cost RTD (FET Open) Projects under Contract No IST-2001-39250 (MOVIE — Motion Planning in Virtual Environments) and IST-006413 (ACS - Algorithms for Complex Shapes) , and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L.E., Thrun, S.: Principles of Robot Motion: Theory, Algorithms, and Implementations, ch.7. MIT Press, Boston (2005)
Gray, A.: Modern Differential Geometry of Curves and Surfaces with Mathematica. In: Logarithmic Spirals, 2nd edn., pp. 40–42. CRC Press, Boca Raton (1997)
Kamphuis, A., Overmars, M.H.: Motion planning for coherent groups of entities. In: Proc. IEEE Int. Conf. Robotics and Automation, pp. 3815–3822 (2004)
Kamphuis, A., Pettre, J., Overmars, M.H., Laumond, J.-P.: Path finding for the animation of walking characters. In: Proc. Eurographics/ACM SIGGRAPH Sympos. Computer Animation, pp. 8–9 (2005)
Kavraki, L.E., Švestka, P., Latombe, J.-C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robotics and Automation 12, 566–580 (1996)
Khatib, O.: Real-time obstacle avoidance for manipulators and mobile robots. Int. J. Robotics Research 5(1), 90–98 (1986)
Latombe, J.-C.: Robot Motion Planning, ch. 7. Kluwer Academic Publishers, Boston (1991)
Lee, D.-T., Drysdale III, R.L.: Generalization of Voronoi diagrams in the plane. SIAM J. on Computing 10(1), 73–87 (1981)
Mitchell, J.S.B.: Shortest paths and networks. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, ch.27, 2nd edn., pp. 607–642. Chapman & Hall/CRC, Boca Raton (2004)
Mitchell, J.S.B., Papadimitriou, C.H.: The weighted region problem: Finding shortest paths through a weighted planar subdivision. J. of the ACM 38(1), 18–73 (1991)
Nieuwenhuisen, D., Kamphuis, A., Mooijekind, M., Overmars, M.H.: Automatic construction of roadmaps for path planning in games. In: Proc. Int. Conf. Computer Games: Artif. Intell., Design and Education, pp. 285–292 (2004)
Nieuwenhuisen, D., Overmars, M.H.: Motion planning for camera movements. In: Proc. IEEE Int. Conf. Robotics and Automation, pp. 3870–3876 (2004)
Nieuwenhuisen, D., Overmars, M.H.: Useful cycles in probabilistic roadmap graphs. In: Proc. IEEE Int. Conf. Robotics and Automation, pp. 446–452 (2004)
Ó’Dúnlaing, C., Yap, C.K.: A “retraction” method for planning the motion of a disk. J. Algorithms 6, 104–111 (1985)
Overmars, M.H.: Path planning for games. In: Proc. 3rd Int. Game Design and Technology Workshop, pp. 29–33 (2005)
Reif, J., Wang, H.: Social potential fields: a distributed behavioral control for autonomous robots. In: Goldberg, K., Halperin, D., Latombe, J.-C., Wilson, R. (eds.) International Workshop on Algorithmic Foundations of Robotics, pp. 431–459. A. K. Peters (1995)
Russel, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice Hall, Englewood Cliffs (2002)
Wein, R., van den Berg, J., Halperin, D.: Planning near-optimal corridors amidst obstacles. Technical report, Tel-Aviv University (2006), http://www.cs.tau.ac.il/~wein/publications/pdfs/corridors.pdf
Wein, R., van den Berg, J.P., Halperin, D.: The visibility-Voronoi complex and its applications. In: Proc. 21st Annu. ACM Sympos. Comput. Geom., pp. 63–72 (2005); In: Computational Geometry: Theory and Applications (to appear)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wein, R., van den Berg, J., Halperin, D. (2008). Planning Near-Optimal Corridors Amidst Obstacles. In: Akella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds) Algorithmic Foundation of Robotics VII. Springer Tracts in Advanced Robotics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68405-3_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-68405-3_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68404-6
Online ISBN: 978-3-540-68405-3
eBook Packages: EngineeringEngineering (R0)