Abstract
The problem can be stated as follows: Given a set of simple polyhedra and two points belonging to the exterior domain of the given polyhedra, determine a near-optimal polygonal line connecting the two points so that the intersection of this polygonal line and the given polyhedra is an empty set. To solve this problem an algorithm is formed for generation of a set of admissible polygonal lines. On the basis of this set, using the optimisation procedure based on ψ-transform, a near-optimal polygonal line is determined.
Zusammenfassung
Es wird folgendes Problem untersucht: Gegeben sei eine Menge von einfachen Polyedern und zwei Punkte außerhalb dieser Polyeder; gesucht ist ein fast-optimaler Polygonzug der die beiden Punkte verbindet und dessen Durchschnitt mit allen Polyedern leer ist. Zur Lösung dieses Problems wird ein Algorithmus angegeben, durch den eine Menge von zulässigen Polygonzügen generiert werden kann. Ausgehend von dieser Menge wird mittels einer auf der ψ-Transformation basierenden Optimierungsprozedur ein fast-optimaler Polygonzug bestimmt.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lozano-Perez, T., Wesley, M. A.: An algorithm for planning collision-free paths among polyhedral obstacles. Comm. ACM22, 560–570 (1979).
Lee, D. T., Preparata, F. P.: Euclidean shortest paths in the presence of rectilinear barriers. Networks14, 393–410 (1984).
Papadimitriou, C.: An algorithm for shortest path motion in three dimensions. Inform. Proc. Letters20, 559–563 (1985).
Sharir, M., Schorr, A.: On shortest paths in polyhedral spaces. SIAM J. Comput.15 (1), 193–215 (1986).
Wong, E., Fu, K.: A hierarchical space approach to three-dimension path planning, IEEE J Rob. Autom.RA-2 (1), 42–58 (1986).
Ashton, J., Hoang, D.: An algorithm for finding optimal paths between points while avoiding polyhedral obstacles. Proc. of the 3rd International Conference on Advanced Robotics1987, 307–312.
Clarkson, K.: Approximation algorithms for shortest path motion planning. ACM1987, 56–65.
Bajaj, C.: An efficient parallel solution for Euclidean shortest path in three dimensions. Proc. Rob. Autom.1986, 1897–1900.
Surla, D., Obradovic, D., Konjovic, Z.: Planning of trajectories for the motion of planar mechanisms in the presence of obstacles. The Fourth Internat. Conf. on Computer Graphics, Dubrovnik, 1990 (to appear).
Surla, D., Rackovic, M.: An algorithm for determing shortest distance between two points a planar containing obstacles. The Fourth Internat. Conf. on Computer Graphics, Dubrovnik, 1990, (to appear).
Lee, D. T., Preparate, F. P.: computational geometry—A survey. IEEE Transactions On ComputersC-33 (12), 1072–1101 (1984).
Чичинадзе, В. К.: Решение невйдпклйх нелинейных задач оптимизации. Москва “Наука”. 1983.
Surla, D., Jerinic, Lj: An algorithm for determining the relation between a straight line (point) and a simple polyhedron. Automatika29, (1–2), A.19-A.29 (1988).
Preparata, F. P., Shamos, M. I.: Computational geometry, monograph. Berlin, Heidelberg, New York: Springer 1985.
Surla, D., Budimac, Z., Detection of the intersection of two simple polyhedra. Informatica1, 49–54 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Surla, D., Rackovic, M. The application of ψ-transform for determining a near-optimal path in the presence of polyhedral obstacles. Computing 48, 203–212 (1992). https://doi.org/10.1007/BF02310534
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02310534