A Minimum Path Algorithm Among 3D-Polyhedral Objects

Aysin Yeltekin

doi:10.1117/12.949080

10 March 1989 A Minimum Path Algorithm Among 3D-Polyhedral Objects

Aysin Yeltekin

Proceedings Volume 1007, Mobile Robots III; (1989) https://doi.org/10.1117/12.949080
Event: 1988 Cambridge Symposium on Advances in Intelligent Robotics Systems, 1988, Boston, MA, United States

Abstract

In this work we introduce a minimum path theorem for 3D case. We also develop an algorithm based on the theorem we prove. The algorithm will be implemented on the software package we develop using C language. The theorem we introduce states that; "Given the initial point I, final point F and S be the set of finite number of static obstacles then an optimal path P from I to F, such that PA S = 0 is composed of straight line segments which are perpendicular to the edge segments of the objects." We prove the theorem as well as we develop the following algorithm depending on the theorem to find the minimum path among 3D-polyhedral objects. The algorithm generates the point Qi on edge ei such that at Qi one can find the line which is perpendicular to the edge and the IF line. The algorithm iteratively provides a new set of initial points from Qi and exploits all possible paths. Then the algorithm chooses the minimum path among the possible ones. The flowchart of the program as well as the examination of its numerical properties are included.

Citation Download Citation

Aysin Yeltekin "A Minimum Path Algorithm Among 3D-Polyhedral Objects", Proc. SPIE 1007, Mobile Robots III, (10 March 1989); https://doi.org/10.1117/12.949080

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