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Simulation-based fast collision detection for scaled polyhedral objects in motion by exploiting analytical contact equations

Published online by Cambridge University Press:  08 August 2014

Jing-Sin Liu*
Affiliation:
Institute of Information Science, Academia Sinica, Nangang, Taipei, Taiwan 115, Republic of China
Wen-Hua Pan
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 105, Republic of China
Wen-Yang Ku
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON M5S 3G8, Canada
Y.-H. Tsao
Affiliation:
Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan 333, Republic of China
Y.-Z. Chang
Affiliation:
Department of Mechanical Engineering, Chang Gung University, Tao-Yuan, Taiwan 333, Republic of China
*
*Corresponding author. E-mail: liu@iis.sinica.edu.tw

Summary

Based on the results of the study of convex object motion1 (J. Hopcroft and G. Wilfong, “Motion of objects in contact,” Int. J. Robot. Res., 4(4), 32–46 (1986)), this paper addresses the problem of exact collision detection of a pair of scaled convex polyhedra in relative motion, and determines the contact conditions of tangential contact features, arbitrary relative motion involving translation and rotation, and uniform scaling of the objects about a fixed point. We propose a new concept of the decision curve based on analytical contact equations that characterize a continuum of scaling factors (or a single scaling factor), which ensures that a pair of objects undergoing a scaling transformation will maintain the same tangential contact feature pair (or make instantaneous tangential contact feature transitions). We propose a reliable simulation-based approach to construct the decision curve by hybridizing analytical contact equations and conventional collision detection method, called the Fast Collision Detection Method (FCDM). This method can determine whether two scaled objects will make contact at specific tangential contact features (vertices, edges, or faces) under particular uniform scaling factors and after distinctive relative motion with better accuracy and less computational time than the existing collision detection methods. Finally, we demonstrate our approach for solving motion design in simple assembly/disassembly problems.

Type
Articles
Copyright
Copyright © Cambridge University Press 2014 

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References

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Simulation-based fast collision detection for scaled polyhedral objects in motion by exploiting analytical contact equations
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