Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra

Authors: M. Khouil, N. Saber, M. Mestari

Abstract:

In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: Collision identification, fixed time, convex polyhedra, neural network, AMAXNET.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1092800

References:

[1] M.Mestari, ‘An analog Neural Network implementation in Fixed Time of Adjustable Order Statistic Filters and Applications’ IEEE transactions on Neural Networks vol 15.No 3 pp 766-785, May2004.
[2] J.Yuan, ‘Collision Identification between Convex Polyhedra Using Neural Networks’, IEEE, April 1995.
[3] M. Mestari and A. Namir, "AMAXNET: A neural network implementation of adjustable MAXNET in fixed time”, IFAC-IFIP- IMACS Proc. Internat. Conf. on Control of Industrial Systems, 20-22 May, Belfort, (France), vol. 2, 543-549, 1997.
[4] M. Mestari, A. Namir, K. Akodadi and A. Badi,"Θ(1) Time Neural Network Minimum Distance Classifier and its Application to Optical Character Recognition Problem", Applied Mathematical Sciences, Vol. 2, 2008, no. 26, 1253 - 1282, November 2007.
[5] M. Mestari and A. Namir, "AOSNET: A Neural Network Implementation of Adjustable Order Statistic Filters In Fixed Time", SAMS, 2000, Vol. 36, pp. 509-535.
[6] F. Chin and C. A. Wang, "Optimal algorithms for the intersection and minimum distance problems between planar polygons", IEEE Trans. Comput., vol. C-32, pp. 1203-1207, 1984.
[7] D. P. Dobkin and D. G. Kirkpatrick, "A linear algorithm for determining the separation of convex polyhedra", J. Algorithms, vol. 6, pp. 381-392, 1985.
[8] H. Edelsbrunner, "On computing the extreme distances between two convex polygons", J. Algorithms, vol. 6, pp. 515-542, 1985.
[9] E. G. Gilbert and D. W. Johnson, "Distance functions and their application to robot path planning in the presence of obstacles", IEEE J. Robotics Automation, vol. RA-1, no. 1, pp. 21-30, 1985.
[10] D. T. Lee and F. P. Preparata, "Computational geometry, A survey", IEEE Trans. Comput., vol. C-33, pp. 1072-1101, 1984.
[11] J. T. Schwartz, "Finding the minimum distance between two convex polygons", inform. Professor. Lett., col. 13, pp. 168-170, 1981.
[12] C. Y. Liu and R. W. Mayne, "Distance calculations in motion planning problems with interference situations", in Proc. 1990 ASME Design Tech. Conf., vol. 23, no. 1, 1990, pp. 145-152.
[13] K. Fukushima, .”A neural network for visual pattern recognition”, IEEE Computer, pp. 65-75, Mar., 1988.
[14] T. Kohonen, ”Correlation matrix memories”, IEEE Trans. Computers, vol.C-21, 353-359, 1972.