EODM-a novel representation for collision detection

Jung and Gupta reported (1996) a representation, called octree distance map (ODM), for efficient collision detection in static environments. ODM captured partial distance information in a hierarchical manner and traded some memory (2 bytes per white node) for speed gains (as compared to an octree) in collision detection. In this paper, we propose a much more complete and systematic hierarchical representation for distance maps, the extended octree distance map (EODM). Like ODM, it utilizes an octree as the base representation. Along the perimeter of each white node in the octree, it stores a distance function that represents the distance of each boundary point of the white node to the obstacle closest to that point. As a result, EODM is more memory intensive than an ODM (and an octree), however, it would significantly decrease the collision detection time compared to either a conventional octree or the ODM. EODM is computed once and then repeatedly used for collision detection queries. We present algorithms for creating the EODM and use it for collision detection. Our preliminary experiments in 2D show that while EODM requires about three to five times more memory than an octree and four to five times extra memory than an ODM, it speeds up collision detection by a factor of three to six compared to an octree and by a factor of three to four as compared to an ODM