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Excerpt from Robotics Research Technical Report: On the Number of Critical Free Contacts of a Convex Polygonal Object Moving in 2-D Polygonal Space We show that the number of critical positions of a convex polygonal object moving amidst polygonal barriers in two dimensional space, at which it makes three simultaneous contacts with the obstacles but does not penetrate into any obstacle is for some s s 6, where k is the number of boundary segments of B, n is the number of wall segments and x, (q) is an almost linear function of q yielding the maximal number of connected graph portions composing the lower envelope of a set of q continuous functions each pair of which intersect in at most s points. We also present an example where the number of such critical contacts is Q(k2n showing that m the worst case our upper bound is almost Optimal. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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