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RESEARCH PAPERS: Mechanisms and Robotics Papers

Discretely Actuated Manipulator Workspace Generation by Closed Form Convolution

[+] Author and Article Information
Imme Ebert-Uphoff, Gregory S. Chirikjian

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218

J. Mech. Des 120(2), 245-251 (Jun 01, 1998) (7 pages) doi:10.1115/1.2826965 History: Received April 01, 1996; Online December 11, 2007

Abstract

We determine workspaces of discretely actuated manipulators using convolution of real-valued functions on the Special Euclidean Group. Each workspace is described in terms of a density function that provides the number of reachable frames inside any unit volume of the workspace. A manipulator consisting of n discrete actuators each with K states can reach Kn frames in space. Given this exponential growth, brute force representation of discrete manipulator workspaces is not feasible in the highly actuated case. However, if the manipulator is of macroscopically-serial architecture, the workspace can be generated by the following procedure: (1) partition the manipulator into B kinematically independent segments; (2) approximate the workspace of each segment as a continuous density function on a compact subset of the Special Euclidean Group; (3) approximate the whole workspace as a B-fold convolution of these densities. We represent density functions as finite Hermite-Fourier Series and show for the planar case how the B-fold convolution can be performed in closed form. If all segments are identical only O(log B) convolutions are necessary.

Copyright © 1998 by The American Society of Mechanical Engineers
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