On the number of links and placement of telescoping manipulators in an environment with obstacles

Abstract

The authors consider the following problem: Given an environment with obstacles, what are the minimum number of telescoping links that will allow a manipulator operating in this environment to reach every point in the environment. A geometrical algorithm is presented for solving this problem in a two-dimensional planar case when the obstacles are polygonal. Solutions to some generalizations of this problem are outlined, including simultaneous design of a manipulator and its environment, design of a moving robot and/or obstacles, and design for a three-dimensional workspace. Some theorems on the bounding limits for the number of links of the manipulator are formulated.<>