On the movement of robot arms in 2-dimensional bounded regions
Date
1982
Authors
Hopcroft, John
Joseph, Deborah
Whitesides, Sue
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
Abstract
The classical mover's problem is the following: can a rigid object in 3-dimensional space be moved from one given position to another while avoiding obstacles? It is known that a more general version of this problem involving objects with movable joints is PSPACE-complete, even for a simple tree-like structure. In this paper, we investigate a 2-dimensional mover's problem in which the object being moved is a robot arm with an arbitrary number of joints. We reduce the mover's problem for arms constrained to move within bounded regions whose boundaries are made up of straight lines to the mover's problem for a more complex linkage that is not constrained. We prove that the latter problem is PSPACE-hard even in 2-dimensional space and then turn to special cases of the mover's problem for arms. In particular, we give a polynomial time algorithm for moving an arm confined within a circle from one given configuration to another. We also give a polynomial time algorithm for moving the arm from its initial position to a position in which the end of the arm reaches a given point within the circle.
Description
©1982 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords
robotics, manipulators, mechanical arms, algorithms, polynomial time
Citation
Hopcroft, J, Joseph, D, Whitesides, S, Foundations of Computer Science, 1982. SFCS 08. 23rd Annual Symposium, pgs 280-289.