Abstract
The kinematic equation of an fi-link manipulator involves the chain product of n homogeneous link transformation matrices and reveals the requirement for computing a large set of elementary operations: multiplications, additions, and trigonometric functions. However, these elementary operations, in general, cannot be efficiently computed in general-purpose uniprocessor computers. The CORDIC (COordinate Rotation DIgital Computer) algorithms are the natural candidates for efficiently computing these elementary operations and the interconnection of these CORDIC processors to exploit the great potential of pipelining provides a better solution for computing the direct kinematics. This paper describes a novel CORDIC-based pipelined architecture for the computation of direct kinematic position solution based on the decomposition of the homogeneous link transformation matrix. It is found that a homogeneous link transformation matrix can be decomposed into a product of two matrices, each of which can be computed by two CORDIC processors arranged in parallel, forming a 2-stage cascade CORDIC computational module. Extending this idea to an n-link manipulator, n 2-stage CORDIC computational modules, consisting of 4n CORDIC processors, can be concatenated to form a pipelined architecture for computing the position and orientation of the end-effector of the manipulator. Since the initial delay time of the proposed pipelined architecture is 80n μs and the pipelined time is 40μs, the proposed CORDIC-based architecture requires a total computation time of (80n + 120)μs for computing the position and orientation of the end- effector of an n-link manipulator.
Date of this Version
2-1-1987
Comments
Supported in part by the National Science Foundation Engineering Research Center Grant CDR-8500022. Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the funding agency.