Computational aspects of the product-of-exponentials formula for robot kinematics

In this article we investigate the modeling and computational aspects of the product-of-exponentials (POE) formula for robot kinematics. While its connections with Lie groups and Lie algebras give the POE equations mathematical appeal, little is known regarding its usefulness for control and other a...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1994-03, Vol.39 (3), p.643-647
Main Author: Park, F.C.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer aided manufacturing
Computer science
control theory
systems
Control systems
Control theory. Systems
Exact sciences and technology
Flexible manufacturing systems
Manufacturing processes
Optimal control
Production systems
Robot kinematics
Robotics
Routing
Stochastic processes
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Summary:In this article we investigate the modeling and computational aspects of the product-of-exponentials (POE) formula for robot kinematics. While its connections with Lie groups and Lie algebras give the POE equations mathematical appeal, little is known regarding its usefulness for control and other applications. We show that the POE formula admits a simple global interpretation of an open kinematic chain and possesses several useful device-independent features absent in the Denavit-Hartenberg (DH) representations. Methods for efficiently computing the forward kinematics and Jacobian using these equations are presented. In particular, the computational requirements for evaluating the Jacobian from the POE formula are compared to those of the recursive methods surveyed in Orin and Schrader (1984).< >
ISSN:0018-9286
1558-2523
DOI:10.1109/9.280779