Journal
IEEE TRANSACTIONS ON ROBOTICS
Volume 24, Issue 6, Pages 1440-1445Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TRO.2008.2006240
Keywords
Approximation; extended Jacobian; Jacobian pseudoinverse; robot kinematics
Categories
Funding
- Foundation for Polish Science
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Extended Jacobian inverse kinematics algorithms for redundant robotic manipulators are defined by combining the manipulator's kinematics with an augmenting kinematics map in such a way that the combination becomes a local diffeomorphism of the augmented taskspace. A specific choice of the augmentation relies on the optimal approximation by the extended Jacobian of the Jacobian pseudoinverse (the Moore-Penrose inverse of the Jacobian). In this paper, we propose a novel formulation of the approximation problem, rooted conceptually in the Riemannian geometry The resulting optimality conditions assume the form of a Poisson equation involving the Laplace-Beltrami operator. Two computational examples illustrate the theory.
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