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Optimal Extended Jacobian Inverse Kinematics Algorithms for Robotic Manipulators

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1 Author(s)
Tchon, K. ; Inst. of Comput. Eng., Wroclaw Univ. of Technol., Warsaw

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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Robotics, IEEE Transactions on  (Volume:24 ,  Issue: 6 )