A closed‐loop jacobian transpose scheme for solving the inverse kinematics of nonredundant and redundant wrists

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Abstract
The solution of the inverse kinematic problem is of the utmost importance in robotic manipulator control. This article proposes a closed‐loop scheme for solving the inverse kinematic problem for nonredundant and redundant wrists based on the computation of the Jacobian transpose. The manipulability measure is suitably introduced as a constraint for redundant wrists, by taking advantage of the null space of the Jacobian matrix. The resulting algorithm provides a computational tool to solve a specified orientation trajectory into a joint trajectory. Numerical results with two spherical wrists show the excellent performance of the scheme.

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