Abstract
The paper addresses the synthesis problem of repeatable Jacobian inverse kinematics algorithms for robotic manipulators. For the kinematics of redundancy 1 this synthesis is accomplished by defining an extended Jacobian inverse that in certain sense approximates the Jacobian pseudo-inverse. The approximation problem is formulated in differential geometric terms, and solved using the existing results on the approximation of a prescribed codistribution by an integrable codistribution. As an illustration, extended Jacobian inverses are derived for the normal form kinematics of a stationary manipulator and a mobile robot.
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