Tracking Manipulator Trajectories With Ordinary Singularities: A Null Space-Based Approach

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Abstract
This article discusses the problem of tracking manipulator end-link trajectories passing through ordinary singularities. It is based on a method developed recently by Kieffer (1992), who suggested parameterizing the end-link trajectory with a parameter that is not time, and considering this parameter as a dependent variable. We show that this is equivalent to a kinematically redundant mechanism comprising the original nonredundant kinematic chain augmented by one more virtual link. The trajectory is actually mapped onto the joint space augmented by the parameter variable. Although the new mech anism performs only a "self-motion" tracking of the projected trajectory through regular points and ordinary singularities, the end-link of the real mechanism tracks the desired trajec tory. Our solution is based on effective null space methods that have been widely applied to kinematically redundant manipula tors. Asymptotic convergence of the tracking error to zero and stability is guaranteed through a closed-loop approach.

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