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Resolved-rate and resolved-acceleration controllers have been proposed for manipulators whose trajectories are determined by real-time sensory feedback. For redundant manipulators, these controllers have been generalized using the pseudoinverse of the manipulator Jacobian. However, near singular configurations, these controllers fail in that they require infeasibly large joint speeds. A damped least-squares reformation of the problem gives approximate inverse kinematic solutions that are free of singularities. Away from singularities the new controllers closely approximate their conventional counterparts; near singular configurations the new controllers remain well-behaved, although the rate of convergence decreases. This paper defines the new controllers and proves their stability. Some aspects of the behavior of the new resolved-rate controller are illustrated in simulations.
Wampler et al. (Tue,) studied this question.