Presented in this paper is an algorithm that allows the numerical kinematic inversion of robot manipulators in the presence of singularities. It is aimed at continuous-path applications, in which known algorithms produce branch switching and hence jump discontinuities in the joint rates. In the algorithm proposed here the joint rates are computed at singularities as the solution of a quadratic-programming problem that eliminates branch switching. Joint accelerations are computed likewise, and joint angles by Taylor expansion using up to quadratic terms.

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