The inverse kinematic problem for manipulator arms consists of computing the time course of the joint free variables, which correspond to a desired time course of the position/orientation of the hand in space. This problem involves the solution of complicated trigonometric equations and furthermore, for anthropomorphic manipulator arms (which have at least seven degrees of freedom), the problem is underdetermined, requiring therefore to solve an associated optimization task. The proposed approach is recursive, partly analytical and partly numerical. From a geometrical model of the arm, based on rotation matrices and Rodrigues vectors, we derive two algorithms: the former computes a sequence of arm configurations (the output variables) from a given sequence of hand positions/orientations (the input variables) and the latter adjusts the updated configurations according to a quadratic optimization criterion.

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