Coordinate transformation and on-line planning for position/force control of constrained robots

A class of coordinate transformations is introduced in order to derive the dynamic equation of a constrained manipulator on the constraining manifold. A theorem of existence is given, and some practical computational guidelines, based on the analytic knowledge of the equation of the constraining manifold, are outlined in order to compute the transformation off-line. If the analytic equations of the constraining manifold are inaccurate, the planned motion will not belong to the true manifold. It is then shown how the desired trajectories, both in the transformed domain and in the joint space domain, may be modified online to force a motion that belongs to the true manifold