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The solution to the inverse manipulation problem for redundant manipulators has mostly been considered from a geometric-kinematic standpoint. A procedure for the inverse problem solution using the dynamic model of the manipulator and its actuators is developed. Nominal trajectories in the space of joint coordinates are generated so as to be optimal with respect to total energy consumption of the actuators (hydraulic or electric). The treatment of constraints on joint coordinates and rates is also involved in the procedure. The algorithm is illustrated by two industrial robots.
Vukobratović et al. (Sun,) studied this question.