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When the minimum-time trajectory of a manipulator along a geometrically prescribed path is planned taking into consideration the manipulator's dynamics and actuator's torque limits, at least one of the joints should be at the torque limit. The execution of such a trajectory by a conventional feedback control scheme results in torque saturation. Consequently, the tracking error cannot be suppressed and the manipulator may deviate from the desired path. In this paper, the author's propose a feedback control method for path tracking which takes the torque saturation into account. Based on the desired path, a coordinate system called path coordinates is defined. The path coordinates are composed of the component along the path and the components normal to the path. The equation of motion is described in terms of the path coordinates. Control of the components normal to the path is given priority in order to keep the motion of the manipulator on the path. Simulations of a two-degree-of-freedom manipulator show the effectiveness of this method.>
Arai et al. (Sat,) studied this question.