Vibrational control of underactuated mechanical systems: Control design through averaging analysis

An open loop vibrational control for an underactuated mechanical system wit h amplitude and frequency modulation is investigated. Since there is no dir ect external input to an unactuated joint, the dynamic coupling between the actuated and unactuated joins is utilized for controlling the unactuated j oint. Feedback linearization has been performed to fully incorporate the kn own nonlinearities of the underactuated system considered. The actuated joi nts are firstly positioned to their desired locations, and then periodic os cillatory inputs ape applied to the actuated joints to move the remaining u nactuated joints to their target positions. The amplitudes and frequencies of the vibrations introduced are determined through averaging analysis. A s ystematic way of obtaining an averaged system for the underactuated system via a coordinate transformation is developed. A manipulator in the zero gra vity space can be vibrationally controlled in the event of actuator failure . A control design example of the 2R planar manipulator with a free joint w ith no brake is provided.