An Open-Loop Control for Underactuated Manipulators Using Oscillatory Inputs: Steering Capability of an Unactuated Joint

Abstract—An open-loop control for underactuated mechanical systems using oscillatory inputs with amplitude and frequency modulations is investigated. Once all actuated joints are moved to their desired positions, oscillatory inputs are applied to an actuated joint to move the remaining unactuated joints. The steering force of the unactuated joints is achieved by utilizing the dynamic coupling between actuated and unactuated joints. Such a dynamic coupling occurs due to the oscillatory motions of an actuated joint. Once the frequency of the oscillatory input is decided, the amplitude is determined by analyzing a time-invariant system, which is derived from the unactuated joint dynamics by the method of averaging. A systematic way, via a generating equation and a coordinate transformation derived from the generating equation, for converting the unactuated joint dynamics into the standard form of averaging is proposed. In the event of an actuator failure in outer space, the failed joint can be steered by adopting the method proposed. Illustrating examples are given. Experimental results are provided. Index Terms—Asymptotic method, averaging, open-loop control, underactuated manipulator, vibrational control