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Generalized Swing-Up Control of Underactuated Mechanical Systems

Time-reversal symmetry, which is one of the main characteristics of mechanical systems without frictional forces, is applied to underactuated mechanical systems to generate desired trajectories for the generalized swing-up control. A novel necessary and sufficient condition is provided to examine whether a system trajectory is time-reversible. A desired trajectory for the generalized swing-up control is experimentally generated by a simple swing-down controller. The time-reverse of the swing-down trajectory is used as the desired trajectory for the generalized swing-up control. With the help of this method, desired swing-up trajectories can be generated also for the popular underactuated mechanical systems with pendulum-like zero dynamics such as the Acrobot, the Pendubot, the Furuta pendulum or the cart-pendulum system. Moreover, it is argued heuristically that a planar robot with an arbitrary number of revolute joints can always be swung up by only one driven joint. The theoretical results are supported by simulations with a planar robot with three revolute joints whose only one joint is actuated.