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In this note, Lyapunov-based methods are used to design a class of energy-based nonlinear controllers to globally asymptotically stabilize/regulate an underactuated mechanical system subject to an impact collision. The impact model is considered as an elastic contact with finite stiffness. One of the difficulties in controlling impact is that the equations of motion are quite different when the system status changes from a noncontact condition to a contact condition. Another difficulty arises when an impact occurs with an underactuated system because the impact may lead to instabilities or excessive transients. An energy coupling approach is developed in this paper that is motivated by the desire to improve the transient response of the system. A Lyapunov stability analysis and numerical simulations are provided to demonstrate the stability and performance of the developed controllers.
Date of Publication: Sept. 2007