Energy-Based Nonlinear Control of Underactuated Euler-Lagrange Systems Subject to Impacts

In this paper, energy-based nonlinear controllers are designed to globally asymptotically stabilize an underactuated mechanical system. An interesting aspect of the problem is that the equilibrium points of some states are defined by contact with a surface while the equilibrium points of remaining states are defined by noncontact positions. To stabilize the states of the system an energy coupling strategy is employed. The energy coupling approach 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.