Energy shaping control of underactuated mechanical systems with fluidic actuation

Energy shaping is a remarkably effective control strategy which can be applied to a wide range of systems, including underactuated mechanical systems. However, research in this area has generally neglected actuator dynamics. While this is often appropriate, it might result in degraded performance in the case of fluidic actuation. In this work we present some new results on energy shaping control for underactuated mechanical systems for which the control action is mediated by a pressurized ideal fluid. In particular, we introduce an extended multi-step energy shaping and damping-assignment controller design procedure that builds upon the Interconnection-and-damping-assignment Passivity-based-control methodology in a modular fashion to account for the pressure dynamics of the fluid. Stability conditions are assessed with a Lyapunov approach, the effect of disturbances is discussed, and the case of redundant actuators is illustrated. The proposed approach is demonstrated with numerical simulations for a modified version of the classical ball-on-beam example, which employs two identical cylinders, either hydraulic or pneumatic, to actuate the beam.