Robust IDA-PBC for under-actuated systems with inertia matrix dependent of the unactuated coordinates: application to a UAV carrying a load

This paper presents a methodology to solve the problem of robustification of Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) scheme for the case of under-actuated systems with inertia matrix dependent of the unactuated coordinates. Specifically, we analyze the robustness of the IDA-PBC strategy with respect to constant external disturbances. This algorithm requires adding an integral action with a particular change of coordinates in an outer-loop to the IDA-PBC strategy to reject constant external disturbances. The asymptotic stability of the proposed controller despite constant external disturbances is proved using the closed-loop Hamiltonian as a Lyapunov candidate function and LaSalle's invariance principle. Finally, as a proof of concept, we have applied the proposed robust IDA-PBC strategy to an Unmanned Aerial vehicle that transports a payload suspended by a cable, which is a class of underactuated system with inertia matrix dependent of the unactuated coordinate. Satisfactory results in numerical experiments demonstrate the applicability of the method.