Modeling and Control of PRP-Gantry Crane Systems via Neural IDA-PBC

In this paper, we present a novel underactuated gantry crane (GC) systems where an extra degree-of-freedom actuation is introduced to control the trolley position and its sway angle during motion. The proposed gantry crane systems resembles a prismatic-revolute-prismatic (PRP) robotic configuration where the revolute joint corresponds to the sway angle which is not actuated. Firstly, an energy-based modeling of the PRP-GC systems is presented where both Euler-Lagrange and port-controlled Hamiltonian formalisms are used. Secondly, we present the design of a Neural Interconnection and Damping Assignment Passivity-Based Controller (N-IDA-PBC) that allows for an automated learning of an IDA-PBC controller, where the solutions to the corresponding IDA-PBC matching PDE are not trivial for underactuated systems. Finally, the efficacy of the proposed N-IDA-PBC is evaluated through Monte Carlo simulations, where the neural networks training of N-IDA-PBC uses $3,000$ randomly generated data points and $20,000$ samples of Monte-Carlo simulation are performed, taking into account uncertainties in the systems’ parameters, including initial states, physical damping, and payload masses. The Monte-Carlo simulations show that the trained N-IDA-PBC is able to regulate the trolley position and sway angle to the set-point position and it is robust against parameter uncertainties.