Energy-Based Discretization with an Application to the Heavy Rope

A finite-dimensional nonlinear model for the heavy rope with a freely moving suspension point is presented using energy-based discretization. The derivation proceeds from the Lagrangian to derive the lumped model by discretizing the Lagrange density and applying the principle of least action. The discretized model is simulated at multiple resolutions, incorporating flatness-based motion planning schemes. The planned trajectory is executed on an industrial robot, with a heavy rope attached to its end-effector. Using camera-based offline tracking of the rope's free end, comparisons are conducted between the simulation model and the planned trajectory, as well as between the measurements and the planned trajectory.