Flatness‐based control of a rigid body carried by multiple heavy ropes

Abstract

Flatness‐based trajectory planning for the distributed‐parameter system consisting of a rigid body carried by multiple heavy ropes is discussed. The suspension points (controlled ends) of the ropes are assumed to be freely movable. The other ends of the ropes are parametrized by a flat output of the nonlinear boundary system at the load that describes the motion of the rigid body. This parametrization is then used to express the solution of the linearized partial differential equations for the heavy ropes under small angle approximations around a vertical equilibrium configuration by the means of operational calculus. It is shown that the system trajectories of the ropes depend on distributed delays and advances of the flat output trajectory at the load‐side boundary system. Evaluating the derived parametrization of the heavy ropes at the controllable ends yields the desired open‐loop controller by using a planned trajectory for the flat output. This control can be used to realize a desired transition of the load position and orientation in finite time. The introduced method is illustrated for the example of a linear infinite‐dimensional model of two heavy ropes carrying a rigid rod.