A Flatness-Based Approach to the Control of Distributed Parameter Systems Applied to Load Transportation with Heavy Ropes

Abstract

The cooperative transport of a rigid body carried by multiple heavy ropes that are suspended by tricopters is used as an example for flatness-based trajectory planning for distributed-parameter systems. At first, the load-side ends of the ropes are parametrized by a flat output of the nonlinear boundary system 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 by the means of operational calculus. Evaluating the derived parametrization at the controllable ends yields the desired trajectories for the tricopter positions. A position controller is used to track the reference trajectories of the tricopters. This control can be used to realize a desired transition of the load position and orientation in finite time. Experimental results of the introduced method are presented for validation.