Motion Planning Through Model Inversion for a Gantry Crane Moving a Double Pendulum

This paper proposes a method for precise motion planning of a gantry crane moving a double pendulum. The payload to be moved is composed by a pendulum and a rigid-body attached to the pendulum terminal mass. The desired output coordinates are the ones of the rigid-body tip. This choice yields a non-minimum phase system, whose internal dynamics is unstable. In this paper it is stabilized through the output redefinition technique, i.e., by assuming a fictitious output within the internal dynamics. The numerical integration of the stabilized ODEs enables to compute the motion commands for the crane platform. Numerical simulations are provided to assess the effectiveness of the proposed method which is corroborated by the low contour and tracking errors obtained while performing a prescribed planar trajectory.