Inverse Dynamics for Feedforward Control of an Underactuated 6-DOF Gantry Crane

Inverse dynamics in underactuated, non-minimum phase multibody systems is addressed in this paper by means of the challenging example of a gantry crane driving a spatial double pendulum. The latter consists of a pendulum plus a spatial rigid body attached to the pendulum terminal mass. The reference to be tracked is imposed to the two planar Cartesian coordinates of the rigid-body tip, while the actuated coordinates are those of the trolley. Because of underactuation and non-flat property of the system, inverse dynamics relies on a mixed algebraic and differential scheme. Additionally, this input-output configuration leads to a system with an unstable internal dynamic, whose integration cannot be done unless stabilization is performed. By exploiting the concept of output redefinition, i.e., by assuming a fictitious output in the internal dynamics equations, stabilization is performed, while ensuring excellent tracking performances. Numerical simulations proof the method effectiveness.