Linearised feedforward control of a four-chain crane manipulator

For a crane manipulator suspending a flexible metal plate by four chains feedforward control is derived that moves the payload along desired spatial trajectories. Due to the statically indeterminate suspension, the stiffness of the payload has to be taken into account. The actuator coordinates can be algebraically calculated from the desired trajectory of the plate at the position, velocity and acceleration levels exploiting the flatness property of the system. As the system is kinematically redundant, a technically meaningful solution like minimal inclination angles of the chains are determined by optimisation. As the iterative calculation of the nonlinear constrained optimisation problem is computationally expensive and not suitable for implementation on the crane controller, a linearised inverse dynamics model is derived that describes small sway motions of the flexible payload around a static equilibrium state. Linearised and nonlinear feedforward control are compared in a numerical simulation of the crane system.