A higher order adaptive approach of the swinging problem — Implementation issues

In the case of a crane that carries its payload swinging on a cable precise control of a subsystem passively connected to a directly controllable one by elastic connection is needed. Normally the connected degree of freedom has little damping and it is apt to keep swinging accordingly. Traditionally the "input shaping technology" is applied for cranes to assist the human operator responsible for the manipulation task. Presently a novel adaptive approach applying robust fixed point transformations based iteration is proposed for tackling the problem of simultaneous presence of the imprécisions of the available dynamic system model and the swinging phenomenon. In the simulations a simple model is used for describing this phenomenon: the payload is connected to a 2 degree of freedom crane that is directly controlled by force control. Though the control can directly influence only the 4^th time-derivative of the trajectory of the dragged system, it is assumed that only the 2^nd time-derivatives of the Cartesian coordinates of the point connecting the payload to the cable can be measured via cheap microscopic acceleration sensors. It is suggested that the 4^th and 3^rd time-derivatives that are needed for the controller can be estimated by using the available approximate dynamic model and the directly measured 2^nd time-derivatives. Preliminary simulation results seem to support this assumption.