Dynamics and flatness-based control of a kinematically undetermined cable suspension manipulator

A kinematically undetermined cable suspension manipulator moves a payload platform in space by several cables with computer-controlled winches, whereby the position of the payload platform is not determined by the lengths of the cables. Trajectory tracking control of the payload platform is achieved by means of the concept of flat systems. A flat system has the property that the state variables and the control inputs can be algebraically expressed in terms of the so-called flat output and a finite number of time derivatives of the flat output. Its application to kinematically undetermined manipulators represents a generalization of computed-torque control. The control forces are algebraically calculated from the desired trajectories of the payload platform and their time derivatives up to the fourth order leading to a feedforward control strategy. Asymptotically stable tracking behavior is achieved by exact linearization of the nonlinear dynamics by means of a so-called quasi-static state feedback. The procedure is described for the trajectory tracking control of the prototype three-cable suspension manipulator CABLEV.