Trajectory Tracking for a Three-Cable Suspension Manipulator by Nonlinear Feedforward and Linear Feedback Control
The kinematically indeterminate cable suspension manipulator Cablev moves a payload platform in space by three spatially arranged cables with independently controllable winches. As the position of the platform is not fully determined by the lengths of the
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Abstract The kinematically indeterminate cable suspension manipulator Cablev moves a payload platform in space by three spatially arranged cables with independently controllable winches. As the position of the platform is not fully determined by the lengths of the cables, undesired sway motions of the payload platform may occur. To make the payload platform track prescribed translational and rotational reference trajectories in space, a two-stage control concept is presented. A nonlinear feedforward control that exploits the flatness property of the system generates control inputs for the undisturbed motion along reference trajectories. Sway motions caused by disturbances are actively damped by a linear feedback of measured state variables enabling an asymptotically stable tracking behaviour. Experimental results from the prototype system Cablev are shown.
1 Introduction Cable suspension manipulators support a payload platform in space by several spatially arranged cables with computer-controlled winches. The winches are mounted either fixed or on movable trolleys. Compared to conventional cranes, not only the translational motion of the payload can be controlled but also its orientation. Cable suspension manipulators can be classified with respect to mobility and statics, see Table 1. The kinematically parallel suspension of a platform by a system of cables is kinematically determinate if the position of the payload platform is geometrically defined by the actual lengths of the tense cables. It is kinematically indeterminate if the platform is (finitely or infinitesimally) movable while the cable lengths are kept constant. The suspension is statically determinate if the cable forces C. Woernle (B) University of Rostock, Rostock, Germany e-mail: [email protected] T. Bruckmann and A. Pott (eds.), Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, DOI: 10.1007/978-3-642-31988-4_23, © Springer-Verlag Berlin Heidelberg 2013
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Table 1 Kinematic and static determinateness
K
K
can be calculated by means of the six (static or dynamic) equilibrium conditions for the platform only, otherwise it is statically indeterminate. A payload platform suspended by six cables in analogy to a Gough-Stewart platform is kinematically and statically determinate as long as all cables are kept under tension by the gravity force [1, 4]. With more than six cables the platform is, in general, kinematically determinate but statically indeterminate. Examples are shown in [3, 9, 12, 13]. A platform suspended by less than six cables is kinematically indeterminate. Three-cable suspensions as described in [2, 10, 17] are, in general, statically determinate. A platform suspension with four parallel cables is statically indeterminate. Workspaces and singularities are investigated in [15]. In this contribution the kinematically indeterminate cable suspension manipulator Cablev is described (Fig. 1). It was developed at University of Rostock as a prototype system to validate control concepts [7, 8, 10]. Its pa
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