Singularity-Free Dynamics Modeling and Control of Parallel Manipulators with Actuation Redundancy

Abstract

The modeling, identification, and control of parallel kinematics machines (PKM) have advanced in the last two decades culminating in successful industrial implementations. Still the acceptance of PKM is far beyond that of the well-established serial manipulators, however. This is mainly due to the limited workspace, the drastically varying static and dynamic properties, leading eventually to singularities, and the seemingly more complex control. Traditionally the number of inputs equals the mechanical degree-of-freedom (DOF) of the manipulator, i.e. the PKM is non-redundantly actuated. Actuation redundancy is a means to overcome the aforementioned mechanical limitations. It potentially increases the acceleration capability, homogenizes the stiffness and manipulability, and eliminates input singularities, and thus increases the usable workspace as addressed in several publications as for instance Garg et al. (2009); Gogu (2007); Krut et al. (2004); Kurtz & Hayward (1992); Lee et al. (1998); Nahon & Angeles (1989); O’Brien & Wen (1999); Wu et al. (2009). These advantages are accompanied by several challenges for the dynamics modeling and for the PKM control. A peculiarity of redundantly actuated PKM is that control forces can be applied that have no effect on the PKM motion, leading to mechanical prestress that can be exploited for different second-level control tasks such as backlash avoidance and stiffness modulation Chakarov (2004); Cutkosky & Wright (1986); Kock & Schumacherm (1998); Lee et al. (2005); Muller (2006),Valasek et al. (2005). This also means that the inverse dynamics has no unique solution, which calls for appropriate strategies for redundancy resolution. The implementation of the corresponding model-based control schemes poses several challenges due to model uncertainties, the lack of globally valid parameterizations of the dynamics model, as well to the synchronization errors in decentralized control schemes calling for robust modeling and control concepts Muller (2011c); Muller & Hufnagel (2011). The basis for model-based control are the motion equations governing the PKM dynamics. Aiming on an efficient formulation applicable in real-time, the motion equations are commonly derived in terms of a minimum number of generalized coordinates that constitute a (local) parameterization of the configuration space Abdellatif et al. (2005); Cheng et al. (2003); Muller (2005); Nakamura & Ghodoussi (1989); Yi et al. (1989). A well-known problem Singularity-Free Dynamics Modeling and Control of Parallel Manipulators with Actuation Redundancy