Redundant Actuation of Parallel Manipulators

High stiffness, low inertia, large accelerations, and high precision are desirable properties attributed to parallel kinematics machines (PKM). However, relatively small workspace and the abundance of singularities within the workspace partly annihilate the aforementioned advantages. Redundant actuation and novel redundant kinematics are means to tackle these shortcomings. Redundant parallel kinematics machines are ideal candidates for use in highprecision applications, such as robot-assisted surgery. Their advantageous features promise to deliver the needed accuracy, stiffness, dexterity and reliability. Redundant actuation admits to eliminate singularities, increase the usable workspace, augment the dexterity, and partially control the internal forces. Actuator redundancy is also a means to improve fault tolerance, as redundant actuators can compensate the failure of other actuators. Redundant actuation increases the payload and acceleration, can yield an optimal load distribution among the actuators, or can reduce the power consumption of the individual drives. Actuator redundancy can also improve the force transmission properties and the manipulator stiffness. It can be purposefully exploited for secondary tasks, such as the generation of internal prestress and the generation of a desired compliance of the PKM. The first can be used to avoid backlash, whereas the second admits to homogenize the stiffness properties within the workspace. Kinematically redundant PKM, i.e. systems that possess a higher mobility then required for the task, allow to circumvent singularities as well as obstacles, and to increase the dexterity. The control of redundantly actuated PKM poses additional challenges, rooted in the resolution of the redundancy within the control schemes. Whereas, model-based control techniques can be directly applied to the control of non-redundantly actuated PKM, redundancy, however, brings up two specific problems, one is the computationally efficient resolution of the actuation redundancy, and the other is the occurrence of unintentional antagonistic actuation due to model uncertainties. This chapter is devoted to the modeling and control of redundantly actuated PKM. The aim of the chapter is to summarize concepts for dynamic modeling of redundantly actuated PKM, with emphasize on the inverse dynamics and control, and to clarify the terminology used in the context of redundant actuation. Based on a mathematical model, PKM are regarded as non-linear control systems. The chapter is organized as follows. A short literature review in section 2 is meant to familiarize the reader with current developments and research directions. In order to point out the potential of redundantly actuated PKM, a motivating example is given in section 3.