Consequences of Geometric Imperfections for the Control of Redundantly Actuated Parallel Manipulators

Actuation redundancy increases and homogenizes the kinematic dexterity and stiffness as well as the force distribution among the actuators of parallel-kinematics machines (PKMs). It also allows for internal prestresses within the PKM without affecting the environment that can potentially be used to account for secondary tasks, such as active stiffness and backlash-avoiding control. However, in the presence of geometric uncertainties, this feature can become a serious problem, since then, control forces may be annihilated, or even some of the intentional prestress components may interfere with the environment. While model uncertainties can generally be tackled with robust-control concepts, actuation redundancy of PKM impedes the use of established robust-control schemes. The effect of such uncertainties and the applicability of standard model-based control schemes are analyzed in this paper. It is shown that geometric uncertainties lead to parasitic perturbation forces that cannot be compensated by adjustment of the controls. An amended version of the augmented PD and computed torque-control scheme is proposed that does not suffer from such effects.