A Robust Geometric Method of Singularity Avoidance for Kinematically Redundant Planar Parallel Robot Manipulators Nicholas Baron 1 , Andrew Philippides 1 , Nicolas Rojas 2 1 School of Engineering and Informatics, University of Sussex, Brighton BN1 9RH, UK {n.baron, andrewop}@sussex.ac.uk 2 Dyson School of Design Engineering, Imperial College London, London SW7 2DB, UK n.rojas@imperial.ac.uk Abstract Jacobian-based methods of singularity analysis are known to be unreliable when applied to kinematically redundant parallel robot manipulators, due to their potential to miss certain singularities and incorrectly identify others in the manipulator’s workspace. In this paper, a geometric method of singularity avoidance for kinematically redundant planar parallel robot manipulators is presented, which firstly determines the manipulator’s proximity to a singu- larity and then computes how the kinematically redundant degree(s) of freedom should be optimised for the given pose of the end-effector. The singularity analysis is conducted by ex- amining the mechanism in terms of the instantaneous centres of rotation of its corresponding mobility one sub-mechanisms when all but one of the actuators are locked, where the manip- ulator is in a type-II singularity when these points either are indeterminable or coincide with one another, and an index, r min , is introduced which describes the minimum normalised dis- tance from such conditions being met. A predictor-corrector method is employed to compute the configuration for which r min is optimised, and is reachable without crossing a singular- ity. Finally, the advantages of the geometric method of singularity analysis are shown in comparison to traditional Jacobian-based methods when applied to kinematically redundant parallel robot manipulators. Keywords: Parallel Robots, Kinematic Redundancy, Singularities 1. Introduction Singularity avoidance is a fundamental aspect of the control of parallel robotic systems, as the failure to detect and bypass singular configurations can lead to a significant deterio- ration in the performance of the robot manipulator. Arguably the most problematic type of singular configuration for parallel robot manipulators are those in which the manipulator’s end-effector gains an additional degree of freedom, referred to as singularities of redundant output [1] or type-II singularities [2], since in these configurations the mechanism loses its inherent rigidity. Some have proposed the use of kinematically redundant architectures to limit the number of singularities in the manipulator’s workspace; robotic systems with such architectures have a greater number of degrees of freedom than the number of parameters required to describe the pose of the end-effector, but become rigid when, and only when, all Preprint submitted to Mechanism and Machine Theory March 2, 2020