A geometric method of singularity avoidance for kinematically redundant planar parallel robots

Methods for avoiding singularities of closed-loop robot mechanisms have been traditionally based on the value of the determinant or the condition number of the Jacobian. A major drawback of these standard techniques is that the closeness of a robot configuration to a singularity lacks geometric, physical interpretation, thus implying that it is uncertain how changes in the robot pose actually move further away the mechanism from such a problematic configuration. This paper presents a geometric approach of singularity avoidance for kinematically redundant planar parallel robots that eliminates the disadvantages of Jacobianbased techniques. The proposed method, which is based on the properties of instantaneous centres of rotation, defines a mathematical distance to a singularity and provides a reliable way of moving the robot further from a singular configuration without changing the pose of the end-effector. The approach is demonstrated on an example robot mechanism and the reciprocal of the condition number of the Jacobian is used to show its advantages.