Closeness to singularities of robotic manipulators measured by characteristic angles

Abstract

SUMMARYSingularities have a great influence on kinematics and dynamics of both serial and parallel robots. In order to prevent a robot from entering singular configurations, it needs to measure the “distance” between the robot current configuration and the singular configuration. This paper presents a novel approach based on characteristic angles to measure closeness to singularities. For the problem of inconsistent dimensions in the scalar product of screws, the physical meanings of twists and wrenches are reinterpreted. For the problem of the metric invariant to origin selection, the origin of the screw frame is required to coincide with the origin of the robotic tool frame. The major merit of the proposed metric lies in the identical result of measuring similar mechanisms with different sizes. Moreover, the measurement is insensitive to screw magnitude, since the metric expression is dimensionless. Furthermore, the geometrical meaning of the determinant of a screw matrix is clarified.