Анализ сингулярных конфигураций мобильного манипулятора KUKA youBot

Abstract

The article considers the KUKA youBot mobile manipulator with open software, which is intended for research and education purposes. Singular configurations of this apparatus have not been described in the literature as yet. The KUKA youBot system is a controlled platform, on which a five-axis manipulator with a grip is mounted. The platform can be moved in the horizontal plane by means of four mecanum wheels. The robot position in the absolute space is determined by eight generalized coordinates. As is known, the KUKA youBot inverse kinematics problem allows its exact analytical solution to be obtained. A rectangular Jacobi matrix for mapping the space of the robot generalized coordinates into the space of its end effector location parameters is constructed. The obtained Jacobi matrix is transformed to an equivalent echelon form by means of elementary operations. An analysis of the echelon matrix entries carried out using analytical tools has shown that, whatever the locations of the KUKA youBot system’s platform and the system arm first, fourth and fifth links, there is a singular configuration in which the robot's arm second and third links are stretched along the vertical line. In this case, the Jacobi matrix rank becomes equal to five (less than its full rank equal to six). When being in the above-mentioned singular configuration, the KUKA youBot system end effector cannot perform some of the movements the pattern of which is described in the presented paper.