Hierarchical kinematic analysis of robots

According to their kinematic structure, serial robot manipulators present singularities, which are defined as the configurations where the mobility of the manipulator is reduced. Singularities introduce problems in the robot operations that need to be avoided. This is usually done by detecting a singular configuration and then deviating from it. The usual methods for singularity avoidance, most of them based on the determinant of the Jacobian matrix, implicitly consider all singularities equally disastrous to the robot kinematics. This paper introduces a new analysis method, the hierarchical kinematic analysis, based on the fact that the robot kinematic singularities are not equally important to the behaviour of the manipulator. Singularities are ranked according to their influence on the robot inverse kinematics. Moreover, this method provides a recursive algorithm to solve the inverse kinematics problem of serial robots faster, and more accurately. The method, based on a graphical interpretation of the Jacobian matrix, is summarised in an algorithm. To illustrate its usefulness, this algorithm is applied in detail to a SCARA and a PUMA robot. Finally, the algorithm is applied to a robot without a spherical wrist, the T3 robot. The results are interpreted and, even in classical examples, some new facts can be extracted by using the hierarchical kinematic analysis.