Generalized kinematic control of redundant manipulators

Abstract

Recently, an interest has increased in applying redundant manipulators in useful practical tasks which are specified in terms of a time parameterized geometric path (a trajectory) to be tracked by the end-effector. Redundant degrees of freedom make it possible to achieve some useful objectives such as collision avoidance in the task space with obstacles, joint limit avoidance and/or avoiding singular configurations when the manipulator moves. An effective approach to the motion control problem for redundant robotic manipulators is the so-called kinematic control. It is based on an inverse kinematic transformation which determines a reference joint (manipulator) trajectory corresponding to the end-effector trajectory given in the task space. One may distinguish between several approaches in this context. Among them, we mainly concentrate on two major approaches. The first approach is the extended or augmented task space formulation of the inverse kinematics problem presented in works [1]-[4]. It is based on extending the dimension of the task space by incorporating as many additional constraints as the degree of the redundancy. These additional constraints are obtained based on e.g. various types of optimization criteria. Consequently, the resulting system becomes non-redundant. © Springer-Verlag London Limited 2007.