Adaptive Extended Jacobian Can Improve the Global Conditioning Index of Redundant Robots

The extended Jacobian is a solution technique of redundant robot’s instantaneous kinematics. It is based on the definition of secondary tasks through constraint functions that are added to the mapping between joint rates and end-effector’s twist. Several approaches showed its potential, its applications and limitations. In general, the constraint functions are a linear combination of basic functions with constant coefficients. This paper proposes the use of adaptive coefficients in such equations by using the conditioning index of the extended Jacobian as a quality measure. A good conditioning of the extended Jacobian keeps the robot far from singularities and contributes to the solution of the inverse kinematics. In this paper, initially the extended Jacobian and the proposed algorithm are discussed, then two tests in different circumstances are presented to validate the proposal.