On numerical techniques for kinematics problems of general serial-link robot manipulators

This paper addresses widely applicable methods for solving the kinematics problem of any class of serial-link robot manipulators. First, the position and orientation of the manipulator hand, the Jacobian matrix and their symbolic generation are clearly presented using recursive relations. Second, the inverse problem to such formulations is posed as an unconstrained non-linear optimization one, where numerical techniques for the overdetermined and underdetermined kinematic problems are considered separately to derive consistent arm solutions. On the basis of several proposals on step lengths involved to maintain good numerical stability, the results of computer simulation show that performance is sufficiently reliable.