Adaptive non-linear least squares for inverse kinematics

The use of an adaptive non-linear least squares algorithm to solve the inverse kinematic problem for robotic manipulators is proposed. The algorithm uses the Gauss-Newton model of the direct kinematic function with the Levenberg-Marquardt iteration. This first-order approximation is supplemented with a quadratic model in certain situations. If required the algorithm can converge to singular configurations, and hence is especially useful when the desired end-effector position is outside the reachable workspace of the manipulator. The authors prove that the task space error function has no local minimizers