A normal form solution to the singular inverse kinematic problem for robotic manipulators: the quadratic case

We present a normal form approach to solving the singular inverse kinematic problem for non-redundant robot kinematics. A standing assumption is made that singular configurations of the kinematics have corank 1 and that the kinematics are equivalent to the quadratic normal form. The approach has been illustrated with a simulation case study of 2R kinematics. A comparison with the singularity-robust inverse technique and the null-space based approach has demonstrated advantages of the normal form approach.