Prioritized inverse kinematics using QR and cholesky decompositions

This paper proposes new methods for the prioritized inverse kinematics (PIK) by using the QR decomposition (QRD) and the Cholesky decomposition (CLD) on the purpose of separation between orthogonalization and inversion processes that are essential parts of the PIK. The distinctive approach eliminates the interference between two processes which usually induces inaccuracy and sometimes instability on the prioritized inverse solutions. Two degenerate properties of using the QRD are explained and the remedies are provided as the modified damped least-squares pseudoinverse and the numerical reconditioning. The effectiveness are examined by the kinematic simulations with the n-link manipulators in the two-dimensional case and the KUKA LWR in the three-dimensional case.