Regularized Jacobian for the differential inverse positioning problem of serial revolute joint manipulators

Singular configurations arise in the kinematics of revolute joint manipulators, and cause problems in solving the inverse kinematics problem. General inverse kinematics schemes are based on the Jacobian of the forward kinematics map of the manipulator, that becomes ill-conditioned in singular configurations, causing numerical instability and loss of direction of motion. This work proposes a method, that regularizes the Jacobian in the case of singularities in the inverse positioning problem. The Jacobian regularization is based on transforming the acting point of the motion generators of the robot. The existance of a regularizing vector is proved for a 2 degrees of freedom planar subassembly, and the effect of regularization is analyzed.