A new method of robotic rate control near singularities

A novel method of controlling robotic manipulators near singularities is introduced. In traditional rate control, a local first-order approximation of the robot kinematics is used, which may fail at a singularity. However, if the approximation is extended to the second order, it becomes possible to solve for the joint rates. The proposed method uses a multidimensional Newton-Raphson technique to solve the resulting set of coupled, quadratic equations. The method is presented in conjunction with a description of rate control in the complex domain, which allows for end-effector locations outside the manipulators workspace. Two examples employing quadratic rate control are presented for a 6R robot in a singular configuration, and one example applying the method to a closed trajectory is shown