A new method of robotic motion control near singularities

A new 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 method presented 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 manipulator's workspace. Examples are presented for a 6R robot in a singular configuration and for a closed trajectory.<>