In controlling the telerobots, the resolved motion rate control algorithms are widely used because of their simplicity and relatively less computational load. However, at singular configurations, those algorithms may fail. This thesis describes a method which finds the required joint rates to perform the assigned velocities of the end-effector in the presence of singularities. The acceleration of the end-effector consists of two components, one caused by joint accelerations and the other caused by joint rates. At singular configurations, the former component cannot cause the robot to move in particular direction, whereas the latter can. The proposed algorithm utilizes the latter component to get the joint rates at singular configurations. Through some examples for a 3R type robot, it is verified that the algorithm is a singularity-tolerant method. Furthermore, by the new defined modified manipulability and manipulability ellipsoid, the physical meaning of the method is explained. The proposed method is efficient to perform the required motions in the presence of singularities.
