Output control barriers of positioning serial manipulators

A broadly applicable formulation for identifying control difficulties in positioning serial manipulators is developed based on the implicit function theorem and a proposed acceleration analysis on singular surfaces. Internal singular surfaces upon which the manipulator exhibits control difficulties are determined in closed form and parameterized as a geometric entity with joint variables as parameters (these surfaces are called barriers). Difficulties in manipulator control are identified based on whether the end-effector admits motion normal to a singular surface. An indicator characterizing the difference between the component of acceleration in the normal direction and the centripetal acceleration on a singular surface yields a quadratic form. Definiteness properties of the quadratic form define directions of admissible output motion associated with a barrier. The paper presents a systematic method for determining all singular entities inside the workspace upon which control problems are encountered and an efficient method for identifying control difficulties and in closed form. The method is illustrated through examples.