Motion planning and control of nonredundant manipulators at singularities

The problem of motion planning and control of nonredundant manipulators through singularities is investigated. It is recognized that several well known control schemes, such as resolved acceleration control and operational space control will fail at singularities. Feasible motions of manipulators at singularities are investigated by introducing the accessible space coordinates. Constraints on the accessible space velocity and accelerations which must be satisfied at singularities are derived. Using these constraints, it is demonstrated that there exists a class of trajectories which are feasible for motions at singularities. These ideas are used to control the motion of manipulators along the feasible trajectories through singularities. Several examples of motion planning and control through singularities demonstrate the effectiveness of this theory