OPERATING ROBOT MANIPULATORS THROUGH KINEMATIC SINGULARITIES USING A CONTINUOUSLY SLIDING MODE CONTROL

Planning the motion of end-effectors of robot manipulators can be carr ied out more directly in the Cartesian space compared to the joint spa ce. Yet, Cartesian paths may include singular configurations where con ventional control schemes suffer from excessive joint velocities and l oss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocit ies in the task and joint spaces loses rank at singularities. The prob lem can be resolved by using a local second-order approximation of rob ot kinematics for the joint velocities, which is called Resolved Motio n Quadratic Rate Control. In this article, we present a control strate gy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolve d motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control sc heme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. (C) 1994 John Wiley & Sons, Inc.