Dynamic control of a manipulator with passive joints in operational space

We present a method to control a manipulator with passive joints, which have no actuators, in operational space. The equation of motion is described in terms of operational coordinates. The coordinates are separated into active and passive components. The acceleration of the active components can be arbitrarily adjusted by using the coupling characteristics of manipulator dynamics. This method is also extended to path tracking control of a manipulator with passive joints. A desired path is geometrically specified in operational space. The position of the manipulator is controlled to follow the path. In this method, a path coordinate system based on the path is defined in operational space. The path coordinates consist of a component parallel to the path and components normal to the path. The acceleration of the components normal to the path is controlled according to feedback based on tracking error by using the dynamic coupling among the components. This in turn keeps the manipulator on the path. The effectiveness of the method is verified by experiments using a two-degree-of-freedom manipulator with a passive joint.