This paper presents a computational method for obtaining an optimal control trajectory for point-to-point motion of a cooperating robot carrying a flexible object. To increase the overall productivity and its efficiency, it is required to move the object as fast as possible using the maximum capacity of actuators of robots. If the carrying object is very sensitive to vibration, the robots should be operated so as not to cause excessive vibration of that object. This work deals with optimal input design for cooperative robots to reduce vibration of flexible objects that are handled at speed, under firm constraints on control torques.

The ability of manipulating flexible objects, such as rubber belts and paper sheets, is important in automated manufacturing systems. This paper describes a novel approach to vision-guided assembly of flexible objects. The operation dealt with in this paper is to assemble a rubber belt with fixed pulleys. By analyzing possible states of the belt based on the empirical knowledge of the belt, we can derive a method to have not only the action planning but also the visual verification planning. We have implemented a belt assembly system using the two manipulators and a laser range finder as the sensor, and succeeded in performing the belt-pulley assembly. The extension of our approach to other kinds of assembly of flexible objects is also discussed.