A Manipulated Deformable Object as an Underactuated Mechanical System Herbert G. Tanner and Kostas J. Kyriakopoulos Abstract. Deformable objects under manipulation can be modeled using finite elements. The resulting model is in fact an underactuated mechanical system. The consequences of any type of constraints revealed by the modeling procedure is explored. The study of deformable object models within the framework of under- actuated mechanical systems indicated the existence of second order nonholonomic constraints. For the identification of this kind of constraints, the authors have devel- oped computationally efficient and significantly simpler mathematical tools. Their methodology is illustrated and tested by an example. 1. Introduction In robot manipulation the object that was being handled was traditionally con- sidered rigid. This assumption on the object's nature simplified significantly the problem. The approach was justified from nearly every point of view. It allowed researchers to focus on the new system being developed, namely the robot, and adjusted its environment to facilitate analysis: no obstacles present, clean and ab- solutely known environment, rigid objects. As problems involved in robot manipulation find their solution with time and great effort by the robotics community, all of these assumptions are gradually re- lieved. Obstacle avoidance has been considered, adaptation methods explored, sensor information taken into account. It is about time we did something about the assumption concerning the object being rigid.