LIAPUNOV STABILITY OF FORCE-CONTROLLED GRASPS WITH A MULTIFINGERED HAND

Holding an object stably is a building block for dexterous manipulatio n with a multi-fingered hand. In recent years a rather large body of l iterature related to this topic has developed. These works isolate som e desired property of a grasp and use this property as the definition of stable grasp. To varying degrees, these approaches ignore the syste m dynamics. The purpose of this article is to put grasp stability on a more basic and fundamental foundation by defining grasp stability in terms of the well-established stability theory of differential equatio ns. This approach serves to unify the field and to bring a large body of knowledge to bear on the field Some relationships between the stabi lity concepts used here and the previously used grasp stability concep ts are discussed. A hierarchy of three levels of approach to the probl em is treated We consider that the grasp force applied is a basic cons ideration, in terms of ensuring both that there is sufficient force to prevent dropping the object and that the forces are not too large to cause breakage. As a result, we first investigate the use of constant force grasps. It is shown that with the proper combination of finger l ocations and grasp forces, such grasps can be Liapunov stable, and met hods are presented that help find such grasps. It is also shown that s uch grasps cannot be asymptotically stable. To produce asymptotic stab ility, one must alter the forces applied to an object when the object deviates from equilibrium, and a linear feedback force law is given fo r this. It results in local asymptotic stability guaranteeing converge nce to the desired grasp equilibrium from all states within a region o f attraction in the state space. Some of the results are similar to re sults obtained previously, but this time they have a stronger meaning in terms of the dynamic response of the system. In the third level, a nonlinear force law is given that, to within certain limitations, prod uces global asymptotic grasp stability, that all initial states are gu aranteed to converge to the desired grasp equilibrium The method is ro bust to large classes of inaccuracies in the implementation.