Neighborhood Equilibrium Grasp for Multiple Objects

1 I n t r o d u c t i o n Multifingered robot hands have a potential advantage to perform various skillful tasks like human hands. So far, much research has been done on multifingered robot hands such as the stability of grasp, realization of the equilibrium grasp, the force closure grasp(the grasped object can exert the 6 DOF external wrench), analysis of contact force[l, 2] and manipulation of an object[3, 4]. However, most of work has implicitly assumed that a multifingered hand manipulates only one object. On the other hand, there is a few works concerning the grasp of multiple objects. Dauchez et al.[5] and Kosuge et al.[6] used two manipulators holding two objects independently and tried to apply to an assembly task. Aiyama et al.[7] studied a scheme for grasping multiple box type objects stably by using two manipulators. For an assembly task, Mattikalli et al.[8] proposed a method to find a stable alignments of multiple objects under the gravitational field. They used a linear programming and the objects are rotated to find the stable alignments. While these works treated multiple objects, they have considered neither the motion of the objects nor any manipulation of objects based on rolling contacts. The authors[9, 10] have first studied the enveloping grasp for multiple objects under rolling contacts. They have shown a necessary and sufficient condition for judging the rolling contact at each contact point and showed the rolling up condition for two objects initially placed on the table. 0-7803-5886-4•00•510.00© 2000 IEEE 215 n i v e r s i t y s h i m a 739-8527 , J A P A N For grasping a single object, a force-closure grasp can be easily achieved by using a robot hand with more than two fingers. It is well known that a robust grasp ag~nst an external force(or moment) can be achieved by increasing an internal force. On the other hand, for multiple objects satisfying the rolling condition at each contact point, although a force-closure grasp can be achieved by increasing the number of fingers until the grasp system can support 6DOF external wrench, the grasp system may result in an impractical number of fingers. Since an equilibrium grasp can impose weaker constraints on the objects than a force-closure grasp, we can expect to realize it with fingers less than the number required for the force closure grasp. Based on this consideration, we focus on an equilibrium grasp aparting from a force-closure grasp in this work. Fig. 1: A cylindrical and an ellipsoidal objects on table Definition of the equilibrium grasp is that the sum of all forces and moments acting on each object balance within the hand. Now, let us introduce an interesting behavior for both a cylindrical and an ellipsoidal objects. Suppose that both are placed on a table as shown in Fig.1. Also, suppose that the table is a bit inclined. For such a small inclination of the table, both objects will lose the initial equilibrium state and start rolling motions. Once the cylindrical object starts a rolling motion, it never stops and finally falls down from the edge of the table. Under the same situation, the ellipsoidal object will also start a rolling motion. However, it soon stops and results in another equilibrium state, while it may not stop for a larger inclination angle of the table. For a small rotational angle of the table, we can see that an ellipsoidal object is more robust in the sense of keeping an equilibrium state than a cylindrical object. We evaluate the robustness of an equilibrium grasp by utilizing the maximum rotating angle where all objects can continuously maintain an