5 Concluding Remarks 4 Parallel Jaw Gripper 2.2 a Variation 3 Two Finger Algorithm Phase 2 2.1 Dealing with Uncertainty 1.2 Sensors Reactive Algorithms for 2 and 3 Finger Grasping

8 allows the algorithm to operate on the same type of objects as the previous algorithm. More speciically, boundary following is achieved by keeping the distance detected by the closest sensor small, and the additional requirement of axis normality is satissed by keeping equal the distance indicated by the two sensors placed at the jaws ends. It remains to be seen how these algorithms perform in practice. We are currently developping a reactive gripper, that will accomodate the implementation of several of these algorithms. Also many variations are possible. For example, we can replace the proximity and angle sensors by force sensors, but we lose the nondisturbing quality. It would be interesting to nd algorithms that require less sensory information, for example require only the sign of the angles at the ngers instead of the exact angle for the three nger case. This would make the algorithm more robust and simplify the sensors. Generalization of these algorithms to non convex objects would be desirable. Finally, these techniques can be extended to three dimensional objects and four ngers, and this will be discussed in a future paper. A design modiication for the parallel-jaw gripper that improves grasp stability for polyhedral parts. 7 3 2 1 1 f 0 f Figure 3: A few steps of the two nger algorithm. There must exist a pair of points on the boundary of the object such that the normal lines at both points are in fact the same line. This can be seen by considering the pair of supporting lines, one on each side of the object, and rotating this pair until it reaches a local minimum. Then the contact points satisfy the above requirement. We nd such a pair of points as follows (refer to gure 3.) We assume that initially the object is somewhere between the two ngers. The ngers close until one of the sensors indicate proximity. Call this nger f 0 , the other f 1. Then the gripper is rotated until the nger normal of f 0 is normal to the object. Such a rotation will in absolute value be by less than 90 degrees. If during this rotation f 1 becomes close to B, then it starts to track the boundary of B in the direction away from f 0. Otherwise, close the ngers along their axis (translating the center if necessary) until f 1 becomes close to …