Phase 2 Palm Approach and Object Hugging: Output: a Sequence of Collision-free Conngurations, Each Representing All M N Links of All

b c d e f Fig. 4. Example of the algorithm's performance. a, b Phase 1, hand reorientation; c to f hand approach and grasp execution: c a rst contact with the object is made, d,e two i n termediate positions. The nal position is shown in f and in Figure 5. Fig. 5. Two views of the nal position of the hand and the object shown in Figure 4f. 88 D. Reznik and V. Lumelsky. Sensor-based motion planning for highly redundant kinematic structures: II. The case of a snake arm manipulator. as the palm. During the step each ngertip is expected to move o ver a xed distance s. The corresponding step of the palm is of variable length, ; ; s execution of many such steps in rapid succession results in continuous motion. Each iteration consists of four operations parts labeled ad , which proceed until all elements of TipState are set to Done that is, until no ngertips can move a n y longer in the directions chosen. No motion takes place until the calculations in all four parts are over. Important remark: the discussion below about motion generated in each step should be thought of as computational procedures , not actual motions, until the end of the iteration. Brieey, part a of the iteration in Phase 2 keeps track of which ngers are in contact with the object. Parts b and d generate motion for the ngers so as to make them wrap around the object. These parts make use of two canned" procedures, Head2Tail and Tail2Head, for snake motion planning directly imported from 8. Part c is responsible for planning a small step forward of the whole unit, palm + Frozen ngers, toward point T along the line P o T. Finally, part d takes care of some gaps between the nger tails and their roots that appear in the previous computational operations. The output from each iteration is a set of step values for all joints of all ngers and for the palm; at this point, the actual step motion takes place, simultaneously in all DOF involved; and then the process repeats. More speciically, in part a of one iteration of Phase 2, the elements of TipState currently set to Frozen are re-set to Contact if the corresponding ngertips sense the surface of O. This latter information is obtained from FTipSensorm, which returns ON …