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Tham khảo tài liệu 'advances in robot kinematics - jadran lenarcic and bernard roth (eds) part 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Kinematics and Grasping 479 Figure 5. Object relative position or it is possible to implement a control law which will allow to move the desired finger without the need of solving any kind of inverse kinematics equations C. Canudas G. Bastin B. Siciliano. Given the the differential kinematics equation V r 1 vf Tf I 1 vf Tf_2 Y . r 1 q1 X 3 L 125X3 L2 375X3 L3 - 35X3 L1 q4 27 If we want to reach the point H s1 t1 we require that the suitable velocity at the very end of the finger should be proportional to the error at each instance Vi -0.7 X 3 H s1 t1 . This velocity is mapped into the phase space by means of using the Jacobian inverse. Here we use simply the pseudo-inverse. with j1 115 X3 L2 375X3 L 3 and j2 3-5 X L1 Aq1 Aq4 j1 A j 2 -1 Vi A j2 j1 A Vi 28 Applying this control rule one can move any of the fingers at a desired position above an object so that an adequate grasp is accomplish. 5. Results In this section we present the experimental results of our grasping algorithm. In Figure 6 the inferior images correspond to the simulated scenario and the other ones are real. In this experiment the object was suspended manually above the grasping hand simply to check whether the has been opened correctly or not. We can see that for each object the algorithm manages to find the singular grasp points so that the object is hold properly and in equilibrium. Note that the found points correspond to the expected grasping points. 480 J. Zamora-Esquivel and E. Bayro-Corrochano 6. Conclusion Using conformal geometric algebra we show that it is possible to find three grasping points for each kind of object based on the intrinsic information of the object. The hand s kinematic and the object structure can be easily related to each other in order to manage a natural and feasible grasping where force equilibrium is always guaranteed. References Li H. Hestenes D. Rockwood A. 2001 . Generalized Homogeneous coordinates for computational geometry . G. Somer editor .
