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A Grasping and Manipulation Scheme  177


                     0.2
                                                                  x d
                    Object position x (m)  0.1 0                 x pre
                                                                 x new








                     –0.1
                        0      2       4       6       8       10
                                         Time (s)
              Fig. 9.4 Transient responses of the x component of the position of the measured-object
              frame, x, where the sampling rate is h ¼ 20 Hz and the time delay due to the
              computational cost of image processing and the latency of data communication is
              t image ¼ 50 ms.


                     40                                         µ z  new
                   Object orientation µ z  (degrees)  20 0       µ z  pre
                                                                 µ zd











                    –20
                       0       2       4       6       8      10
                                        Time (s)
              Fig. 9.5 Transient responses of θ z , which is the measured rotational angle around the
              z-axis expressed in terms of XYZ Euler angles, where the sampling rate is h ¼ 20 Hz and
              the time delay due to the computational cost of image processing and the latency of
              data communication is t image ¼ 50 ms.


              u o tðÞ are used for the case in which the sampling rate is h ¼ 20 Hz and the
              time delay due to the computational cost of image processing and the latency
              of data communication is t image ¼ 50 ms. Fig. 9.6 shows the x components
              of the positions of the measured-object frame, x; the virtual-object frame,
                                                     . Fig. 9.7 shows the θ z com-
              x vir ; and the desired virtual-object frame, x d vir
              ponent of the orientations of the measured-object frame, R; the θ z vir
              component of the orientation of the virtual-object frame, R vir ; and the
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