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5.10 Experiments with the Utah/MIT Hand

   

The Utah/MIT hand is a relatively imprecise and difficult to control manipulator. Each joint is actuated by a pair of pneumatically-driven antagonist tendons. This results in a compliant response, but it also makes reliable and consistent positioning difficult to achieve due to hysteresis and friction effects. Furthermore, especially during long manipulation sequences, slipping in the grasp points add to these errors. The details on how to maintain a stable grasp while manipulating the object are described in [Fuentes and Nelson, 1994, Jägersand et al., 1996]. The purpose of this section is to show the effects of visual servoing and model estimation.

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Figure 5.10: Examples of manipulation of a grasped object using a Utah/MIT hand.

We tested repeatability under closed loop visual control and compared the results to traditional joint control. The test object was a piece of standard 2 by 4 wooden construction stud, approximately 2 inches long. Positions were measured using a dial meter with 0.001'' accuracy. Accurate visual measurements were provided, in the first experiments, by tracking special surface markings, see Fig. 5.11. The markers could be placed arbitrarily on the object, since the servoing algorithm is self calibrating. Placement near the corners gives better conditioned visual measurements with respect to rotations. In the second experiment, for improved visual accuracy, we track LED's mounted on wood screws. Two cameras were positioned approximately 90 degrees apart. One pixel corresponds approximately to a 0.3mm object movement. Repeatability was measured by moving the object on a random trajectory towards the dial meter until it was in contact, reading the dial value and visual or joint values, then retreating on a second random trajectory, and then trying to reachieve the visual or joint goal. No explicit 3D world coordinate system is used in the manipulation. However for the purpose of presenting the results we set up a system. With reference to Fig. 5.11, let x be the optic ray, y the image row and z the column. Around the x, y and z axis respectively, a grasped object can be translated about 40mm, 60mm and 30mm, and rotated 70, 45 and 90 degrees (see Fig. 5.10). We tested but did not find any correlation between trajectory length and positioning error.

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Figure 5.11: Setup testing repeatability of hand fine manipulation using the Utah/MIT hand.

5.10.1 Repeatability in 3 and 4 DOF

  In Table 5.2 we compare repeatability for four different positioning methods, based on 50 trials with each method. The 3 DOF visual feedback controls only translations of the object. The 4 DOF visual feedback controls the translations and rotation around the optical axis of Fig 5.11. Visual feedback in both cases consists of m=16 feature values from 8 markers, and 2 cameras. The two joint feedback methods differ in that one uses only joint feedback, while in the Cartesian one, the error vector is projected onto the 6 DOF space defined by the grasp tetrahedron (The tetrahedron formed by the contact points between the four fingers of the Utah/MIT hand and the grasped object). As seen in Table 5.2 visual servoing performs on the average a little better than joint feedback methods. When studying maximum errors visual servoing is significantly better. This is because the visual feedback can compensate for slip in the grasp contact points.

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Table 5.2: Measured repeatability of the Utah/MIT hand fine manipulating a rigid object under visual and joint feedback control.

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Table 5.3: Condition numbers tex2html_wrap_inline3470 of different degree of freedom (DOF) Jacobians.

Visual feedback gets more difficult in high DOF systems. One reason is that the number of parameters estimated in the Jacobian increases. Another is that high DOF tasks are often more ill conditioned. In particular, there is a difference between pure translations (3 DOF) and combinations of translations and rotations (4-6 DOF). The condition numbers of the 3 to 6 DOF estimated Jacobian are shown in Table 5.3. We tried 5 and 6 DOF visual servoing using the setup described above, but could not get reliable performance. For 5 DOF 37 % of the trials failed (diverged), and for 6 DOF nearly all failed. This is not surprising given the mechanical difficulties in controlling the hand. When trying to make the small movements needed for convergence the actual response of the manipulator has a significant random component. The signal to error ratio in visual control space is then further decreased by the bad condition number of the transformation between motor and visual space. The high condition numbers in the 5 and 6 DOF cases stem from two distinct problems. With the two camera setup we use, the rotation around the z-axis is (visually) ill-conditioned (differentially similar to the translation along the optic axis.) This problem occurs with a two camera setup, when the points tracked in each camera are planar. The other problem is that two of the manipulations are differentially very similar in Cartesian motor space. By taking out the two problematic DOF's we get the low condition numbers of the 3 and 4 DOF manipulations.

6 DOF Visual Servo Control of the Utah/MIT Hand

In order to evaluate visual servoing in the full 6 DOF pose space, we improved the visual measurements by tracking LED's mounted on adjustable screws attached to the test objects. The LED's facilitate more precise tracking than the surface markings, and using the screws we adjusted them into a non-coplanar configuration, avoiding the singularity we got from tracking the planar surfaces of the object. With this setup we were able to do both 5 and 6 DOF visual servoing, achieving accurate end positions in over 90% of the trials, and only diverging completely in two out of 67 trials.

We performed the same positioning experiment as described in Section 5.10.1, but here in the full 6 DOF of the rigid object. Positioning errors were measured along the 3 major axes. For the Y and Z axes the measuring axis coincides with the center of rotation, so the errors measured are purely translational. For the X axis, the fingers are in the way, and we used a measuring point below the fingers, and thus measure the sum of rotational and translational error components.

The results are shown in Table 5.4. The positioning error along the X-axis is much worse than the two others. We propose two reasons for this: (1) The difference in the measuring location discussed above and (2) along the Y and Z axes the translation is effected by all fingers moving in parallel, which tend to average random disturbances in an individual finger, while along the X axis only the thumb opposes the force of the three other fingers, so positioning is no more precise than for one finger.

Visual feedback improves the positioning in all cases. The improvement is significant along the Y and Z axes, but only marginal along the X axis. This result is consistent with our earlier observations that visual feedback improves an already precise manipulator more than an imprecise one. We don't have a good analysis of the exact reasons for this. In part it can probably be attributed to the visual feedback needing a monotonic response to very small movements, while in an imprecise manipulator the response is random. For a more precise manipulator the response may be monotonic, but non-linear, which affects only open loop accuracy.

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Table 5.4: Measured repeatability of the Utah/MIT hand fine manipulating a rigid object under 6 DOF visual and Cartesian joint feedback control.

Error distributions for the 6 DOF positioning experiment are shown in Fig. 5.12. For open loop joint feedback, the object positioning errors are of two distinct types. The first is due to the inaccurate response of the fingers themselves, the second is due to slippage in the grasp points. The mode around 0.5 mm is due to manipulator inaccuracies. The errors caused by slippage are represented in the mode around 2 mm.

In the visual servoing behavior we noted that trials fell into three categories. About half the trials converged very quickly. Most of the rest converged, initially quickly, but more slowly towards the end. Last a small percentage did not converge at all (2 out of 67 visual feedback trials). We have not observed this difference in convergence speed when using the same visual feedback controller on robot arms. We think a partial explanation may be that mechanical phenomena in the hand and remotiser linkage cause some positions to be harder to reach than others. We have also observed that when the visual servo controller is turned off, the hand often does not remain in the same position, but drifts significantly, despite the joint setpoints remaining the same.

Not all visual servoing trials converged satisfactory. Specifically along the x axis errors were sometimes as large as 2mm (see Table 5.4). The controller convergence criterion is partly causing this. When convergence is unsatisfactory over several sample intervals, the controller adjusts the expected positioning accuracy down, and also the derived gain. This is to stop long oscillatory behaviors near the goal. In some cases the adjustment is too large, impairing accuracy.

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Figure 5.12: Distribution of translational positioning errors for joint and visual feedback positioning of the Utah/MIT hand.


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Next: 6 Appearance Based View Up: 5 Visual Servo Control Previous: 12 DOF Control of

Martin Jägersand