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Next: 5.8 Effects of Over-determined Up: 5 Visual Servo Control Previous: 5.6 Repeatability

3 and 6 DOF Adaptive v.s. Non-adaptive Control

  In this experiment we compared performance of adaptive and non-adaptive visual controllers in 3 DOF and 6 DOF. The adaptive controller can adjust its internal model (using the on-line model estimation) tex2html_wrap_inline4110 to environment changes at different times k, whereas the non-adaptive controller has a fixed model tex2html_wrap_inline4114 . The accuracy of the internal model affects controller performance. In particular it affects oscillations and the speed of convergence.

At first it may seem that the most relevant evaluation measure for an adaptive controller is how accurately it can estimate the visual-motor model. However, accurate model estimation has to be traded off for efficiency, and ideally one would do this so the internal model ( tex2html_wrap_inline3874 ) gets estimated only as precisely as necessary to perform the task at hand. Tuning of this accuracy is accomplished by varying tex2html_wrap_inline3958 and tex2html_wrap_inline3960 in eq. 5.4. For a 3 DOF task we have found that estimating the partial derivatives (entries tex2html_wrap_inline4136 in the Jacobian) with tex2html_wrap_inline4124 accuracy is sufficient. This finding is in line with Hosoda and Asada's observations for their visual servoing controller in [Hosoda and Asada, 1994].

Instead of studying internal aspects of the adaptive and non-adaptive controllers, we wanted to compare how robustly the two controllers react to a suddenly introduced discrepancy between the internal model and the real world. In real world applications this discrepancy can stem from a variety of sources such as errors in initial model estimate, errors in visual data used to adjust the model, and for the non-adaptive case, poor correspondence between model (linearized) and real world (typically non-linear).

The basic experimental plan was to add varying amounts of noise to the Jacobian model, and then compare final endpoint positioning error and trajectory error, for the adaptive and non-adaptive cases. (Trajectory error is the average deviation in visual space from the planned straight line between the initial feature values tex2html_wrap_inline3536 and the goal tex2html_wrap_inline3540 .) An initial Jacobian approximation tex2html_wrap_inline3874 , valid in the center of the workspace, is obtained by executing a sequence of test moves near the middle of the (visually defined) workspace. The disturbed Jacobian is defined as tex2html_wrap_inline4132 where tex2html_wrap_inline4134 indicates the model accuracy and tex2html_wrap_inline4136 is a random tex2html_wrap_inline4138 matrix with elements drawn from a uniform distribution on the interval tex2html_wrap_inline4140 . This typically (barring some unlikely cases, such as J = I, the identity matrix) restricts the gain, but not the direction (angular transformation) of the random Jacobian. Each test consisted of 50 runs with varying values of the model accuracy parameter a.

In Fig. 5.6 we see that for the non-adaptive algorithm, the percentage of the trials which converged ( tex2html_wrap_inline4148 ) quickly falls to zero for model accuracies a below 0.5. The adaptive algorithm has no problem, even with completely random initial Jacobians.

The trajectory error for the adaptive algorithm increases slightly with high amplitudes of injected noise. This increase comes from a few early erroneous movements, and is quickly eliminated as the model is adapted. For the non-adaptive algorithm, we find a huge increase in trajectory error. This is caused by divergent trials, where the robot goes off in a completely incorrect direction and exhibits long period oscillatory behavior at the transition between convergence and divergence, which occurs near a = 0.25. A typical oscillatory move is shown in Fig. 5.7.

   figure851
Figure 5.6: Results from 50 runs of an experiment with a disturbed internal model in the controller. Convergence for an adaptive and a non adaptive 3 DOF controller (left). Average final endpoint error per feature in tex2html_wrap_inline3468 feature space (right) for 16 tracked features and a 6 controlled DOF problem (right).

   figure856
Figure 5.7: Left: Visually planned path. Right: Typical oscillatory path of non-adaptive controller when model accuracy is near the convergence limit.

When controlling the full 6 DOF of the manipulator we do not get quite the same robustness against model errors as in the 3 DOF case. Model errors worse than a = 0.6 yield a significant and increasing proportion of divergent trials. To get near tex2html_wrap_inline4160 convergence we needed to restrict model accuracy a to be .6 or above. In a test of 50 trials in this range, two did not converge. One showed oscillatory behavior, and the other diverged immediately. In general, average visual endpoint errors as well as trajectory errors remain low even at low model accuracies, as can be seen in Fig. 5.6.

A practical method to make 6 and higher DOF control work well without a new Jacobian, calibrated a-priori, is to bootstrap from the Jacobian of a 3 DOF manipulation. For instance assume that during the 3 DOF transportation move, one feature (e.g. the object centroid) has been tracked in the two cameras. In order to control the angular DOF's of the object more visual pose estimation is needed, and we use point features physically separated on the object surface. Assume k point features on the objects are found in camera 1 and l in camera 2. When switching between 3 and 6 DOF mode, the first three columns of the tex2html_wrap_inline4170 DOF Jacobian are filled from the tex2html_wrap_inline4172 DOF Jacobian, the last three with random numbers.

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This technique is used to switch between the 3 DOF control used for transportation moves, to high DOF control (typically 4-6 DOF for rigid objects) used for the fine manipulation required for alignments and insertions. The bootstrapping works because the visual feature motions are correlated. See Chapter 7 for details.


next up previous contents
Next: 5.8 Effects of Over-determined Up: 5 Visual Servo Control Previous: 5.6 Repeatability

Martin Jägersand