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5.6 Repeatability

  We tested repeatability under closed loop visual control and compared the results to traditional joint control, both with our own experiments and with published figures. Repeatability is the ability of the robot to re-achieve a previously attained pose. Accuracy measures the ability to achieve any prespecified pose [Andersen, 1988]. Visual feedback control overcomes those problems in traditional inverse kinematics approaches where positioning accuracy is limited by the accuracy of the kinematic model. Positioning performance is improved also by reducing the effect of some non-kinematic disturbances, such as gear backlash and manipulator flexibility. We did not explicitly measure accuracy. However, since no additional calibration errors are introduced for visual feedback control, when specifying the goals in the same visual space from which the sensory feedback is taken, it can be argued that the accuracy of visual control should be similar to the repeatability. (This is not the case in standard inverse kinematics approaches to robot control. For example the repeatability of a PUMA is 0.2mm, while accuracy has been reported to be 10mm [Andersen, 1988].)

Positions were measured through a dial meter with 0.001'' accuracy mounted on the robot end effector. Accurate visual measurements were provided by LED's mounted on the robot end effector. Two uncalibrated cameras were positioned about 30 degrees apart. The positioning is fairly arbitrary, except that the controlled object needs to be visible though the whole manipulation, and a reasonable camera separation is needed to obtain a well conditioned visual-motor model. For reference in comparing the repeatability figures, it was noted that 1 pixel corresponds approximately to a 0.25mm robot movement near the goal. Repeatability was measured by moving the robot on a random trajectory towards a rigid reference surface until the dial meter was in contact, reading the dial value and visual or joint values, retreating on a second random trajectory, and then trying to reachieve the visual or joint goal. The algorithm is specially designed to execute the final approach from a different, random direction each time.

   table801
Table 5.1: Measured and specified repeatability of our Unimation PUMA 762 and 761 robots under visual and joint feedback control.

We tested the two robot arms in our lab. "Bill" is our old PUMA 762. Over the years it has developed a significant backlash in the gears, as well as some sticktion. "Hillary" is a PUMA 761, a more recent acquisition, that is in better shape. Table 5.1 shows our results for visual feedback repeatability. The results indicate convergence to subpixel accuracy. We think ``vernier accuracy'' effects from the high dimensional (m=16) input space can account for this. Compared to joint control repeatability measured under the same conditions, visual space repeatability is about 5 times better for Bill. Results for Hillary show that for a robot in good mechanical shape, visual control is at least as good as joint control.

The perfect visual alignment shows the repeatability when the measured visual error is 0, i.e. the test object has been positioned so that the visually measured positions tex2html_wrap_inline4104 exactly matches the commanded positions tex2html_wrap_inline3540 . This is not achieved at all trials. For Bill, for instance, 22 of 50 trials resulted in 0 visual error. We believe the main reason why not all trials achieve 0 visual error is the difficulty in positioning the manipulator, near or below its joint encoder resolution limit (about 0.12 mm here). Very close to the goal, noise in the controller causes it to drive the motors randomly back and forth. This samples a lot of possible positions below the resolution limit, and by stopping when (or if) we hit 0 visual error, we can sometimes achieve positioning below the resolution limit.

The distribution of positioning errors for Bill can be seen in Fig. 5.5. The two modes, around 0.25mm and 1mm, in the open loop distribution are most likely due to the different backlash errors introduced by driving joint j1 in one of two directions during a measurement. Note that both the bimodality and the variance are substantially reduced under visual control.

   figure821
Figure 5.5: Distribution of repeatability positioning errors. Left: closed loop visual feedback. Right: joint feedback only.


next up previous contents
Next: 3 and 6 DOF Up: 5 Visual Servo Control Previous: 5.5 Experiments with Visual

Martin Jägersand