3.2 Repeatability



next up previous
Next: 3.3 Adaptive vs. Non-adaptive Up: 3 Experiments with the Previous: 3.1 Experimental Procedure

3.2 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. Visual feedback control overcomes those problems in traditional inverse kinematics approaches where positioning accuracy is limited by the accuracy of the kinematic model. We can also improve positioning performance 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, it can be argued that visual control accuracy should be similar to repeatability.

To make the measurements, we mounted a 0.001'' accuracy dial meter on the robot end effector, allowing us to make very precise position measurements. Watching a semiconductor junction from the side on standard LED's mounted on the robot end effector provided us with very accurate visual positions. As a reference surface, we use a piece of glass mounted on a very heavy tripod. To sample different parts of the robot workspace, we positioned the tripod in different locations and orientations. Repeatability was measured by moving the robot on random trajectory towards the glass measuring surface until the dial meter was in contact with the glass, reading the dial value and visual or joint values, and then retreating on a random trajectory, before 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.

The cameras are placed close to the end effector for high visual accuracy. One pixel image offset represents about .25mm in the real world. The measurements are made in 1 DOF, and roughly along the direction of joints 1 and 4 (neither of which are gravity loaded). Joints 1-4 are driven, but they are coupled so only 3 DOF's are controlled in the robot. The experiments were performed with the arm near full extension.

  
Table 1: Measured repeatability of our Unimation PUMA 762 robot under visual and joint feedback control, compared to figures given in the PUMA manual

Table 1 shows our results for visual feedback repeatability. The results indicates convergence to subpixel accuracy. We think ``vernier accuracy'' effects from the high dimensional () input space can account for this. Compared to joint control repeatability measured under the same conditions, visual space repeatability is about 5 times better. The figure published by Unimation for the PUMA 762 joint control repeatability is three times better than ours. We can only hypothesize why, since Unimation does not give any details of their experiment. One hypothesis is that our robot is just old and wear on the mechanics account for our higher error. Another is that Unimation measures same-path repeatability, i.e. the robot reaches the goal point the same way both times in a measurement, while we measure different path repeatability. Same path measurements tend to cancel out many sources of error, and can explain the better figure. We measured same-path repeatability on our arm to be about .12 mm. The precision limit imposed by the joint angle encoders is also .12mm.

  
Figure 5: Left: Distribution of errors in closed loop visual feedback experiment. Right: Showing only the trials which converged to zero visual (image) error

22 of 50 trials converged to 0 visual error. The average positioning error on these is much better than on the whole data set. We believe the main reason why more trials did not converge is due to the difficulty in positioning the manipulator, near or below its resolution limit. 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 if/when we hit 0 visual error, we can achieve positioning below the resolution limit. The error distribution of 50 repeatability trials is shown in fig. 5.

  
Figure 6: Left: Distribution of errors under standard joint control only. Experiment otherwise identical to the visual feedback one. Right: Varying the length of the (random) trajectory does not affect joint control repeatability

The distribution of positioning errors for the open loop experiments can be seen in fig. 6. The two big modes in the distribution are most likely due to the different backlash errors introduced by driving joint j1 in one of two directions during a measurement. The visual feedback and open loop repeatability experiments were both performed using only the small workspace visible in the cameras. To investigate whether joint control repeatability changed when doing bigger movements, we varied the trajectory length. We did not find any dependence on trajectory length. We don't see any reason why this should not hold for visual feedback control as well.



next up previous
Next: 3.3 Adaptive vs. Non-adaptive Up: 3 Experiments with the Previous: 3.1 Experimental Procedure



jag@cs.rochester.edu