Servo-Gaussian Model to Predict Success Rates in Manual Tracking

Abstract

We propose a Servo-Gaussian model to predict success rates in continuous manual tracking tasks. Two tasks were conducted to validate this model: path steering and pursuit of a 1D moving target. We hypothesized that (1) hand movements follow the servo-mechanism model, (2) submovement endpoints form a bivariate Gaussian distribution, thus enabling us to predict the success rate at which a submovement endpoint falls inside the tolerance, and (3) the success rate for a whole trial can be predicted if the number of submovements is known. The cross-validation showed R 2 > 0.92 and MAE < 4.9% for steering and R 2 > 0.95 and MAE < 6.5% for pursuit tasks. These results demonstrate that our proposed model delivers high prediction accuracy even for unknown datasets.

Sample-size and Repetition Effects on the Prediction Accuracy of Time and Error-rate Models in Steering Tasks

“…For the Retry rule, the differences in R 2 , MAE, and RMSE were 0.00040, 0.0019, and 0.018 points. These trivial effects of the T sampling choice on prediction accuracy were consistent with our original study on the ER model [40]. We thus consistently applied T sampling = 300 ms hereafter.…”

“…In contrast, in the Retry rule, because a failed trial must be retried until successfully Fig. 2 Submovement distribution proposed in the previous study [40]. The cursor's endpoints for the first and second submovements are indicated by red "X" marks, which normally distribute along the y-axis (as visualized by blue curves).…”

“…When the cursor deviates from the path width, several researcher groups asked the participants to immediately return to the path and continue the task until the end, as shown in Fig. 1 (a) [17], [28], [40], [44]. We call this the "Keep" rule.…”

“…In our original study [40], five participants joined an experiment with four As and five Ws. The result showed that Eq.…”

“…This is because (1) the hand corrective-reaction time is 273 ms on average [19] or 190 to 260 ms [14], and (2) a typical end-to-end latency ranges from 50 to 80 ms for conventional red-LED mice and LCD monitors [5], or much shorter values for recent laser mice such as 25 [21] and 40.5 ms [40]. Thus, we used 250 reaction time + 50 latency = 300 ms, which was the same setting as in our original study on the steering ER model [40]. Figure 6 shows that the predicted ERs are well-correlated with the observed ERs: R 2 > 0.97, MAE < 2%, and RMSE < 2%.…”