Fitts Law Extended to Trajectory Tracking or Steering Tasks

Steering Tasks

One of the fundamental aspects of the Fitts Law relationship is that the target size constraint is at the terminal point of the movement task. In general, no bound is placed on the intermediary trajectory along the amplitude until crossing the initial edge of the target. Accot and Zhai [123] in an earlier study chose to investigate the application of Fitts Law to trajectory-based tasks that required steering the end- effector through a “tunnel” region where the was a directional constraint on the path along the entire amplitude of the movement. To develop and validate a trajectory- based task the authors first used an experimental setup similar to the standard Fitts tapping test but with some alterations to the protocol. Subjects started from an initial position outside the bounds of the tunnel. Employing one-way discrete movements, the end-effector was tracked as it passed within a given height1, H, perpendicular to the intended path at the start of the tunnel, then along the straight-line trajectory of amplitudeA until it crossed the end of the tunnel within an identical terminal height constraint. Given a height constraint at both the initial point and the terminal point, Accot et al. reclassified this as a two-goal passing task. They verified that the two- goal passing task had a log-linear relational between A, H, and M T, just as Fitts Law and then further extended the model to a N + 1-goal passing task with each success goal being H in height and _NA further along the path. This generates a index of difficulty, ID_N = Nlog₂(_{N H}A + 1). As _Nlim_→∞ID_N = _HA_{ln 2}. Thus producing a linear-linear relationship between A, H, M T so that

M T =a+bA

H (4.21)

Using thirteen subjects in a fully-crossed, within-subjects factorial design in- corporating four amplitudes and eight tunnel heights the authors were able to get strong agreement between their model and the experimental data captured. The re- sults produced a linear fit of M T = −188 + 78·ID with r2 = 0.968, and average

1. The authors of [123] used the terminology of width (W) for the constrained size of the tunnel boundary, but that is in conflict with the convention terminology used in Fitts Law studies. Width (W) refers to target dimension along the line of approach not perpendicular to it. We have adjusted the terminology here, and use “height” (H) where appropriate to avoid confusion.

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error rate of 6.4%.

Friedlander et al. [124] similarly proposed the use of a linear-linear model relationship for their non-visual user interface element, called a bullseye menu. The example configuration is shown in Figure 4.3, and is essentially a goal-passing task similar to what was described above. While the target(s) are two dimensional, the height constraint is not strictly imposed given that it expands radially within each sector. The segment widths bounding each submenu item region within the sector are constant. Friendlander et al. conducted a series of experiments to determine employing a Fitts performance model or an alternative linear model for this type of user interface element. Deriving A = r(x−0.5) as the amplitude of movement for target selection of a particular menu item ring, with r being the width of each ring andx being the index for each ring. The Fitts Law model for a bullseye menu is then

M T =a+b·log₂(x+ 0.5) (4.22) in comparison to the linear model which is

M T =a+b·x (4.23)

The authors collected movement time experimental data from 12 subjects performing a menu item selection task through 2208 trials over four sessions, and found better agreement between the data and the linear model that with the Fitts model. One of their key rationales for this result stems from the fundamental difference in targeting feedback loop. With a non-visual stimulus2, there is a greater sensitivity to the large amplitudes of required movement.

4.2.2

Application of Fitts’ Law to Non-sighted Reaching

Tasks

Most formulations of Fitts’ law are given in polar form assuming that the subject performing the reaching task will move their hand along a direct vector from the initial point to the target. This is a natural consequence of investigating pointing/reaching tasks undertaken by sighted individuals. We propose to examine a that validity

2. Friendlander et al. tested both tactile and auditory cues for signalling the index of each menu ring crossed

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of a Fitts’ law based performance measure for this visually assisted reaching task undertaken by non-sighted subjects.

Given that it is not feasible to issue motion cues that require the user to track precise joint angles; the motion cues must follow some easily referenced directions such as the axial components of an egocentric reference frame. This Fitts’ law based measure could be created from the sum of one dimensional Fitts’ law for each hor- izontal and vertical axial movement subtasks and Steering law for the depth axial movement subtask. Thus the total predicted time M T_T to complete the reaching task is given by

M T_T =M Tx₁+M Tx₂+M Tx₃ (4.24) where areM Tx₁ and M Tx₂ are the expected subtask completion times to resolve the motions cues given by equation (2.3) and M Tx₃ is the expected subtask completion time to resolve the motion cues related to the appropriate depth estimation technique for the various feature extraction techniques presented in Chapter 3.