IEEE Robotics & Automation Magazine - March 2022 - 90

linear effect on MT is not supported by our analysis. Instead, it
is crucial to separate these two terms, which can be accomplished
by introducing different constants for each, as
explained in the " Model Derivation " section. Second, it should
be noted that the rotational tolerance ~ has a nonlinear relationship
with MT in our study, in contrast to a linear relationship,
as in [11]. This difference implies that higher degrees of
difficulty require matching the rotation of an object on all 3D
axes instead of one as in the work of [11], which was limited to
2D space. Third, we can also conclude that from the 2D formulations,
Hoffmann's model [8] works well and indicates the
necessity of adding the size of the object F, which is why it is
included in our version. We can thus infer that W and F
inversely affect MT and should be included in a model.
We found no evidence to support the significance of directional
and inclination angles in a consistent manner. More specifically,
we observed that directional angles presented a significant
influence on MT, which was limited in experiment 2 to pointing
(p < 0.05). Furthermore, while inclination angles affected MT for
pointing and manipulation in experiment 2 (p < 0.05), they presented
an insignificant effect in experiment 4, where the translational
and rotational variables influenced MT significantly more
than inclinations and directions. Nevertheless, despite its negligible
effect on MT, our study shows marginally worse performance
in front-to-back (90 and 270º) than in lateral i.e., left-to-right (0
and 180º), movements. This is in line with [1].
Finally, manipulation tasks took longer to complete in all
cases except purely rotational trials (experiment 3), where
pointing proved significantly more difficult, especially with the
lowest target tolerance at
~ 25= ..
c Overall, this difference can
be partially explained by the time spent grasping the object.
An important finding was that manipulation can be modeled
under Fitts's model if the important variable of object size F is
taken into account. The object size is mostly overlooked in the
state of the art but is mitigated in Hoffmann's work [8], as seen
in (2). In Table 4, we summarize the main findings from our
work and the implications for task design involving 3D user
interfaces, VR, and robotic teleoperation.
Limitations and Future Work
Limitations to overcome in a future study involve considering
the multitude of different input devices, hand types, and
grasping types one can use, which may affect the formulation
of human models [2]. Furthermore, human perception is a
complex phenomenon and subject to each individual's exposure
to technologies as well as personality-related factors [2].
Due to the significant number of variations introduced in our
work to study the effects of all spatial variables in 3D space,
we limited the investigation of each variable to a maximum of
four levels. Future studies are advised to investigate an even
wider range of these variables with more levels and how task
difficulty is affected. For example, changing the cube shape in
our study to a more complex 3D shape, such as a toy car, will
facilitate a wider range of rotations to be investigated. As for
all human performance models derived from Fitts's law, the
main limitations are stationary tasks. All models studied in
this article do not take into account upper-body movements,
such as those from torsos and/or shoulders. Biomechanical
variations in participants, such as placing objects near the
dominant hand, may also be determining factors.
Conclusion
In this work, we investigated a new human performance metric
in full 3D for pointing and manipulation tasks with combined
translational and rotational movements. We conducted
four experiments, each adding progressively higher spatial
Table 4. A summary of the main results and key implications for object interaction
in VEs and simulated teleoperation tasks.
Research Implications and Findings
R.1
R.2
R.3
R.4
R.5
Fitts's law can be extended toward 3D but does not adequately explain all spatial settings, and it requires a clear definition
of the distances associated in 3D.
Translation and rotation should be classified as separate concepts and quantities. We observed that rotation predominantly
influenced MT over translation by almost 66% of the total contribution. Hence, a model has been built, incorporating
a constant for each, as these do not have an equal weight toward MT.
Pointing and manipulation are perceived as inherently different types of tasks, but they do follow, and can be modeled,
by Fitts's law, even in 3D space.
Object size does matter. During pointing but especially in manipulation, this holds. For the latter, the object size is an
integral part of the metric. This is achieved by adding the object size F to the equation, as suggested by Hoffmann [8] and
confirmed in our model extension.
Rotation tolerance ~, or simply the rotational accuracy, significantly affects MT. This is particularly the case for very low
rotational tolerances (2.5°). Hence, strict rotational accuracy requirements during object placement (i.e., teleoperation)
are likely to significantly lengthen operator completion times.
Recommendations for Task Design in Pointing and Manipulation Tasks in VR and Teleoperation
RC1
RC2
Avoid having " strict " accuracy requirements since low rotational tolerances, in particular, contribute to high MTs, following
a nonlinear relationship.
Avoid, if possible, having pointing tasks that require movements toward or away from the view direction of a user. Our
results marginally showed that front-to-back movements take significantly longer than left-to-right ones and vice versa.
90 * IEEE ROBOTICS & AUTOMATION MAGAZINE * MARCH 2022

IEEE Robotics & Automation Magazine - March 2022

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2022