Takumu Okada, Shogo Okamoto, and Yoji Yamada*1 Abstract  –   A passive haptic interface based on the damping brake of a DC motor was used to present surface roughness.  Virtual roughness stimuli were expressed by using periodic resistance forces caused by switching the damping brake on and off at regular intervals.  We investigated the ability of humans to discriminate such roughness stim- uli through information transfer and signal detection theory.  Our results revealed that the passive haptic interface can present three to four levels of roughness stimuli without confusion, which is slightly inferior to an active-type haptic interface. Keywords  :   passive haptic interface, discrimination of roughness, damping brake
Introduction
1.
Haptic interfaces where the hardware itself con- sists of passive elements have the merits of inherent safety and low-energy consumption. Thus far, pas- sive force displays have been developed by several re- search groups. Such haptic interfaces are expected to be used in applications for many unspecified users. We previously assembled a passive haptic interface that uses the damping brake of a DC motor [1]. The device can present virtual roughness by repeatedly braking and releasing the hand. In addition to audiovisual information, presenting surface textures can assist with human-computer in- teraction, such as virtual buttons with different tex- tures.  When using roughness stimuli as tools for such information transmission, the discriminability of the stimuli is important.  In order to accurately deliver as much information (textures) as possible, there is a need to both increase the number of stimuli and design each stimulus to be discriminable from the others.  Although studies have investigated the char- acteristics of human perception of roughness stimuli from passive haptic interfaces [2], [3], their objectives were mainly to specify dominant parameters that af- fect roughness perception.  Thus far, the discrim- inability of roughness stimuli from passive haptic in- terfaces has rarely been investigated. The objective of this research was to investigate the discriminating characteristics of roughness stim- uli presented by a passive haptic interface through an identification experiment on six levels of roughness stimuli. This research was approved by the internal review board of the School of Engineering, Nagoya University (#15–12).
Roughness stimuli from a passive haptic
2.
interface
Damping brake of a DC motor
2.1
We adopted the damping brake of a DC motor as a passive element. The damping brake functions by the back electromotive force of a short-circuited DC motor.  Figure 1(a) shows a schematic of a computer- controlled short circuit in which R and L are the re- sistance and inductance, respectively, of the circuit. When a human rotates the short-circuited DC mo- tor, he or she experiences the resistive torque of the damping brake. Based on Kirchhoff’s law, the rela- tionship between the angular velocity ω(t) and brake torque τ(t) is expressed as follows:
where K is the torque constant of the motor. Given that the inductance L is negligible, the brake torque τ(t) is proportional to the angular velocity ω(t), which indicates that the braking torque corresponds to a damping resistance. Figure 1(b) shows the pas- sive haptic interface that uses the damping brake of a DC motor.  This device consists of a DC motor fixed on a frame and a crank with a handle connected to the output shaft of the motor.  The short cir- cuit is switched by using a motor driver (TB6643KQ, TOSHIBA) at a control frequency of 2 kHz. The Transactions of Human Interface Society   Vol.20,  No.2, 2018
Roughness via the passive brake
2.2
Figure 2(a) shows the brake operations for present- ing virtual roughness.  When an operator rotates the crank, he or she experiences roughness from periodic resistance forces applied to the hand, which is caused by switching the brake on and off at regular inter- vals (∆θ).  Previous researchers have demonstrated that such a resistive force field on a plane can be ef- fectively used to express virtual roughness without displacement in the normal direction [2]~[5 ]
3.
Identification experiment
We performed an identification experiment for six levels of roughness stimuli to investigate the discrim- inating characteristics of roughness stimuli presented by a passive haptic interface [6 ] 3. 1 Six levels of roughness stimuli Six levels of roughness stimuli from the finest stim- ulus S'1 to the roughest stimulus S'6 were used in the experiment.  The perception of roughness stim- uli from a passive haptic interface is largely depen- dent on the spatial frequency of the stimuli [2]. The on/off intervals of the brake (∆θ) correspond to the spatial frequency.  Stimuli with extremely small or large Δθ do not feel like roughness.  Hence, we set the lower and upper boundaries of ∆θ to be 0.15 deg (S 1 : finest) and 7.3 deg (S 6 : roughest), respectively. Stimuli located at equal psychological distances are easy to distinguish.  Additionally, Weber’s law generally holds for roughness stimuli by passive hap- tic interfaces [² ]  Therefore, we designed stimuli S 2 to S'5 with each ∆θ increasing by the same ratio from S 1 to S 6 , as shown in Fig. 2(b).  Because the length from the center of rotation to the handle was 100 mm, the spatial periods of S 1 to S 6 were 0.26, 0.56, 1.2, 2.7, 5.8, and 13 mm, respectively. Fig- ure 2(c) shows examples of force at hand measured by a force sensor and crank speed for stimuli S 2 and S4.
Participants
3. 2
Participants were five naive males in their 20s and 30s, and informed consent was obtained from all be- fore the experiment. 3. 3 Task Participants were asked to identify randomly pre- sented stimuli S 1 S 6 according to the six levels of roughness.  They rotated the crank at any speed to explore the roughness and responded with numbers from 1 to 6 in each trial. Each participant performed 20 trials for each of the six types of stimuli, which amounted to 120 trials.  Each participant took part in four sessions, with one session comprising 30 trials. Participants memorized the stimuli during a 3-min training session prior to the first session in which they could experience the stimuli freely.  Addition- ally, a similar 1-min training session was provided prior to the other sessions. This combination of free active exploration and training sessions enabled the participants to achieve the best performance.
Results
4.
As presented in Table 1, the average correct an- swer ratio was in the range of 65.8%–81.7%.  The average for all participants was 71.7%.  No signif- icant increases in the correct answer ratio between the first and final sessions was observed for all par- ticipants.  In other words, the learning effect was not observed. The results for each participant were summarized in the form of a 6×6 stimulus-response confusion matrix. The information transfer (IT) for
Average confusion matrix.  S i and R i
each participant was calculated from the confusion matrix.  As given in Table 1, the IT values ranged from 1.32 to 1.88 bits with an average of 1.60 bits. As discussed in the subsequent section, individ- ual differences were relatively small.  Therefore, we treated the average answer ratio.  The average an- swer ratio of the participants is presented as a con- fusion matrix in Table 2.  We calculated how far each stimulus was psychologically located from each other based on the signal detection theory [7]. We assumed that a response to each stimulus on the psychological continuum followed a Gaussian distribution and that the standard variations of all stimuli were equal (as- sumption of a case V score). Figure 3 shows the loci of roughness stimuli on the psychological continuum estimated from the confusion matrix in Table 2. We put the response to S 1 as zero. One unit on this con- tinuum is equal to a standard deviation of the distri- bution for a stimulus. When two stimuli are distant from each other by 1 unit, they are distinguishable with a probability of 84%.  In order to confirm the validity of the case V assumption, we calculated an- other confusion matrix for the answer ratio from the estimated loci and tested the goodness of fit with the matrix in Table 2. There was no significant discrep- ancy between the estimated and sample confusion matrices (χ² = 26.3, d.o.f = 30, p > 0.05), which does not deny the use of the loci shown in Fig. 3.
Discussion
5.
The results showed that the average IT values of roughness stimuli was 1.60 bits.  Thus, our system
Fig. 3 can present at least three levels of roughness with- out confusion (2¹.60 = 3.0).  Nonetheless, IT values can be underestimated when there are a number of stimuli involved in the experiment [8 ]. According to the displacements of the stimuli on the psychologi- cal continuum, as shown in Fig. 3, S 2 and S 3 were close and frequently confused. This led to a decrease in the average correct answer ratio and IT value.  If S 2 to S 5 were placed at equal intervals between S 1 and S 6 , then the IT and average correct answer ratio would be estimated to be 1.73 bits and 80.4%, re- spectively. Furthermore, if two stimuli were located at equal psychological distances between S 1 and S 6 and four stimuli were used in total, IT would reach its maximum value at 1.76 bits, and the average cor- rect answer ratio would increase to 96.4%. Consider- ing the high average correct answer ratio, our system may be able to deliver four levels of distinguishable roughness at most. When the loci of stimuli are cal- culated for individual participants and four equally distant stimuli are used, the IT values for each par- ticipant range from 1.59 to 1.82 bits with the average correct answer ratios of 92.9% and 97.6%. Thus far, the discriminating characteristics for the roughness of textured surfaces or roughness stimuli by active haptic interfaces have been investigated. The Weber fractions for textured samples with a spa- tial period ranging from 0.77–1.0 mm and 2.5–10 mm were reported to be 5% and 6.4%–11.8%, respec- tively [9], [10 ]. Biet et al. [11 ] reported that the Weber fractions for spatial periods from 2.5 to 10 mm was 8.1%–9.6% when roughness stimuli were presented by a friction-based tactile texture display. The spa- tial period of the stimuli used in our experiment was 0.25–13 mm, which was in the range of those used in the previous studies.  The discrimination threshold of the spatial period calculated based on the loci of the roughness stimuli was 28% at a threshold level of 84% and 20% at a threshold level of 75% for each spa- tial frequency.  Although a comparison with previous studies is not accurate because of the differences in experimental designs or calculation methods of the
The Transactions of Human Interface Society   Vol.20,  No.2, 2018
Weber fraction, the Weber fraction calculated from our experimental results is two to four times larger than that when using an active haptic display and actual textured surfaces. In other words, the passive haptic interface used in this research is slightly infe- rior to the active haptic interface in terms of present- ing roughness, which is a tradeoff for the benefits of passive haptic interfaces.  Nonetheless, the discrim- inability may be improved by employing a DC motor with a greater torque constant or smaller inductance and optimizing the moment arm.
Conclusion
6.
We investigated the discriminating characteristics of roughness stimuli from a passive haptic interface. In the results of an identification task for six lev- els of roughness stimuli, the average correct answer ratio was 71.7%. The average IT value was approx- imately 1.60 bits, which indicates that the interface can present at least three levels of distinguishable roughness. It is estimated that the system used in this research can present four levels of roughness stimuli at most without confusion by locating the stimuli at equal psychological distances from each other.  This passive haptic interface is slightly inferior to active haptic in- terfaces in terms of the presentation of roughness. The results will help us design stimuli when using roughness stimuli by a passive haptic interface as a tool of information transmission. [1] [2] [3] [4] [5]
Reference
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Biography
Takumu   Okada
Takumu Okada received a BS degree from Nagoya University in 2017. He is currently a graduate student of the department of Mechanical Systems Engineering in Nagoya University.
Okamoto
Shogo
(Member)
Shogo Okamoto received MS and PhD degrees in Information Sciences in 2007 and 2010, respectively, from the Graduate School of Information Sciences, Tohoku University.  Since 2010, he has been with the Graduate School of Engineering, Nagoya Uni- versity. Yoji
(Member)
Yoji Yamada received a PhD degree from the Tokyo Institute of Tech- nology in 1990.  In 2008, he moved to Nagoya University, as a profes- sor after being an associate professor at the Toyota Technological Institute and a group leader at AIST.