NFCSense: Data-Defined Rich-ID Motion Sensing for Fluent Tangible Interaction Using a Commodity NFC Reader

Tangible user interfaces (TUIs) seamlessly couple digital information with physical forms [22] and leverage our existing cognitive and spatial knowledge to make digital information embodied and comprehensible. Token+Constraint TUI systems [44] combine the physical/digital artifacts of tokens and constraints, allowing the users to map structured compositions of these tokens onto a variety of computational interpretations. The affordance [14] of physical constraints can facilitate and guide user interaction [13] and limit the possible range of token movements to make the future state of such movement predictable. With physical constraints, researchers can further explore the design space of passive TUIs that are actuated only by gravity, such as the Marble Answering Machine [8].

Passive NFC/RFID technologies are useful for prototyping TUI systems involving multiple objects with ease. Compared with object sensing technologies that can identify passive objects (e.g., audio recognition [18, 26, 40] and the use of a capacitive sensing matrix [46] and pressure sensors [17]), An NFC tag provides a smaller footprint while yet providing a virtually infinite number of IDs; furthermore, it does not require physical contact for a reliable reading. Unlike the tags used in computer vision, the sensing of NFC tags does not suffer from line-of-sight problems. Therefore, NFC technology provides a reliable identification mechanism that helps the system identify both the object in action and the action set bound to the object [4]; in doing so, the system helps users easily associate the content with the symbolic appearance of the content's original form and functions [35]. Commercial products use NFC tags in toys-to-life applications, such as Nintendo Amiibo ¹ and Lego Dimensions ², where in-game content is unlocked by the player placing NFC-tagged toy figurines on an NFC reader. Researchers have also applied near-field RFID to prototype token+constraint interactions, such as DataTiles [37] or to detect page-flipping events in interactive book applications [3].

Because NFC systems do not primitively support far-field tag identification, the tag and reader must be tightly coupled in the application. Another subset of the literature involves applying ultra-high-frequency (UHF) RFID systems to sensing touch inputs on tags [19, 23, 28, 47, 48], making tangible user interfaces [20, 27, 43], and making wearable input devices [24, 30]. Although UHF RFID systems support a longer distance (∼ 6m) and room-scale deployment using a single reader, the deployment cost of UHF RFID readers is significantly higher than their NFC counterparts. The much higher sensing latency (∼ 200 ms [43]) of UHF RFID systems also limits their application in time domain.

Beyond focusing on NFC's basic capability to identify tags, researchers have also enabled interactivity on NFC tags by leveraging their signals to detect presence [3], touch [38], and rotation [11]. Furthermore, advanced techniques have been applied, such as using on–off keying to encode 1D inputs on a tag-embedded widget [42], embedding additional electromechanical switch circuitry for additional input [34], and forming multiple tags as compound widgets [1, 15]. Project Zanzibar [45] explored a broad range of tangible interactions, including multi-object tracking, stacking, translation, and rotation with an NFC antenna array. Nonetheless, the focus among researchers has been directed more toward tracking the static states of tokens rather than tracking their transient states, such as speed and frequency, and the use of physical constraints.

Researchers have also applied sensor fusion to extend the capability of NFC systems, such as incorporating magnetic sensing with the RFID tag to realize a 5-degree-of-freedom (5DoF) input of an RFID tag [31], implementing NFC with capactive sensing [16], or using an extended NFC reader as a two-dimensional antenna array that is coupled with a capacitive touch sensor [45]. By incorporating an additional motion sensor, previous studies have also proposed wearing motion sensing RFID readers in apparel and devices such as gloves [12], bracelets [5, 12], wristbands [9], rings [7], and finger-worn devices [32] for ubiquitous computing applications. Nonetheless, for makers who wish to prototype rich-ID motion sensing systems with some existing set of objects, these delicate sensor fusion systems are more complex and difficult to obtain than is a single commodity NFC reader.

In the context of designing a fluent tangible interaction design space, occlusion-free NFC technology can differentiate itself from occlusion-sensitive computer vision [2, 39] by allowing users to use a tagged object with greater freedom. NFC provides a much larger ID space than other contactless and wireless sensing technologies that do not provide rich ID (e.g., magnetic tracking [6, 29]). NFC also reduces the physical contact that is otherwise required by other rich-ID technologies that are dependent on physical contact [17, 18, 20, 46]. NFC technology can do so because it requires no electromechanical connectors that may constrain object movement or material choice. With the rich-ID motion sensing proposed in this paper, users can enjoy not only effortless operation but also hot-swappable interactivity, which provides the user a fluent experience with time when using an occlusion-free, contactless, and rich-ID NFCSense system.

This session examined the presence signal pertaining to a tag's 3D location. In this session, the angle θ between the tag and the reader surfaces was set to 0; in other words, the tag was not tilted.

Apparatus. Figure 4 a depicts the experiment apparatus. A modified delta 3D printer was used as a robotic arm holding the tags. We replaced its nozzle with a tag holder built from Duplo blocks and 3D printed components, and we put a reader holder, which was also made from Duplo blocks, on the printbed. We programmed the printer to move the tag holder at a precision of 0.2 mm, and we placed an ADXL335 three-axis accelerometer, which had a 250 Hz sampling rate, next to the holder to monitor the motion of the print head. A Mifare S50 PVC coin RFID tag and an MFRC522 NFC reader, which we used in the feasibility study, were mounted on the tag and reader holders, respectively. To eliminate electromagnetic interference, both the tag and reader were placed at least 5 cm away from the metal components of the 3D printer. The centers of the tag holder and reader holder were carefully aligned at a precision that allowed for the stacking of two Duplo blocks together.

Procedures. Because the magnetic field emitted from the rectangular antenna had a reflectional symmetry in the three Cartesian axes with its center as the origin, the tag activation could be described through measurements of only one quadrant. An NFC tag is used in the measurement. We first aligned the center of the tag to the center of the reader antenna at 1 mm above the center of the sensor. Then, we took a measurement as the 3D printer moved a tag to every 1 mm grid location in a 39 (W) × 39 (L) × 40 (height; H) mm³ volume. After the tag was moved to a location, as determined by the motion sensor, the system took 20 samples of the binary presence state, and the tag then moved to the next location until a full traversal had been made. A measurement took 100 ms at each location. In total, 40 (W) × 40 (L) × 40 (H) × 20 = 1,280,000 samples were taken, and the total measurement time was ∼ 1.6 h.

Results. The measurement results are presented in Figures 4 b, in which a 3D scatter plot shows the locations that had at least 95% (19 out of 20) of tag presence instances being detected. The tag presence distribution agreed with the electromagnetic field distribution of the antenna. In the z axis, the cross-sectional area of the tag presence was dependent on the hover height of the tag. Figures 4 d shows the maximum hover height was detected at z_max = 33mm. The maximum cross-sectional quadrant area A = 457mm² was detected at z = 11mm, where we obtained the maximum distances of L_x = 22mm (x axis) and L_y = 22mm (y axis) from their central component. Notably, when a tag was at a hover height of z ≤ z^* = 6mm, the tag was first, activated not only at the center but also at the periphery of the antenna and second, was inactivated between the two activation zones. Within the range of 21 ≥ z ≥ z^* = 6mm, the measurement was of similar validity because the distances to the center were ≤ 1mm less than L_x = 22mm.

Figures 4 e and 4 f present the cross sections at z > z^* and z < z^*, respectively. They both show that L_i = L_y = 22mm when i ≤ w_z and w_z > 0 in the cross section of every z value except for z = 32mm. This result indicates that the activation area formed by the rectangular reader antenna was mostly of a round-rectangular shape; this meant that a valid measurement along the x axis (or y axis) did not have to strictly align with y = 0 (or x = 0).

Discussion. With regard to our application to sensing a moving NFC tag, the most important insight extracted from the results was that knowing where the NFC reader ought to be deployed makes the tag presence signal pattern more predictable. We recommend keeping the tag-to-reader distance steady at either z > z^* or z < z^* throughout the speed measurement to simplify the algorithm used for motion sensing. The z^* value may vary between tags and antennas because their electromagnetic-field coupling can differ.

In this session, we further examined the presence signal of the same tag used in Session 1 with respect to its 3D location and tilt angle θ.

Apparatus. The apparatus used in this session was identical to that in Session 1. An additional 3D-printed adapter was used to affix the tag at seven angles (0°, 15°, 30°, 45°, 60°, 75°, 90°), as shown in Figure 5 a.

Procedures. Because the cylindrical NFC tag was rotationally symmetric, measurements of only pitch angle were sufficient to describe the effect on the angle of the tag. Nonetheless, we had to measure two quadrants to be able to sufficiently describe the tag activation distribution on this antenna. Seven pitch angles were measured in this session. Similar to Session 1, prior to taking measurements, we located the 12.5-mm radius tag 13 mm above the center of the antenna. Subsequently, we took measurements as the 3D printer moved a tag to every 1 mm grid location in a 3D [-40, 39] (W) × [0, 39] (L) × [13, 35] (H) mm³ volume. After the tag was moved to a location, 20 samples of the binary presence state were recorded. Thereafter, the tag was moved to the next location until a full traversal had been made. A measurement took 100 ms at each location. In total, 7 (angles) × 80 (W) × 40 (L) × 23 (H) × 20 = 10,340,000 samples were taken, and the total measurement time was ∼ 14.3 h.

Results. Figure 5 b shows the measurement results. The cross-sectional area of the tag presence along the z axis was dependent on the tilt angle θ of the tag. The maximum hover height z_max = 28 mm was the same when 0 ≤ θ ≤ 30°. However, when θ > θ^* = 30°, a blind gap was observable in the antenna area (20 > x > -20 and 20 > y > -20) at every hover height on the z axis. Increasing the tilt angle θ broadened the blind gap, centered the blind gap, and reduced the maximum hover height. The thinnest gap observed at θ = 90° was 16 mm, which lay between x = -8 mm and x = 8 mm.

Discussion. To reliably sense a moving cylindrical NFC tag, the tag should not be tilted more than an angle of θ^*. Because a slight ≤ θ^* tilt still allows for reliable sensing, the orientation of a tag does not need to be strictly fixed. However, embedding the tag into a 6-degree-of-freedom (6DoF) object, such as a sphere, does not guarantee that the presence signal can be picked up by a rectangular antenna. The angle θ^* may vary between tags and antennas because their electromagnetic-field coupling can differ.

In this session, we further examined the presence signal pertaining to the 3D location of a pair of cylindrical NFC tags that were separated at various distances.

Apparatus. The apparatus used in this session was similar to that in Session 1, except for the addition of two different NFC tags, Tag_A and Tag_B (both z^*=5 mm) for measurement. An additional 3D printed adapter was used to affix the two tags at different gap distances from 0 to 18 mm.

Procedures. We had to take measurements in two quadrants to sufficiently describe the tag activation distribution on this antenna. Nine gap distances d_gap between Tag_A and Tag_B from 0 to 18 mm (2 mm step) were measured in this session. Prior to taking measurements, we aligned the center of Tag_A to the center of the reader antenna at z^* = 6mm above the center of the sensor. Subsequently, we took measurements as the 3D printer moved a tag to every 1 mm grid location in a [-65, 24] (W) × [0, 24] (L) × [6, 34] (H) mm³ volume. After the tag was moved to a location, 20 samples of the binary presence state were recorded; thereafter, the tag was moved to the next location until a full traversal had been made. A measurement took 100 ms at each location. In total, 10 (gap distances) × 90 (W) × 25 (L) × 29 (H) × 20 = 13,050,000 samples were taken, and the total measurement time was ∼ 18.1h.

Results. Figure 6 shows the measurement results. When d_gap ≤ 14mm, intersections were observed between the activation maps of Tag_A and Tag_B. Notably, neither Tag_A nor Tag_B was reliably detected in these intersections due to the signal collisions, causing a blind gap between the two tags. The smaller the d_gap was, the wider the blind gap was. When d_gap = 0, the maximum hover height of Tag_A was also reduced. When d_gap = 0 mm and y = 0mm, the widest gap between Tag_A and Tag_B was 11 mm, where z = 6mm, and the maximum combined length of the presence of Tag_A and Tag_B was 66 mm, where z = 15mm.

Discussion. The detection of the presence of two side-by-side tags does not seamlessly transition from one to another if the gap distance d_gap between the two tags is too small. The blind gap turns part of both tags’ active area into an unstable or even inactive area, making the detection not only less efficient but also less reliable. The remaining activated area may still be sufficiently large for the tag to be reliably identified by the reader, but the maximum allowable speed is reduced. Accordingly, the maximum throughput is also reduced. When the d_gap is too large, the gap between the two activation areas also reduces the channel utilization and throughput. Hence, an optimized d_gap should be sufficiently large to allow the two areas to touch each other without intersecting. The users can define a $d_{gap}^*$ as a threshold of signal quality in their application.

To understand how the aforementioned results generalize, we tested various tags with the sample apparatus and procedures used in Session 1. Figure 7 a depicts the tags that we used for measurements, which were as follows:

• 20 × T0: 12.5 mm (R) × 1 mm (T) Mifare 1k Classic NFC Coins (the same one used in Session 1-3)
  
• 1 × T1: 12 mm (W) × 22 mm (L) NTAG213 Micro NFC Tag
  
• 1 × T2: 5.5 mm (W) × 16 mm (L) NTAG203 NFC Tag
  
• 1 × T3: Keychain embedded an NFC tag with a 13-turn 23 mm (outer diameter) × 18 mm (inner diameter) coil
  
• 1 × T4: 15 mm (R) × 0.1 mm (T) NTAG215 NFC Tag Sticker
  
• 1 × T5: 50 (W) × 70 (L) × 1 (T)mm³ NFC Card
  

We measured a two-dimensional 39 (W) × 39 (L) × 40 (H) mm³ sensing plane, where the (x, y) = (0, 0) point was defined to be 1 mm above the center of the reader antenna.

Figures 7 b and 7 c present the measurement results. Among the six types of tags, T4 and T2 performed the best (z_max = 35mm, z^* = 6mm) and worst (z_max = 7mm, z^* = 0mm), respectively. This result demonstrates that the performance of the tag is correlated to the form factor of the tag antenna, as depicted in Equation 1. Because tags T1 to T4 exhibited an activation map that was similar to T0, the preceding results applied to them. The different activation map of T5 indicated that our preceding findings cannot be generalized to T5, which was the only tag that was larger than the reader antenna.

Regarding the internal validity of the 20 T0 tags, their mean maximum height was $\overline{z_{max}}$ = 31.55 mm (SD = 1.99 mm), their mean maximum distance to the center was $\overline{L_y}$ = 21.55 mm (SD = 0.89 mm), and their mean minimum hover height for signal activation was $\overline{z^*}$ = 5.55 mm (SD = 0.76 mm). The low variance between these 20 samples indicated that the parameters obtained from a tag can be transferred to another tag with the same specification.

This section introduces the form primitives of the tokens and the physical constraints. Figure 8 presents the four basic form primitives of token design, where the token comprises an NFC coin and a physical support made of nonconductive materials. For single-tag tokens, we recommend a single NFC tag to be deployed under three configurations:

• z < z^*: z < z^*, θ < θ^* (Figure 8 a)
  
• z > z^*: z > z^*, θ < θ^* (Figure 8 b)
  
• θ > θ^*: z > z^*, 90° > θ > θ^* (Figure 8 c)
  

where z and θ are the tag-to-reader distance and angle, respectively, and z^* and θ^* are empirically determined thresholds of z and θ, respectively. With a linear physical constraint that fixes the θ and z values of a tagged token moving above the reader, these three configurations can be recognized by the different number of pulses (Figure 9).

When using multiple single-tag tokens or a sole multi-tag token, we recommend for the tags to be deployed according to the following configuration:

• $d_{gap}> d_{gap}^*$: $d_{gap}> d_{gap}^*$, z > z^*, θ < θ^* (Figure 8 d),
  

where d_gap is the tag-to-tag distance and $d_{gap}^*$ is the user-defined signal quality threshold. According to the study results, we recommend a sufficiently large d_gap (between the tags) to be maintained to optimize both the usability and the signal-to-noise-ratio. Making each tag z > z^* and θ < θ^* also reduces unwanted minor components in the activation map.

NFCSense's input space can be further extended by using physical constraints, which can modulate the primitives’ physical states (z, θ, d_gap) and provide a physical reference for manual operation. Figure 10 shows the form primitives of linear, rotational, and simple harmonic motion (S.H.M.) constraints. For linear translation, putting a track above the reader can fix the θ and z values of a tag moving on it. A track-to-reader distance of z_p can reduce a z > z^* tag's required thickness to z^* − z_p, thus allowing the tags to be thinner, lighter, and therefore more amenable to further integration. Without compromises to sensing validity, the track can be made two times $w_z< w_z^*$ wider than the primitives, depending on the tag-to-reader distance z. To allow for rotation or simple harmonic motion, a spinner or a swing can be added to modulate the θ and z values of a primitive. A (loose) location constraint is required to ensure that a z > z^* tag enters the activation area once every cycle.

Figure 11 depicts the workflow of extracting the tag motion features from the rich-ID square waves. The binding between the event trigger's NFC tag ID and its use of algorithm can be predefined, so the system can reliably determine which software algorithms to use without the user manually selecting the algorithms or without a machine learning classifier. Tag motion features can be extracted from the rich-ID square wave of time-series state information using three algorithms.

• I. Linear Translation. When z and θ are known, the linear translation speed V_L of a tag sliding through a reader can be computed by V_L = L(z, θ)/T_M, where L is path length across the major component of the active sensing area at z and θ and where T_M is the pulse duration of the major component that has the largest T_on. Furthermore, L(z, θ) can also be determined from the activation map (Figures 4 and 5). When the pulse width of a tag absence, T_off, is longer than two times the tag read duration, the token's primitive type can be identified from the pulse count N obtained from the segment. If a θ > θ^* (N = 2) token is identified, the direction of motion can be resolved from the asymmetric pattern (Figure 9 c). A valid segmentation mechanism can be achieved by setting the time-to-live timer t_TTL1 larger than the length of T_off between the pulses at a predefined minimal speed.
  
• II. Rotation or Simple Harmonic Motion. When a tag is identified to be one with constrained rotation or in simple harmonic motion, the rotation frequency f can be computed using $f_{R} = \frac{1}{T_i}$, where T_i is the interval between the rising edges. For simple harmonic motion, the frequency can be computed by $f_{SHM} = \frac{1}{2T_i}$. The acceleration can be derived from the first-order derivative of the frequency. The algorithm outputs either f_R or f_SHM based on the event trigger's NFC tag ID. The algorithm reset the state of measurement when the time-to-live timer t_TTL2 gets expired.
  
• III. Compound. When a tag is identified to be part of a compound that comprises multiple tags, its linear translation speed $V_L = \frac{\sum ^{N-1}_{n=1}L(d_{gap},D_{tag})/t_i^{n}}{N-1}$, where L = d_gap + D_tag (diameter of the tag), or the rotation frequency $f_{R}^n = \frac{1}{T_i^n}$ are resolved using the rising edge interval T_i because doing so yields more robust results. When the same type of tags is used and the d_gap is sufficiently large, knowing L(d_gap, D_tag) does not require a lookup table. The tag presence order PO also indicates the input mode. For V_L, a valid segmentation mechanism can be achieved by setting the time-to-live timer t_TTL1 larger than the length of T_off between the pulses at a predefined minimal speed.
  

Based on a lookup table constructed from the activation maps in the studies described in Section 5 and on the feature extraction algorithms described in Section 6, time-series signals were collected, which could be used to resolve the frequency and translation speed and to infer the state of a tag from the motion signal patterns.

Frequency. Figure 13 a shows the resolution of the frequency of the black spinner that was spun by a user. As shown in Figures 13 b and 13 c, not only the frequency but also the rotation direction of the white spinner could be resolved based on the f_R of each tag and on the order of appearance of the three tags, respectively. Notably, the T4 tag had an activation area with a diameter of >4 cm when 25mm > z > z^* = 5mm (Figure 7). Therefore, aligning the tag to the reader is not difficult if the visual affordance of the reader's location is clearly observable. Additional support such as a stabilizer (e.g., an armrest) or visual feedback pertaining to the reader can further improve usability.

Figure 13 d depicts the frequency f_SHM of the simple harmonic motion of the swing hanging on the rack was resolvable. By leveraging the ID of NFC tags, the system can automatically switch the detection mode by using the algorithm corresponding to each tag.

Speed. Figure 14 a shows a user sliding a boat along the track to resolve its speed V_L. Figure 14 b shows a user releasing the boat from the top of the track to resolve its speed V_L. When the angle of incline of the track is known, the location at which the boat is released can be further inferred through the observed speed. Figure 14 c shows a user playing a balancing game with the trolley on the track. The user moves the trolley by tilting the track using both hands. The direction of motion and the acceleration were resolved. These examples demonstrate that both hands-on and hands-off interaction styles are supported by this system.

Additional Tag States from Presence Signal Patterns. Figures 15 a and 15 b show a triple-pulse pattern being generated after a user walked the figurine along the track; this pattern differed from the monopulse pattern generated after a user jumped the figurine over the reader. Figures 15 c and 15 d depict a short-long pattern generated after a user moved the car forward along the track; this pattern differed from the long-short pattern generated after the user moved the car backward along the track. The speed V_L of the action was resolved in both cases.

If carefully designed, physical constraints can extend the input space by localizing a tag from various input sources, thus preserving a meaningful tag order, easing the inputs, and increasing the throughput by preventing collisions.

Maintaining the Distance Between Two Tags. The white fidget spinner (Figure 12 e) and the trolley (Figure 12 i) featured a placeholder that maintained the distance between the two tags to reduce interference in tag reading. In the multiplexer example (Figure 16 a), we also added a 30-mm-diameter × 3-mm-thick cylindrical nylon ring to each tag ensure that the tags rolled along the track smoothly.

Localizing a Tag from Various Input Sources. Figure 16 a depicts the multiplexer, which comprised a stack of two tracks that allowed an NFC coin to roll along them. The inner and outer tracks were deployed at a z_inner = 4mm < z^* and z_outer = 10mm < z^* distance to the reader, respectively. The signal patterns for tag presence after the user placed the coin tag in each slot differed because the tri-pulse was for the inner track and the mono-pulse was for the outer track. Therefore, the system could recognize where the tag was placed based on these signals. More tracks can be distinguished by adding more outer tracks either with different slopes within a distance z_outer < z_max to the reader or at a different angle θ_outer < θ^* to create more speed-related patterns. ³

Preserving a Meaningful Tag Order. Figure 16 b illustrates an educational Montessori-inspired [49] TUI for learning mathematical concepts with a Duplo-block compatible linear tag holder; this was the sorter, which supported four tag-embedded Duplo blocks to be mounted on it in a linear order. Each block, which was embedded in a T0 tag with a Nylon-printed Duplo compatible tag holder, was associated with a certain numerical quantity (e.g., 1, 2, and 3) or an object (e.g., apple, banana, and carrot). The user answers the quiz by putting these blocks together in the correct order, where the block order is read by having the blocks be effortlessly released from the top of the stack. Visual feedback, such as incorrect elements, is shown on the screen, motivating the user to try again.

Easing the Inputs. The funnel (Figure 17 a) extends the entry area of a track and outputs one tag at a time. Users were allowed to throw a tag into the filter to get the tag through instead of placing it carefully on the track. Such easy tag placement can increase the throughput and thus accelerate the workflow. This extension is minimal yet effective, although it only supports a few (e.g., 3–5) tags at a time. Throwing too many tags simultaneously into the funnel may cause jamming, which requires extra time for manual intervention, although the user is also aware of this problem and capable of solving it.

Increasing Throughput by Preventing Collisions. The modulator (Figure 17 b-d) prevents collisions by modulating each tag's location before they are read. We adapted the coin separation mechanism of a mechanical coin sorting machine ⁴ to the NFC coin tags and constructed a tilted gear-shaped rotating plate with a handle at the back; this plate allowed the users to roll the plate with it. A user was allowed to throw multiple tags into the container with one hand and to resolve any jams by rocking the handle to separate the tag and modulate their locations before they were read.

The modulator requires users to perform simple rolling movements; without the modulator, the user must manually separate tags, which is cognitively taxing and requires fine motor control. Such savings in time and effort are especially apparent in batch operations when many tags are used. Furthermore, this mechanism is inexpensive to deploy and maintain because it requires no electrical power; however, it introduces a body-scale device, which may be too bulky for some mobile applications.

The solid flat-form antenna on the printed circuit boards is not expected to be the bottleneck in applications because many methods are available for flexibly allowing a magnetic dipole antenna to achieve reasonable power transfer efficiency. Several breakout board modules for NFC readers (e.g., Grove NFC readers ⁵) provide an interface for the users to hook up a custom antenna. Nonetheless, for a module that has no such interface, such as the MFRC522 reader board that we used in this study, antenna modification can be achieved by first cutting the existing circuit trace at both ends of the on-board capacitors, then connecting a low-impedance coil inductor of similar inductance to both ends of the capacitors, and finally experimenting with antenna designs using Equation 1 and an NFC tag.

In this section, we present two examples of custom antennas: 1) a wearable antenna to support mobile applications and embodied interaction and 2) a non-planar antenna to improve the reliability of detecting a tag-embedded marble, which is a 6-DoF object that cannot be monitored with a planar coil when its tilt angle is θ > θ^*.

Wearable Reader Antenna for Always-Available Input. Figure 18 a shows a finger-worn NFC reader antenna, which was made of a two-turn 20 mm (W) × 18 mm (H) coil using AWG30 wire. This thin-form antenna had a sensing range of ∼ 2cm for the T4 tag, allowing a user to wear it on their finger as a part of a ring or a skin patch. Figures 18 b and  18 c show a user wearing this antenna to detect the rotation speed and direction of the white spinner. Without being constrained by the location of a fixed NFC reader antenna, users can freely use the spinner in a mobile context and even perform a larger range of bodily inputs, such as blowing on the wing to make the spinning more rapid [33]. These new types of embodied interactions can be captured through the speed pattern, enriched by an additional display on the smartwatch or smartphone, and used as an intervention, in, for example, stress management [33].

Multi-Coil, Non-Planar Reader Antenna for Sensing Tag-Embedded Marbles. Figure 19 a shows a 1 × 3 two-turn 4-cm-diameter round antenna array made of AWG24 single-core wire. Each coil unit had a sensing range of ∼ 3cm for the T0 tag, which we embedded at the center of the 25-mm-diameter marble. The antenna array was deployed on the track. To capture the tag-embedded marble, the middle of the three coils was pointed toward the x axis as the side antenna, whereas the other two faced the z axis (the surface normal of the track) as the bottom antenna. A tag that was in the activation area of any coil could trigger a read. Figures 19 b and 19 c show that the marble movement was captured once by the side antenna when the tag was tilted θ = 90° and was captured twice by the bottom antenna when the tag was tilted θ = 0°. Therefore, the speed of the bottom antenna was calculated using the algorithm III (Figure 11) to approximate the speed at the location of the side antenna calculated by the algorithm I.

Because calculations of speed are less precise for the rolling spheres than for the sliding object, more coil units may be required in the array for statistical estimates of a more precise speed value. Nonetheless, the non-planar antenna design allows designers to use simple hardware to enable fluent interaction experiences for such a spherical form [25].