RF-Dial:An RFID-based 2D Human-Computer Interaction via Tag Array Yanling Buf,Lei Xief,Yinyin Gongf,Chuyu Wangt,Lei Yang,Jia Liuf and Sanglu Lut fState Key Laboratory for Novel Software Technology,Nanjing University,China Department of Computing,The Hong Kong Polytechnic University,Hong Kong yanling @smail.nju.edu.cn,Ixie@nju.edu.cn,[yygong,wangcyu217}@dislab.nju.edu.cn, young@tagsys.org,{jialiu,sanglu@nju.edu.cn Abstract-Nowadays,the demand for novel approaches of 2D Movement Daily Objects human-computer interaction has enabled the emergence of a Decomposition RFID Antennas number of intelligent devices,such as Microsoft Surface Dial. 1.Rotation Surface Dial realizes 2D interactions with the computer via simple clicks and rotations.In this paper,we propose RF-Dial,a battery- Trajectory Tag Array free solution for 2D human-computer interaction based on RFID 2.Translation tag arrays.We attach an array of RFID tags on the surface of an object,and continuously track the translation and rotation of the tagged object with an orthogonally deployed RFID antenna pair.In this way,we are able to transform an ordinary object like a board eraser into an intelligent HCI device.According Fig.1.An example application scenario of RF-Dial to the RF-signals from the tag array,we build a geometric by the viewing angle and light condition.Sensor-based meth- model to depict the relationship between the phase variations odsusually use the commercial-off-the-shelf (COTS)sensors of the tag array and the rigid transformation of the tagged such as the infrared sensors or inertial sensors to track the object,including the translation and rotation.By referring to movement of the HCI device.The key limitation of sensor- the fixed topology of the tag array,we are able to accurately based schemes is that the sensors usually suffer from the extract the translation and rotation of the tagged object during the moving process.Moreover,considering the variation of phase limited battery life and high cost of hardwares.Fortunately, contours of the RF-signals at different positions,we divide the the battery-free sensing from RFID [2-16]has brought new overall scanning area into the linear region and non-linear region opportunities to design novel HCI schemes.Therefore,accord- in regard to the relationship between the phase variation and ing to these considerations,in this paper,we aim to answer the tag movement,and propose tracking solutions for the two regions,respectively.We implemented a prototype system and the following question by leveraging the RFID technology:"Is evaluated the performance of RF-Dial in the real environment. it possible to design a light-weight and battery-free scheme of The experiments show that RF-Dial achieved an average accuracy 2D human-computer interaction,such that even an ordinary of 0.6cm in the translation tracking,and an average accuracy of object can be simply turned into an intelligent HCI device?" 1.9 in the rotation tracking. In this paper,we propose RF-Dial,a battery-free solution I.INTRODUCTION for 2D human-computer interaction based on RFID tag ar- rays.We attach an array of RFlD tags to the surface of an 2D human-computer interaction (HCD)has always been object,and continuously track the rigid transformation of the a mainstream approach for the human to interact with the tagged object,including the translation and rotation,with computer,such as the mouse and touch screen.People use an orthogonally deployed RFID antenna pair,as shown in these devices to perform the operations such as moving and Fig.1.In this way,we are able to transform an ordinary object stroking in the 2D plane,so that the objects in the computer like a board eraser into an intelligent HCI device.According can be easily accessed and manipulated.As the rising of novel to the RF-signals from the tag array,we build a geometric applications such as the computer aided art design,the demand model to depict the relationship between the phase variations for brand-new approaches of 2D human-computer interaction of the tag array and the rigid transformation of the tagged has enabled the emergence of a number of intelligent devices, object.By referring to the fixed topology of the tag array, such as Microsoft Surface Dial [1].Surface Dial realizes 2D we are able to accurately extract the translation and rotation interactions with the computer via simple clicks and rotations. of the tagged object for each snapshot during the moving It provides a more natural and friendly approach of the human- process.Moreover,considering the variation of phase contours computer interaction with more functionalities. of the RF-signals at different positions,we divide the overall The state-of-the-art HCI solutions are mainly based on scanning area into the linear region and non-linear region computer vision or sensor-based approaches.Computer vision- in regard to the relationship between the phase variation and based approachesusually use the camera to capture the lim-the tag movement,and propose tracking solutions for the two b/finger movement and perform activity recognition or track-regions,respectively. ing based on vision technologies.The key limitation of There are two key challenges to address in this paper. camera-based schemes is that they are more or less affected The first challenge is to estimate the rigid transformation
RF-Dial: An RFID-based 2D Human-Computer Interaction via Tag Array Yanling Bu† , Lei Xie† , Yinyin Gong† , Chuyu Wang† , Lei Yang‡ , Jia Liu† and Sanglu Lu† †State Key Laboratory for Novel Software Technology, Nanjing University, China ‡Department of Computing, The Hong Kong Polytechnic University, Hong Kong yanling@smail.nju.edu.cn, lxie@nju.edu.cn, {yygong, wangcyu217}@dislab.nju.edu.cn, young@tagsys.org, {jialiu, sanglu}@nju.edu.cn Abstract—Nowadays, the demand for novel approaches of 2D human-computer interaction has enabled the emergence of a number of intelligent devices, such as Microsoft Surface Dial. Surface Dial realizes 2D interactions with the computer via simple clicks and rotations. In this paper, we propose RF-Dial, a batteryfree solution for 2D human-computer interaction based on RFID tag arrays. We attach an array of RFID tags on the surface of an object, and continuously track the translation and rotation of the tagged object with an orthogonally deployed RFID antenna pair. In this way, we are able to transform an ordinary object like a board eraser into an intelligent HCI device. According to the RF-signals from the tag array, we build a geometric model to depict the relationship between the phase variations of the tag array and the rigid transformation of the tagged object, including the translation and rotation. By referring to the fixed topology of the tag array, we are able to accurately extract the translation and rotation of the tagged object during the moving process. Moreover, considering the variation of phase contours of the RF-signals at different positions, we divide the overall scanning area into the linear region and non-linear region in regard to the relationship between the phase variation and the tag movement, and propose tracking solutions for the two regions, respectively. We implemented a prototype system and evaluated the performance of RF-Dial in the real environment. The experiments show that RF-Dial achieved an average accuracy of 0.6cm in the translation tracking, and an average accuracy of 1.9 ◦ in the rotation tracking. I. INTRODUCTION 2D human-computer interaction (HCI) has always been a mainstream approach for the human to interact with the computer, such as the mouse and touch screen. People use these devices to perform the operations such as moving and stroking in the 2D plane, so that the objects in the computer can be easily accessed and manipulated. As the rising of novel applications such as the computer aided art design, the demand for brand-new approaches of 2D human-computer interaction has enabled the emergence of a number of intelligent devices, such as Microsoft Surface Dial [1]. Surface Dial realizes 2D interactions with the computer via simple clicks and rotations. It provides a more natural and friendly approach of the humancomputer interaction with more functionalities. The state-of-the-art HCI solutions are mainly based on computer vision or sensor-based approaches. Computer visionbased approachesusually use the camera to capture the limb/finger movement and perform activity recognition or tracking based on vision technologies. The key limitation of camera-based schemes is that they are more or less affected Daily Objects RFID Antennas Trajectory Tag Array Tag Array 1. Rotation 2. Translation Movement Decomposition Fig. 1. An example application scenario of RF-Dial by the viewing angle and light condition. Sensor-based methodsusually use the commercial-off-the-shelf (COTS) sensors such as the infrared sensors or inertial sensors to track the movement of the HCI device. The key limitation of sensorbased schemes is that the sensors usually suffer from the limited battery life and high cost of hardwares. Fortunately, the battery-free sensing from RFID [2–16] has brought new opportunities to design novel HCI schemes. Therefore, according to these considerations, in this paper, we aim to answer the following question by leveraging the RFID technology: “Is it possible to design a light-weight and battery-free scheme of 2D human-computer interaction, such that even an ordinary object can be simply turned into an intelligent HCI device?”. In this paper, we propose RF-Dial, a battery-free solution for 2D human-computer interaction based on RFID tag arrays. We attach an array of RFID tags to the surface of an object, and continuously track the rigid transformation of the tagged object, including the translation and rotation, with an orthogonally deployed RFID antenna pair, as shown in Fig.1. In this way, we are able to transform an ordinary object like a board eraser into an intelligent HCI device. According to the RF-signals from the tag array, we build a geometric model to depict the relationship between the phase variations of the tag array and the rigid transformation of the tagged object. By referring to the fixed topology of the tag array, we are able to accurately extract the translation and rotation of the tagged object for each snapshot during the moving process. Moreover, considering the variation of phase contours of the RF-signals at different positions, we divide the overall scanning area into the linear region and non-linear region in regard to the relationship between the phase variation and the tag movement, and propose tracking solutions for the two regions, respectively. There are two key challenges to address in this paper. The first challenge is to estimate the rigid transformation
of the tagged object,including the translation and rotation, However,most approaches figure out the absolute positions of according to the phase variations from the tag array.To address tags in a separate manner,whereas RF-Dial aims to track the this challenge,we build a geometric model to depict the movement of the tag array in a comprehensive manner.By relationship between the phase variations of the tag array referring to the fixed topology of tag array,RF-Dial is able to and the rigid body motion of the tagged object.Specifically, accurately track the rigid transformation of the tagged object. we investigate the relationship between the corresponding tag RFID-based Motion Tracking:Prior RFID-based motion movement and the rigid transformation of the tagged object, tracking systems propose various approaches for the trajectory including translation and rotation,respectively.By referring to tracking [7-12]and orientation tracking [13,14].Representa- the fixed topology of the tag array,we are able to accurately tive work such as RF-IDraw [9]and PolarDraw [10]use a decompose and extract the translation and rotation of the single tag to reconstruct the handwriting by tracking the tag tagged object for each snapshot during the moving process, movement,which regard the tagged object as a mass point for by leveraging the RF-signals from at least two RFID tags. the motion tracking.Further,recent work such as Pantomime The second challenge is to tackle the variation of phase [11,Tagyro [14],and Tagball [15]use the tag array to track contours at different positions of the effective scanning area. the trajectory or orientation of the moving object.Specifically, Our empirical study shows that the phase contours in the Pantomime [11]enables the accurate trajectory tracking of the effective scanning area of the antenna are close to concentric tagged object with a tag array,using a multiple tag single circles with the antenna at the center.Thus,for the rigid antenna system.Tagyro [14]realizes the 3D orientation track- transformation of the tagged object,the antenna might detect ing with an array of RFID tags,by converting the real-time different phase variations at different positions,even if the phase offsets between tags into the orientation angle.However, object is performing the same movement.To address this these approaches track either the trajectory or the orientation challenge,we divide the overall scanning area into the linear of the moving object,without detecting the translation and region and non-linear region in regard to the relationship rotation of the tagged object simultaneously.Tagball [15]is the between the phase variation and the tag movement.Specif- closest work to RF-Dial.which studies the motion behavior. ically,for the linear region,the tag movement is linear to including the translation and rotation,of a ball attached with a the phase variation of the RF-signal,thus we directly derive tag array.However,Tagball solves the problem by the absolute the tag movement according to the phase variations detected localization on multiple tags.Specifically,it first estimates from two orthogonal antennas;for the non-linear region,we the absolute positions of multiple tags via the phase values, propose a solution to first locate the tag,and then derive the and then figure out the translation and rotation of the tagged tag movement from the phase variations according to the phase object based on the estimated positions of tags.Hence,the contours at the tag's position. localization errors are further introduced to the estimation We make three key contributions in this paper.First,we of the translation and rotation.Therefore,it requires plenty propose a novel scheme of 2D human-computer interaction,by of tags,i.e.,12 tags in total,to provide enough data to the attaching a tag array on the the surface of an ordinary object, Extended Kalman Filter-based tracking model to guarantee thus turning it into an intelligent HCI device.Second,to track the tracking accuracy.In comparison,in this paper,RF-Dial the rigid transformation including translation and rotation,we tracks the rigid transformation,i.e.,the translation and rotation, build a geometric model to depict the relationship between the of the tagged objects simultaneously,by directly referring to phase variations of the tag array and the rigid transformation phase variations from at least two tags,thus it achieves more of the tagged object.By referring to the fixed topology of at accuracy in the translation/rotation tracking least two tags from the tag array,we are able to accurately estimate the 2D rigid body motion of the object.Third,we III.EMPIRICAL STUDY implemented a prototype system of RF-Dial with COTS RFID In RFID systems.the RF phase is a common attribute of the and evaluated its performance in the real environment.The wireless signal,ranging from 0 to 2m.It is very sensitive to experiments show that RF-Dial achieved an average accuracy the tag-antenna distance.Suppose the distance between the tag of 0.6cm in the translation tracking,and an average accuracy and the antenna is d,so the signal traverses a distance of 2d of 1.9 in the rotation tracking. in the backscatter communication.Then,the phase provided by the antenna can be expressed as: II.RELATED WORK RFID-based Localization:A straightforward solution for ×2d+4 m0d2π (1) RFID-based human-computer interaction is to use the RFID localization schemes to absolutely locate the tagged objects where A is the wavelength,u represents the phase offset caused [2-6].State-of-the-art systems use phase values for accurate by the diversity of hardware characteristics localizations [2-5].PinIt [2]uses the multi-path profiles of tags to accurately locate tags with the synthetic aperture radar A.Phase Contour created via the antenna motion.Rather than the absolute According to the phase expression in Eq.(1),besides the localization,STPP [5]is the first work to tackle 2D relative diversity term,the phase value mainly depends on the distance localization,which uses the spatial-temporal dynamics in between the tag and the antenna.Therefore,the phase contours the phase profiles to identify the relative positions of tags. should form concentric circles with the antenna at the center in
of the tagged object, including the translation and rotation, according to the phase variations from the tag array. To address this challenge, we build a geometric model to depict the relationship between the phase variations of the tag array and the rigid body motion of the tagged object. Specifically, we investigate the relationship between the corresponding tag movement and the rigid transformation of the tagged object, including translation and rotation, respectively. By referring to the fixed topology of the tag array, we are able to accurately decompose and extract the translation and rotation of the tagged object for each snapshot during the moving process, by leveraging the RF-signals from at least two RFID tags. The second challenge is to tackle the variation of phase contours at different positions of the effective scanning area. Our empirical study shows that the phase contours in the effective scanning area of the antenna are close to concentric circles with the antenna at the center. Thus, for the rigid transformation of the tagged object, the antenna might detect different phase variations at different positions, even if the object is performing the same movement. To address this challenge, we divide the overall scanning area into the linear region and non-linear region in regard to the relationship between the phase variation and the tag movement. Specifically, for the linear region, the tag movement is linear to the phase variation of the RF-signal, thus we directly derive the tag movement according to the phase variations detected from two orthogonal antennas; for the non-linear region, we propose a solution to first locate the tag, and then derive the tag movement from the phase variations according to the phase contours at the tag’s position. We make three key contributions in this paper. First, we propose a novel scheme of 2D human-computer interaction, by attaching a tag array on the the surface of an ordinary object, thus turning it into an intelligent HCI device. Second, to track the rigid transformation including translation and rotation, we build a geometric model to depict the relationship between the phase variations of the tag array and the rigid transformation of the tagged object. By referring to the fixed topology of at least two tags from the tag array, we are able to accurately estimate the 2D rigid body motion of the object. Third, we implemented a prototype system of RF-Dial with COTS RFID and evaluated its performance in the real environment. The experiments show that RF-Dial achieved an average accuracy of 0.6cm in the translation tracking, and an average accuracy of 1.9 ◦ in the rotation tracking. II. RELATED WORK RFID-based Localization: A straightforward solution for RFID-based human-computer interaction is to use the RFID localization schemes to absolutely locate the tagged objects [2–6]. State-of-the-art systems use phase values for accurate localizations [2–5]. PinIt [2] uses the multi-path profiles of tags to accurately locate tags with the synthetic aperture radar created via the antenna motion. Rather than the absolute localization, STPP [5] is the first work to tackle 2D relative localization, which uses the spatial-temporal dynamics in the phase profiles to identify the relative positions of tags. However, most approaches figure out the absolute positions of tags in a separate manner, whereas RF-Dial aims to track the movement of the tag array in a comprehensive manner. By referring to the fixed topology of tag array, RF-Dial is able to accurately track the rigid transformation of the tagged object. RFID-based Motion Tracking: Prior RFID-based motion tracking systems propose various approaches for the trajectory tracking [7–12] and orientation tracking [13, 14]. Representative work such as RF-IDraw [9] and PolarDraw [10] use a single tag to reconstruct the handwriting by tracking the tag movement, which regard the tagged object as a mass point for the motion tracking. Further, recent work such as Pantomime [11], Tagyro [14], and Tagball [15] use the tag array to track the trajectory or orientation of the moving object. Specifically, Pantomime [11] enables the accurate trajectory tracking of the tagged object with a tag array, using a multiple tag single antenna system. Tagyro [14] realizes the 3D orientation tracking with an array of RFID tags, by converting the real-time phase offsets between tags into the orientation angle. However, these approaches track either the trajectory or the orientation of the moving object, without detecting the translation and rotation of the tagged object simultaneously. Tagball [15] is the closest work to RF-Dial, which studies the motion behavior, including the translation and rotation, of a ball attached with a tag array. However, Tagball solves the problem by the absolute localization on multiple tags. Specifically, it first estimates the absolute positions of multiple tags via the phase values, and then figure out the translation and rotation of the tagged object based on the estimated positions of tags. Hence, the localization errors are further introduced to the estimation of the translation and rotation. Therefore, it requires plenty of tags, i.e., 12 tags in total, to provide enough data to the Extended Kalman Filter-based tracking model to guarantee the tracking accuracy. In comparison, in this paper, RF-Dial tracks the rigid transformation, i.e., the translation and rotation, of the tagged objects simultaneously, by directly referring to phase variations from at least two tags, thus it achieves more accuracy in the translation/rotation tracking. III. EMPIRICAL STUDY In RFID systems, the RF phase is a common attribute of the wireless signal, ranging from 0 to 2π. It is very sensitive to the tag-antenna distance. Suppose the distance between the tag and the antenna is d, so the signal traverses a distance of 2d in the backscatter communication. Then, the phase provided by the antenna can be expressed as: θ = 2π λ × 2d + µ mod 2π, (1) where λ is the wavelength, µ represents the phase offset caused by the diversity of hardware characteristics. A. Phase Contour According to the phase expression in Eq.(1), besides the diversity term, the phase value mainly depends on the distance between the tag and the antenna. Therefore, the phase contours should form concentric circles with the antenna at the center in
Central Beam Region Linear Region 0.6×0.6m 11.5 Non-linear Region X Ay Fig.3.The effective scanning area:the linear region vs non-linear region -100 -60 -40 04060 80 100 Fig.2.Phase contours of the RF-signals an ideal situation.We thus conduct an experiment to validate the above hypothesis.We build a 2D coordinate system according to the parallel direction (X-axis)and perpendicular direction (Y-axis)of the antenna,and set the origin (0,0) at the center of the antenna.Then,we collect the phase values in a rectangle space in front of the antenna,ranging 0 X O →X from -100cm to 100cm along the X-axis and from 100cm Fig.4.Rigid transformation in the Fig.5.The relationship between the to 180cm along the Y-axis.The collected phase values are continuous moving process tag movement and the phase variation plotted in Fig.2.Based on the experiment results,we have the rotates around a rotation center,and the translation means a following observation: linear movement that every point of the device moves with Observation 1:The phase contours are very close to the same displacement.As the continuous movement of an concentric circles with the antenna at the center.Besides,in object consists of a series of instant movements at different the central beam region ranging from -30cm to 30cm along time,we denote the instant movement as the micro-movement, the X-axis and from 100cm to 180cm along the Y-axis,which each micro-movement can be expressed with the rotation and is marked with the blue rectangle in Fig.2,the phase contours translation.Thus,we can use the rigid transformation to depict are almost parallel to each other and stretching along the X- the micro-movement. axis.That is to say,in the central beam region of the antenna, By attaching a tag array on the surface of an object,it is the phase values can be regarded as linearly related to the possible to detect the rigid transformation according to the perpendicular distance from the tag to the antenna plane. movement of each tag in the tag array.Note that,different B.Linear Region and Non-linear Region from the rigid body,ie..the tagged object,the tag attached Assume that two antennas A and Au are deployed in a on the object actually represents a single point of the object, mutually orthogonal manner and separated with a fairly large so its movement can be regarded as the particle movement, distance,as shown in Fig.3.Then,according to Observation which only has the translation rather than the rotation.E.g., /in the intersection area of the central beams of the two assume an object is attached with a tag array with the layout antennas,the displacement of a tag along the X-axis and of rectangle,as shown in Fig.4,the tags are denoted as Y-axis should be linear to the phase variations received by solid points on the rectangle.For any micro-movement in the antenna Ar and Ay,respectively.We thus denote this the continuous movement,it can be intuitively observed that, intersection region as the linear region.According to our the rigid transformation of the tagged object,including the empirical study,the linear region is usually of size 0.6x0.6m2. translation and rotation,can be derived from the movement of Apart from the linear region,the phase variations in the other different tags scanning area do not follow the above linear relationship with B.Tag Movement and Phase Variation the corresponding displacement any more,we thus denote the According to the empirical study,the phase contours can be other area as the non-linear region.For the non-linear region, depicted as concentric circles with the antenna at the center. the phase variations are not linear to the displacements along Thus,we can build a polar coordinate system by setting the either the X-axis or Y-axis,the actual relationship depends center of the antenna as the origin.Then,given a tag movement on the exact position of the tag. s,we can further depict the relationship between the phase IV.MODELING THE RIGID TRANSFORMATION OF variation and the movement s in this polar coordinate system As shown in Fig.5,the antenna is deployed at position A,we TRANSLATION AND ROTATION use the vector s to denote the tag movement,the starting point A.Rigid Transformation of s is P.Besides,we use the vector I to denote the polar axis During the continuous movement of an object,its position AP,and use y to denote the angle between s and 1.Thus,if and orientation are changing all the time.For a rigid body, we use Ad to denote the projection of s on the polar axis 1, such change of the position and orientation in the 2D space then△d=Isll cos?. can be defined by the rigid transformation R,S,where R Note that,for any tag movement in the micro-movement, is a 2 x 2 rotation matrix and S is a 2 x 1 translation matrix. its moving distance should be smaller than half-wavelength, Here,the rotation means a circular movement that the device i.e.,lsll≤≥≈l6.4cm.According to Eq.(1,by offsetting
−100 −80 −60 −40 −20 0 20 40 60 80 100 100 120 140 160 180 1 2 3 4 5 6 Central Beam Region Fig. 2. Phase contours of the RF-signals an ideal situation. We thus conduct an experiment to validate the above hypothesis. We build a 2D coordinate system according to the parallel direction (X-axis) and perpendicular direction (Y -axis) of the antenna, and set the origin (0, 0) at the center of the antenna. Then, we collect the phase values in a rectangle space in front of the antenna, ranging from −100cm to 100cm along the X-axis and from 100cm to 180cm along the Y -axis. The collected phase values are plotted in Fig.2. Based on the experiment results, we have the following observation: Observation 1: The phase contours are very close to concentric circles with the antenna at the center. Besides, in the central beam region ranging from −30cm to 30cm along the X-axis and from 100cm to 180cm along the Y -axis, which is marked with the blue rectangle in Fig.2, the phase contours are almost parallel to each other and stretching along the Xaxis. That is to say, in the central beam region of the antenna, the phase values can be regarded as linearly related to the perpendicular distance from the tag to the antenna plane. B. Linear Region and Non-linear Region Assume that two antennas Ax and Ay are deployed in a mutually orthogonal manner and separated with a fairly large distance, as shown in Fig.3. Then, according to Observation 1, in the intersection area of the central beams of the two antennas, the displacement of a tag along the X-axis and Y -axis should be linear to the phase variations received by the antenna Ax and Ay, respectively. We thus denote this intersection region as the linear region. According to our empirical study, the linear region is usually of size 0.6×0.6m2 . Apart from the linear region, the phase variations in the other scanning area do not follow the above linear relationship with the corresponding displacement any more, we thus denote the other area as the non-linear region. For the non-linear region, the phase variations are not linear to the displacements along either the X-axis or Y -axis, the actual relationship depends on the exact position of the tag. IV. MODELING THE RIGID TRANSFORMATION OF TRANSLATION AND ROTATION A. Rigid Transformation During the continuous movement of an object, its position and orientation are changing all the time. For a rigid body, such change of the position and orientation in the 2D space can be defined by the rigid transformation R, S , where R is a 2 × 2 rotation matrix and S is a 2 × 1 translation matrix. Here, the rotation means a circular movement that the device ܺ ܻ ܣ௫ Linear Region 1~1.ͷ݉ 1~1.ͷ݉ 0.6 × 0.6݉ଶ Non-linear Region ௬ܣ ܱ Fig. 3. The effective scanning area: the linear region vs non-linear region ܺ ܻ Trajectory ܱ ܣ ܲ ܛ ܔ ߛ ݀߂ ܺ ܻ ܱ Fig. 4. Rigid transformation in the continuous moving process ܺ ܻ ܣ ܲ ܛ ܔ ߛ ݀߂ ܱ ܣ ܲ ܛ ܔ ߛ ݀߂ ܺ ܻ ܱ Fig. 5. The relationship between the tag movement and the phase variation rotates around a rotation center, and the translation means a linear movement that every point of the device moves with the same displacement. As the continuous movement of an object consists of a series of instant movements at different time, we denote the instant movement as the micro-movement, each micro-movement can be expressed with the rotation and translation. Thus, we can use the rigid transformation to depict the micro-movement. By attaching a tag array on the surface of an object, it is possible to detect the rigid transformation according to the movement of each tag in the tag array. Note that, different from the rigid body, i.e., the tagged object, the tag attached on the object actually represents a single point of the object, so its movement can be regarded as the particle movement, which only has the translation rather than the rotation. E.g., assume an object is attached with a tag array with the layout of rectangle, as shown in Fig.4, the tags are denoted as solid points on the rectangle. For any micro-movement in the continuous movement, it can be intuitively observed that, the rigid transformation of the tagged object, including the translation and rotation, can be derived from the movement of different tags. B. Tag Movement and Phase Variation According to the empirical study, the phase contours can be depicted as concentric circles with the antenna at the center. Thus, we can build a polar coordinate system by setting the center of the antenna as the origin. Then, given a tag movement s, we can further depict the relationship between the phase variation and the movement s in this polar coordinate system. As shown in Fig.5, the antenna is deployed at position A, we use the vector s to denote the tag movement, the starting point of s is P. Besides, we use the vector l to denote the polar axis AP, and use γ to denote the angle between s and l. Thus, if we use ∆d to denote the projection of s on the polar axis l, then ∆d = ksk cos γ. Note that, for any tag movement in the micro-movement, its moving distance should be smaller than half-wavelength, i.e., ksk ≤ λ 2 ≈ 16.4cm. According to Eq.(1), by offsetting
Pe oPa (a)Translation (b)Rotation (c)Translation with rotation Fig.6.Micro-movement decomposition the constant diversity term,the phase variation A caused by C.Rigid Transformation Decomposition s is as follows: As aforementioned,during the continuous moving process △0= 2T×2△d 2T×2 scosT- (2)of the rigid body.the micro-movement can be defined by the rigid transformation including the rotation and translation. Meanwhile,as 1.s=llsl cos,according to Eq.(2). Meanwhile,the tag movement can be regarded as the particle 1 movement only with the translation.Therefore,we investigate 阿s 4T (3)the relationship between the tag movement and the rigid transformation of the tagged object,i.e.,translation,rotation Note that,is a normalized vector of 1,it depends on the and translation with rotation,respectively. position ofp relative to A.Assume s=(△z,△y,而= 1)Translation:The translation means a linear movement (,y),then,according to Eq.(3), that every point of the device moves with the same displace- x1△x+l△y= 0. ment.Suppose a rigid body is attached with a tag array T, when the center of the rigid body translates from position (4) x+7=1. Ps to position Pe,each tag Ti in the tag array has the same translation Then,to compute the tag movement s=(△z,△y)）according (=[)Let and be the coordinates of tag Ti when the rigid body is at position to the phase variations,we investigate their relationships in P and P,respectively,then: the linear region and non-linear region,respectively. 1)Tag Movement in the Linear Region:In the linear Ti,e Ti,s +S. (7) region,the phase variations detected from the two orthogonally Vi.e Vi.s deployed antennas are linear to the tag's moving distances Fig.6(a)shows an example of the translation when the rigid along the two orthogonal axes,respectively.E.g.,as shown body is attached with a rectangle tag array. in Fig.3,antenna A detects the phase variation of the tag 2)Rotation:The rotation means a circular movement that movement along the X-axis,whereas antenna Ay detects the phase variations of the tag movement along the Y-axis.Let the device rotates around a rotation center.Suppose a rigid body is attached with a tag array T.when the rigid body Ar and A0y be the phase variations from antenna A and Ay, rotates around a rotation center Pa by the angle of o,all respectively,so the tag movement s is computed as follows: the tags should have the same rotation angle.Specifically,let △x 「△0 andT be the coordinates of tag T when 六△， (5) the rigid body starts rotation and ends rotation,respectively, 2)Tag Movement in the Non-linear Region:In the non- let (a,ya)be the coordinates of rotation center P,then linear region,since the corresponding phase variations are Ti,e-Ta 工i,s-a not linear to the tag movement,we need to figure out their =R (8) yi,e-Ya yi,s-Ya relationship according to the geometric property.Given the phase variations A and A0y respectively collected from the -sin a where R is a rotation matrix two orthogonally deployed antennas A and Ay,according to sin a cosa representing Eg.(4),we have: the counter-clockwise rotation of angle a.Fig.6(b)shows an example of the rotation when the rigid body is attached with 2△x十功△y= a rectangle tag array. 4π (6) 3)Translation with Rotation:According to the definition 9y x,△x+功，△y=4 of the rigid transformation,any arbitrary rigid body motion can be decomposed into the combination of the rotation and where (and denote the normalized vector translation.Suppose a rigid body is attached with a tag array for the polar axis AP from the antenna A and Au.respec- T,when the center of the rigid body translates from the tively.Therefore,as long as the starting position of movement position P to the position Pe,the rigid body also rotates s,i.e,P,is known,the values of (L)and ()can around a local rotation center Pa by the angle of a,the be figured out.Then,by solving the linear equations in Eq.(6), local rotation center has the same translation as the rigid we can directly compute[△x,△f. body as well.Without loss of generality,we can model the
௬ݏ ܲ௦ ܲ ௫ݏ ܺ ܻ ܱ (a) Translation ܺ ܻ ܲ ܲ௦ ߙ ܲ ܱ (b) Rotation ܲ ௬ݏ ௫ݏ ܲ௦(ܲ) ߙ ܺ ܻ ܱ (c) Translation with rotation Fig. 6. Micro-movement decomposition the constant diversity term, the phase variation ∆θ caused by s is as follows: ∆θ = 2π λ × 2∆d = 2π λ × 2 ksk cos γ. (2) Meanwhile, as l · s = klk · ksk cos γ, according to Eq.(2), l klk · s = λ 4π ∆θ. (3) Note that, l klk is a normalized vector of l, it depends on the position of P relative to A. Assume s = h∆x, ∆yi, l klk = hxl , yli, then, according to Eq.(3), xl∆x + yl∆y = λ 4π ∆θ, x 2 l + y 2 l = 1. (4) Then, to compute the tag movement s = h∆x, ∆yi according to the phase variations, we investigate their relationships in the linear region and non-linear region, respectively. 1) Tag Movement in the Linear Region: In the linear region, the phase variations detected from the two orthogonally deployed antennas are linear to the tag’s moving distances along the two orthogonal axes, respectively. E.g., as shown in Fig.3, antenna Ax detects the phase variation of the tag movement along the X-axis, whereas antenna Ay detects the phase variations of the tag movement along the Y -axis. Let ∆θx and ∆θy be the phase variations from antenna Ax and Ay, respectively, so the tag movement s is computed as follows: ∆x ∆y = λ 4π ∆θx λ 4π ∆θy . (5) 2) Tag Movement in the Non-linear Region: In the nonlinear region, since the corresponding phase variations are not linear to the tag movement, we need to figure out their relationship according to the geometric property. Given the phase variations ∆θx and ∆θy respectively collected from the two orthogonally deployed antennas Ax and Ay, according to Eq.(4), we have: xlx∆x + ylx∆y = λ 4π ∆θx, xly∆x + yly∆y = λ 4π ∆θy, (6) where hxlx , ylx i and xly , yly denote the normalized vector for the polar axis AP from the antenna Ax and Ay, respectively. Therefore, as long as the starting position of movement s , i.e, P, is known, the values of hxlx , ylx i and xly , yly can be figured out. Then, by solving the linear equations in Eq.(6), we can directly compute [∆x, ∆y] T . C. Rigid Transformation Decomposition As aforementioned, during the continuous moving process of the rigid body, the micro-movement can be defined by the rigid transformation including the rotation and translation. Meanwhile, the tag movement can be regarded as the particle movement only with the translation. Therefore, we investigate the relationship between the tag movement and the rigid transformation of the tagged object, i.e., translation, rotation and translation with rotation, respectively. 1) Translation: The translation means a linear movement that every point of the device moves with the same displacement. Suppose a rigid body is attached with a tag array T, when the center of the rigid body translates from position Ps to position Pe, each tag Ti in the tag array has the same translation S = sx, sy T . Let [xi,s, yi,s] T and [xi,e, yi,e] T be the coordinates of tag Ti when the rigid body is at position Ps and Pe, respectively, then: xi,e yi,e = xi,s yi,s + S. (7) Fig.6(a) shows an example of the translation when the rigid body is attached with a rectangle tag array. 2) Rotation: The rotation means a circular movement that the device rotates around a rotation center. Suppose a rigid body is attached with a tag array T, when the rigid body rotates around a rotation center Pa by the angle of α, all the tags should have the same rotation angle. Specifically, let [xi,s, yi,s] T and [xi,e, yi,e] T be the coordinates of tag Ti when the rigid body starts rotation and ends rotation, respectively, let (xa, ya) be the coordinates of rotation center Pa, then xi,e − xa yi,e − ya = R xi,s − xa yi,s − ya , (8) where R is a rotation matrix cos α − sin α sin α cos α , representing the counter-clockwise rotation of angle α. Fig.6(b) shows an example of the rotation when the rigid body is attached with a rectangle tag array. 3) Translation with Rotation: According to the definition of the rigid transformation, any arbitrary rigid body motion can be decomposed into the combination of the rotation and translation. Suppose a rigid body is attached with a tag array T, when the center of the rigid body translates from the position Ps to the position Pe, the rigid body also rotates around a local rotation center Pa by the angle of α, the local rotation center has the same translation as the rigid body as well. Without loss of generality, we can model the
process of the rigid body motion into two successive steps Data Preprocessing RF-signals one after the other,i.e.,performing the rotation first and then Data Segmentation Initial State Estimation the translation.Specifically,the rigid body first rotates around Pa by the angle of o,then it translates from position Ps to Movement Tracking position P.According to Eq(7)and Eq.(8).letT Tag Movement Rigid Transformation Derivation and [T be the coordinates of tag T when the rigid Tracking body starts moving and ends moving,respectively,let(a,ya) Movement Calibration be the coordinates of local rotation center Pa when the rigid Outlier Detection Outlier Elimination [RS] body starts moving,then: Fig.7.System framework Ti,e -Fa=Ri-a +S. (9) diversity term in Eg.(1),each tag has its own phase offset, Vi,e-Va yi,s-Va so we measure the diversity term among tags in advance According to Eq.(9).the movement of tag Ti.e.[AAy and eliminate the tag diversity by offsetting the diversity term.Further,we utilize the Kalman Filter to filter the cor- can be decomposed into the following components: responding noises in the phase values.After that,suppose △xl Ti,e -Ti,s 工i,s-a there are n tags in the tag array,we segment the phases of (10) △y =(R-I) +S yi,e -Vi.s Vi,s-ya n tags from the two antennas into m snapshots,denoted as Θ1,1Θ1,2… 日1，m where I is an identity matrix.Fig.6(c)shows an example of the moving process of the translation with rotation,when the rigid whereθi,j=(0x,i,0y,i》 日n,1曰n.2… body is attached with a rectangle tag array.Such rigid body 日n,m」 means the phase values of tag Ti in the jth snapshot,0.i.j motion is equivalent to first rotating around Pa with angle o, and y.ii represent the phase values from antenna A and Ay. i.e.,from the green array to the blue one,then translating from respectively.The time interval At for each snapshot is usually P.to Pe,i.e.,from the blue array to the yellow one. set to a small value,e.g,At =200ms in our implementation. V.SYSTEM DESIGN 2)Initial State Estimation:According to Eq.(10),to com- A.Overview pute the rigid transformation R,S,it is essential to deter- The basic idea of RF-Dial is to track the rigid transfor- mine the initial state of the rigid body first.E.g.,the matrix mation,i.e.,the rotation and translation,of the tagged object T= Ti,s-Ta in Eq.(10)depends on the relative positions according to phase variations of the tag array received by yi.s-Ya the orthogonal deployed RFID antenna pair.Fig.7 shows the of tags in the tag array,i.e.,the topology and rotation state of system framework,which includes the following components: the tag array.Hence,since the rotation state of the tag array 1)Data Preprocessing:After receiving the RF-signals from depends on both initial and subsequent rotation angles of the the tag array,we extract the series of phase values for each tag array,we need to estimate the initial rotation angle first. tag from the two antennas and segment them into the phase Without loss of generality,we use the rectangle tag array value for each snapshot.Then,we estimate the initial state of as an example to illustrate our method to compute the initial the tagged objects,including the rotation state and the rough rotation angle for the tag array.As shown in Fig.8,we set the position.2)Movement Tracking:We derive the tag movement rotation center Pa at the center of the rectangle,and set two according to the phase variations,respectively,according to the orthogonal polar axes l and lu according to the X and Y-axis situations of the linear region and vast region(including both in the global coordinate system.Each tag can be regarded as the linear region and non-linear region).Further,we estimate a particle point in the coordinate system,e.g.,T~T.The the rigid transformation of the tagged object,including the ro- initial rotation angle of the tag array,i.e..the angle between tation and translation.3)Movement Calibration:We detect the Ir and PaTi,is B. outliers of the phase values from the tag array,by comparing Topology Matrix T.According to the rotation angle B,we the estimated movement of each single tag with the estimated can depict the matrix T= Ti,s -Ta 头，s-a for each tag Ti.E.g., movement of the tag array.Then,we eliminate the outlier(s) for the rectangle tag array in Fig.8,let TTll =T2T3 =h, and re-estimate the rigid transformation of the tagged object ITT2l=T3T4‖l=w,‖PaTl=l,LTiPaT2=n, with the remaining tags for calibration. these parameters can be regarded as constants,as long as B.Data Preprocessing the topology of the tag array is fixed.Then,according to the 1)Data Segmentation:Due to the issues such as the multi- relative positions of the tags in the rectangle tag array, path effect and ambient noises,the measured phase values may contain some fluctuations in the waveforms.Hence,after [F1-ta:y-ya]T [l cos B,Isin B]T, receiving the RF-signals from the tag array,we extract the [2-za:v2-ya]T [cos(B+n),lsin (8+n)]T, (11) series of phase values for each tag from the two antennas, [z3-za,y3-Va]T=[-l cos(B),-Isin (B)T, and calibrate the phase values first.Specifically,due to the operation of mod in Eq.(1),the measured phase values are [4-za:y4-ya]=[-l cos(B+n),-lsin (B+n)] discontinuous.Thus,we stitch the phase values and remove As aforementioned in Section 4.2,the distances between tag the periodicity among the phase values.Besides,due to the pairs are linear/non-linear to the phase differences between tag
process of the rigid body motion into two successive steps one after the other, i.e., performing the rotation first and then the translation. Specifically, the rigid body first rotates around Pa by the angle of α, then it translates from position Ps to position Pe. According to Eq.(7) and Eq.(8), let [xi,s, yi,s] T and [xi,e, yi,e] T be the coordinates of tag Ti when the rigid body starts moving and ends moving, respectively, let (xa, ya) be the coordinates of local rotation center Pa when the rigid body starts moving, then: xi,e − xa yi,e − ya = R xi,s − xa yi,s − ya + S. (9) According to Eq.(9), the movement of tag Ti , i.e. [∆xi , ∆yi ] T , can be decomposed into the following components: ∆xi ∆yi = xi,e − xi,s yi,e − yi,s = (R − I) xi,s − xa yi,s − ya + S, (10) where I is an identity matrix. Fig.6(c) shows an example of the moving process of the translation with rotation, when the rigid body is attached with a rectangle tag array. Such rigid body motion is equivalent to first rotating around Pa with angle α, i.e., from the green array to the blue one, then translating from Ps to Pe, i.e., from the blue array to the yellow one. V. SYSTEM DESIGN A. Overview The basic idea of RF-Dial is to track the rigid transformation, i.e., the rotation and translation, of the tagged object according to phase variations of the tag array received by the orthogonal deployed RFID antenna pair. Fig.7 shows the system framework, which includes the following components: 1) Data Preprocessing: After receiving the RF-signals from the tag array, we extract the series of phase values for each tag from the two antennas and segment them into the phase value for each snapshot. Then, we estimate the initial state of the tagged objects, including the rotation state and the rough position. 2) Movement Tracking: We derive the tag movement according to the phase variations, respectively, according to the situations of the linear region and vast region (including both the linear region and non-linear region). Further, we estimate the rigid transformation of the tagged object, including the rotation and translation. 3) Movement Calibration: We detect the outliers of the phase values from the tag array, by comparing the estimated movement of each single tag with the estimated movement of the tag array. Then, we eliminate the outlier(s) and re-estimate the rigid transformation of the tagged object with the remaining tags for calibration. B. Data Preprocessing 1) Data Segmentation: Due to the issues such as the multipath effect and ambient noises, the measured phase values may contain some fluctuations in the waveforms. Hence, after receiving the RF-signals from the tag array, we extract the series of phase values for each tag from the two antennas, and calibrate the phase values first. Specifically, due to the operation of mod in Eq.(1), the measured phase values are discontinuous. Thus, we stitch the phase values and remove the periodicity among the phase values. Besides, due to the Data Preprocessing Movement Tracking Movement Calibration Outlier Detection Outlier Elimination Tag Movement Derivation Rigid Transformation Tracking Data Segmentation Initial State Estimation RF-signals ܜ܀] [ܜ܁ , Fig. 7. System framework diversity term in Eq.(1), each tag has its own phase offset, so we measure the diversity term among tags in advance and eliminate the tag diversity by offsetting the diversity term. Further, we utilize the Kalman Filter to filter the corresponding noises in the phase values. After that, suppose there are n tags in the tag array, we segment the phases of n tags from the two antennas into m snapshots, denoted as Θ = Θ1,1 Θ1,2 · · · Θ1,m · · · · · · · · · · · · Θn,1 Θn,2 · · · Θn,m , where Θi,j = hθx,i,j , θy,i,j i means the phase values of tag Ti in the jth snapshot, θx,i,j and θy,i,j represent the phase values from antenna Ax and Ay, respectively. The time interval ∆t for each snapshot is usually set to a small value, e.g, ∆t = 200ms in our implementation. 2) Initial State Estimation: According to Eq.(10), to compute the rigid transformation R, S , it is essential to determine the initial state of the rigid body first. E.g., the matrix T = xi,s − xa yi,s − ya in Eq.(10) depends on the relative positions of tags in the tag array, i.e., the topology and rotation state of the tag array. Hence, since the rotation state of the tag array depends on both initial and subsequent rotation angles of the tag array, we need to estimate the initial rotation angle first. Without loss of generality, we use the rectangle tag array as an example to illustrate our method to compute the initial rotation angle for the tag array. As shown in Fig.8, we set the rotation center Pa at the center of the rectangle, and set two orthogonal polar axes lx and ly according to the X and Y -axis in the global coordinate system. Each tag can be regarded as a particle point in the coordinate system, e.g., T1 ∼ T4. The initial rotation angle of the tag array, i.e., the angle between lx and PaT1, is β. Topology Matrix T. According to the rotation angle β, we can depict the matrix T = xi,s − xa yi,s − ya for each tag Ti . E.g., for the rectangle tag array in Fig.8, let kT1T4k = kT2T3k = h, kT1T2k = kT3T4k = w, kPaTik = l, 6 T1PaT2 = η, these parameters can be regarded as constants, as long as the topology of the tag array is fixed. Then, according to the relative positions of the tags in the rectangle tag array, [x1 − xa, y1 − ya] T = [l cos β, lsin β] T , [x2 − xa, y2 − ya] T = [l cos (β + η), lsin (β + η)]T , [x3 − xa, y3 − ya] T = [−l cos (β), −lsin (β)]T , [x4 − xa, y4 − ya] T = [−l cos (β + η), −lsin (β + η)]T . (11) As aforementioned in Section 4.2, the distances between tag pairs are linear/non-linear to the phase differences between tag