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Remote monitoring of human hand motion using induced electrostatic signals
Journal of Electrostatics 69 (2011) 571e577
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Remote monitoring of human hand motion using induced electrostatic signals Wei Zheng a, *, Zhan-zhong Cui a, Zhi Zheng b, Yan Zhang a a b
State Key Lab of Mechatronics Engineering and Control, Beijing Institute of Technology, Beijing 100081, PR China School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350108, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 May 2011 Received in revised form 28 June 2011 Accepted 26 July 2011 Available online 11 August 2011
In this paper, the electrostatic detection equation of moving hand is proposed based on Gauss’ Law and electric field superposition theorem, and experimental results match the theoretical calculation well, which confirms that we can monitor hand motion under non-contact condition effectively. Then we develop an effective non-contact, passive and low cost technique using induced electrostatic signals measurement for determination of the velocity and direction of human hand motion based on the variation tendency in the electric field strength between moving hand and electrodes, which doesn’t require complex data processing even in an open unshielded environment close to sources of power line interference and resistance noise generated by computer and electric iron respectively. Experimental results confirm that hand gesture can be recognized by non-contact electrostatic detection by adopting multiple electrodes array. Ó 2011 Elsevier B.V. All rights reserved.
Keywords: Remote monitoring Electrostatic induction current Hand motion
1. Introduction In this decade, with the rapid development of information technology, increasing interests have been attracted to the field of human motion analysis, the information extracted from which can be used for the purpose of improving the efficiency and comfort of industry applications such as human machine interface, security protection and medical monitoring [1]. Most examples of traditional human motion gesture recognize techniques are based on image recognition method [2], wearable sensors network installation [3] and the fusion of these two techniques [4]. The vision based gesture recognition method with cameras has the advantages of passive sensing and non-attached deployment without discomforting human nor disturbing the normal motion gesture. However, this method is limited in its camera blind area and the complex logic algorithm for image processing to exclude interference caused by varying lighting conditions and cluttered backgrounds. Although adopting wearable sensors can avoid the shortcomings mentioned above, the limitation of requiring attachment of sensors makes it constrained in many situations. The current research focus is on the combination of these techniques, while by contrast, we investigate other suitable method for human motion monitoring with the characteristics of simple and non-
* Corresponding author. Tel.: þ86 13811564898; fax: þ86 01068918503. E-mail address: [email protected] (W. Zheng). 0304-3886/$ e see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2011.07.011
contact deployment, passive detection and low complexity for signal processing, which is electrostatic detection. As moving human bodies will be charged by static electricity in the form of contact and friction charging [5], electrostatic detection technology utilizes the induced charges to achieve the purpose of human motion recognition. Early work concerning electrostatic detection of living creatures was carried out to study the electrification by walking of creeping insects [6]. Inspired by this work, human body potential characters during walking were studied through the electrometer mounted on the object [7,8]. Further improvements of this technique were achieved by adopting noncontact method to achieve the remote sensing of human stepping movement [9e11]. Meanwhile, a set of research achievements on measuring the electrophysiological signals by placing electrodes near the surface of human body based on capacitive coupling method has been reported [12e17], comparing with results obtained by conventional methods such as electrocardiography, the signals of induced electrostatic measurements have the similar waveform characteristics, which confirms its effectiveness in remote sensing of human motion. Although non-contact electrostatic detection has attracted more attention from researchers, there is still lack of relevant research results on monitoring of hand motion revealed until recently [18]. However, the authors focused on qualitative analysis of human hand motion and discussing the moving trend of hand motion without further mathematical quantitative investigation. So in this study, we present a physical model for moving human hand detection, which is based on the measurement of induced electrostatic signals generated by the
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Fig. 3. Simulation results when the hand is moving along the routes with different included angle to electrodes.
Fig. 1. Schematic diagram of the human capacitance.
variation of electric field strength to implement the quantitative analysis of hand motion, and propose a new effective, non-contact, passive and simple construction technique for tracking human hand. 2. Analysis of induced electrostatic signals generated by human hand motion
Q ¼ QB fCr1 ðUB VÞ:
Human capacitance is composed of coupling capacitance Cf between two feet and the floor and the capacitance of the rest of human body Cri (i ¼ 1,2,.) relative to nearby objects on floor. Therefore, the human capacitance can be expressed as the sum of Cf and Cri in parallel:
CB ¼ Cf þ
N X
Cri ;
(1)
i¼1
in which Cf ¼ Cfl þ Cfl ¼ 23 eSe/de, 3 e, Se and de stand for permittivity, area and thickness of shoes sole separately. Schematic diagram of the human capacitance is illustrated in Fig. 1. As human body is a good conductor, we assume the equivalent capacitance between body and electrode is Cr1, then the potential of standing body UB can be expressed as equation (2).
UB ¼ QB = Cf þ Cr1 þ
N X
! Cri ;
i¼2
Fig. 2. Schematic of the interaction between hand and electrode.
where QB is the instantaneous charge on the human body. Assuming that the potential of electrode is V, the equivalent capacitance between body and electrode is Cr1, while the equivalent capacitances between human body and other objects in the environment are expressed as Cri (i ¼ 2,3,.), then the amount of induced charge on electrode can be expressed as:
(2)
(3)
Based on the theories of electrodynamics [19], the capacitance value between electrodes is proportional to the equivalent area 3 hS, permittivity 3 a between them, while inversely proportional to distance dp between two electrodes in their initial positions. So when the person is moving hand perpendicularly to the electrode plane, the capacitance between body and electrode can be determined by: 3a3hS ; Cr1 ¼ dp Dx
(4)
in which Dx is the motion distance in the region between hand and electrode, which is set as the negative value when hand moves away from electrode while becomes positive when hand move toward the electrode. Moreover, the parameter 3 h is inversely proportional to the horizontal distance between hand and electrode that, it is set as 1 when the horizontal distance is 0 between hand and electrode. Then the induced potential on electrode when hand moves vertically to the electrode plane can be obtained by the following equation:
Fig. 4. Schematic diagram of measurement system for measuring the velocity and direction of human hand motion.
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
573
point charges and the electric field generated by the target is composed of the ones generated by numerous point electric charges [24], so we assume that the induced electrostatic signal brought by hand motion is equal to that produced by moving point charge. In Fig. 2, S stands for the charged point target, the horizontal distance and vertical distance between the center of electrode O 0 and S are x and y respectively. Moreover, O is the projection of O on the route of hand motion. Assuming that the quantity of charge on hand is Q, then the normal component of electric field in the position of O is expressed by the following equation [25]:
En ¼
Q cos v : 4p3 0 x2 þ y2
(6)
According to the geometrical relationship in Fig. 2, v can be obtained by:
Fig. 5. Relationship among projection of movement route and electrodes.
v ¼ 90 ð4 þ qÞ:
(7)
Then
dQ dC 3a3hS U ¼ RI ¼ R fRUB r1 fRUB 2 v; dt dt dp Dx
(5)
in which R is the equivalent resistance value of measurement system, and v is the velocity of hand motion. According to equation (5), the induced electrostatic potentials should be determined by effective equivalence area between electrodes, velocity and distance of hand motion as well as the polarity of body electric potential. So it is feasible to recognize the status of hand motion based on the induced electrostatic potentials by analyzing variations of capacitance between body and electrode when the hand is moving perpendicularly to the electrode plane. During the hand motion when moving parallel to the electrode, as the hand is not right against the electrode to form the typical parallel-plate capacitor, the equivalent capacitance can hardly be obtained quantitatively due to the complicated geometry relationship [20e23]. So by analyzing the variation tendency in electric field strength, we study the characteristics of induced electrostatic signals generated by the hand motion parallel to the electrodes. Fig. 2 illustrates the geometrical relationship among the angles of intersection q, v and 4, while q is the angle between human hand motion direction and the plane where electrode is located, v is the angle between the electric field direction and normal direction of electrode surface and 4 represents the angle of intersection between the connection line of hand and electrode surface and the moving route. When the distance between target and electrode is larger than target’s dimension, the charged target can be regarded as a set of
h i cos v ¼ cos 90 ð4 þ qÞ ¼ sin 4 cos q þ cos 4 sin q;
(8)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi in which sin 4 ¼ y= x2 þ y2 , cos 4 ¼ x= x2 þ y2 . By substituting equation (8) into equation (6), we can get
En ¼
Q 3 4p3 0 x2 þ y2 2
ðy cos q þ x sin qÞ:
(9)
In order to simplify the analysis, we focus on the situation that the hand is moving along a straight line approximately. During the period of movement, the electric field strength En varies with different horizontal distance x and vertical distance y. Then we can have the following expression of induced electrostatic current in the form of the change rate of electric field strength [5]:
2 6 6 d6 4
3
7 7 ðy cos q þ x sin qÞ7 3 5 4p x2 þ y2 2 dQE dEn dx i¼ ¼ 30 ¼ dx dt dt dt Q sin q y2 2x2 3xy cos q dx ¼ : 5 4p dt x2 þ y 2 2 Q
0
(10)
If O is set as the origin point of coordinates, the horizontal distance of moving hand can be expressed as:
Fig. 6. Waveforms on electrodes generated during the hand motion perpendicularly to electrodes.
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W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
Fig. 7. Waveforms of induced electrostatic signals generated on electrode when hand was moving at different speeds (a) and in the regions with different distance vertically to the electrode (b).
x ¼ d0 þ vt;
(11)
in which d0 stands for the initial position of human hand and v is the horizontal component of human hand motion velocity. While t 0 represents the time scale, and its values on left side area of O are set to be negative ones. According to equation (11):
dx ¼ v: dt
(12)
By substituting the above expression to equation (10) we can obtain the electrostatic detection equation of human hand motion in the form of induced electrostatic current:
Q v sin q y2 2x2 3xy cos q i ¼ : 5 4p 2 2 x þy 2
(13)
The simulation waveforms obtained when the angle q between human hand motion and the electrodes array plane varies from 0 to 90 are illustrated in Fig. 3. During the simulation, charge amount of hand Q, moving velocity of human hand v and vertical distance y between hand and electrodes array plane are set as 104 C, 2 m/s and 0.2 m separately. According to the simulation results in Fig. 3, it is clear that when q is set as 0 and 90 , the moment when hand is moving pass the nearest position in its motion route between itself and electrode occurs when the waveform is crossing the zero value and
Fig. 8. Induced electrostatic signals generated on 4 electrodes when hand was moving at the direction of 60 .
Fig. 9. Waveforms of induced electrostatic signals on electrodes 1, 3 when hand was moving from down to up at slow speed (a) and from up to down at high speed (b) at the direction of 60 .
reaching the negative peak value respectively. Due to this obvious signal waveform feature, the moment when hand is nearest to electrode can be obtained precisely.
3. Experiment deployment for the hand motion recognition Non-contact human body detection system based on quasielectrostatic field designed in this paper is composed by 4 detection units, D.C. stabilized source and high-speed A/D converter, which is LeCroy WaveRunner 6000A Oscilloscope. The detection unit includes electrode, charge amplifier circuit, IeV converter circuit, notch filter circuit and low pass filter circuit. The analog induced electrostatic signals collected by electrodes are stored in storage space of A/D converter. This detection system has the advantage of simple design. During the experiment, the researcher was wearing cotton T-shirt, shoes with soft rubber sole and jeans standing on marble floor. The temperature and humidity of experiment environment were around 25 C and 40% respectively. Fig. 4 shows a schematic representation of the measurement system for analyzing the status of hand motion based on noncontact electrostatic detection technique. The geometric center of electrodes array is fixed 1.5 m above the floor, and the distance d between centers of the opposite electrodes is 0.5 m.
Fig. 10. Boxplot of measured direction of hand motion.
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
As the waveform of induced electrostatic signal obtained when the hand is moving along the route with the angle q of 90 is similar to the one generated when hand is implementing perpendicular motion toward electrode, which will cause misjudgment for obtaining the moment when hand is closest to electrode. Moreover, under the circumstance that human hand is charged with large amount of electric charge or the moving velocity is too fast, it is common for electrodes to be charged by the induced electrostatic signals over the measurable range of signal process circuit, which will cause the part of signal waveform near peak value be cut off and leads to the failure of negative peak value judgment. So during
575
the verification experiment, we keep moving hands parallel to the electrodes array plane, which means the angle q is set as 0 . Geometric relationship between the projection of human hand movement trajectory on the electrodes array plane and the electrodes is illustrated in Fig. 5. As shown in Fig. 5, O1, O2, O3, O4 are the geometric centers of electrodes 1, 2, 3, 4. The distances between O1, O3 and O2, O4 are both set as d. The electrodes array plane is divided into 4 regions by straight lines O1 O3 and O2 O4 as depicted in Fig. 5. 0 Moreover, O is the geometric centers of electrodes array while O is the point of intersection between the movement route and O2 O4 . O01 ; O02 ; O03 ; O04 are projections of O1, O2, O3, O4 on the movement
Fig. 11. Flow chart of humanecomputer interface system based on remote electrostatic signals measurement.
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W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
route, which means the hand is closest to the corresponding electrodes in these positions separately. According to the former discussion, the induced electrostatic signal waves on electrodes should cross zero in these moments. The angle of intersection a between movement route O02 O01 O0 O03 O04 and O2 O4 is exact the direction of hand motion we want to obtain. ! It’s clear in Fig. 5(b) that jO02 O04 j ¼ d$cos a. Assuming the cross zero moment of induced electrostatic signals on electrodes 2, 4 are tzero2 and tzero4 respectively, then the velocity of hand can be calculated by:
v ¼
d cos a : tzero4 tzero2
(14)
Similarly, the velocity can also be expressed based on the waveform characteristics of signals on electrodes 1, 3 by:
v ¼
d sin a : tzero3 tzero1
(15)
By solving equations (14) and (15) simultaneously, we can obtain the following detection equation for the direction and velocity of human hand motion:
8 tzero3 tzero1 > > a ¼ arctg > < tzero4 tzero2 : d > q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ > > : 2 2 ðtzero3 tzero1 Þ þðtzero4 tzero2 Þ
(16)
In order to verify the effectiveness of non-contact electrostatic detection technique on hand motion monitoring, the hand was moving along different straight lines parallel to the multiple electrodes array plane back and forth repeatedly. During the experiment, we put tips of our fingers together and kept the finger tips pointing to the electrodes plane with the vertical distance of 40 cm between them. 4. Experimental results and discussion Waveforms of induced electrostatic signals on electrodes when hand was moving forth and back perpendicularly to the electrodes array plane are illustrated in Fig. 6, in which the signals in regions I, II, III and IV were generated when hands moved forth and back vertically to electrodes 1, 2, 3 and 4 with the horizontal distance of 0 separately. According to experimental results in Fig. 6, it is obvious that the equivalent area 3 hS between hand and electrode in equation (5), which is decided by the horizontal distance between hand and electrode, determines the amplitude of induced electrostatic signals during the vertical motion to electrodes. Experimental results of hand motion with different velocity in different motion regions are depicted in Fig. 7, from which we can conclude that equation (5) effectively describes the characteristics of the induced electrostatic signals due to the hand motion when people are moving their hands perpendicularly to the electrode. Furthermore, we adopt a group of data generated from electrodes array when hand was moving back and forward along the same route parallel to the electrodes array plane to analysis the accuracy of direction and velocity determination based on induced electrostatic signal measurement. During the experiment, the direction of hand motion was fixed at 60 , and the speed of forward movement was around 3 times than that of back movement. The experiment result is shown in Fig. 8. Signal waveforms obtained on electrodes 1, 3 are illustrated in Fig. 9, from which it is obvious that experiment result shows good agreement with the theoretical analysis in equation (13) for the waveform of induced electrostatic signals generated by hand
motion. According to detection equation (16), the measurement results of moving direction and velocity of hand illustrated in Fig. 9(a) and (b) are ama ¼ 67.3 , vma ¼ 2.86 m/s and amb ¼ 66.9 , vmb ¼ 7.73 m/s respectively. The measurement results match the real situation well, in which the real direction and velocity of hand motion are ar z 60 and vr2 z 3vr1 z7.5 m/s. Furthermore, it is clear that the amplitude of peak value of waveform obtained from electrode 1 is obviously higher than the ones from other electrodes, by which we can conclude that the vertical distance between moving route and electrode 1 was closer than other electrodes. Based on this conclusion, by comparing the signals on different electrodes, we can determine the location of hand motion route in the three dimensional space which will be our future work. Experimental results obtained when hand was moving along different directions parallel to the electrodes array plane at various speeds agree with the real situation, and this experiment has the high repeatability which proves that the moving direction and velocity can be measured effectively by the method of non-contact electrostatic detection based on multiple electrodes array. Due to the characteristic of symmetry of 4 electrodes array, we only list the experimental results obtained when hand was moving along routes with the direction angle between 0 and 90 in Fig. 10, which is within the Region I illustrated in Fig. 5. From experimental results shown in Fig. 10, it is obvious that the non-contact electrostatic detection technique is effective in monitoring the direction of human hand motion. The minor errors exist in the experimental results compared to real situation is probably caused by the slight vibrations of hand when moving parallel to the electrodes array plane. According to the theoretical analysis and experimental results mentioned above, a new humanecomputer interface system based on the electrostatic signals measurements can be implemented as in Fig. 11: 5. Conclusion By measuring the induced electrostatic signals, we proposed an effective non-contact technique for monitoring the hand motion. A principle for the electrostatic induced current flowing through electrode due to the variation in electrostatic field strength generated by the relative movement between hand and electrode has been described. Furthermore, we prove that by comparing differences of signals on electrodes with spatial variability, it is possible to obtain the accurate velocity and direction of hand motion using non-contact electrostatic detection technique. We believe that this technique opens up a new area of remote biometric measurements which can be applied in the field of human machine interface, health care and security. References [1] S. Mitra, T. Acharya, IEEE Trans. Syst. Man Cybern. C Appl. Rev. 37 (2007) 311. [2] M. Vincze, M. Zillich, W. Ponweiser, V. Hlavac, J. Matas, S. Obdrzalek, H. Buxton, J. Howell, K. Sage, A. Argyros, C. Ebert, G. Umgeher, Comput. Vis. Image Und. 113 (2009) 682. [3] J. Liu, Z. Pan, X. Li, ComSIS 7 (2010) 177. [4] J. Cheng, C. Xie, W. Bian, D. Tao, Feature fusion for 3D hand gesture recognition by learning a shared hidden space, Pattern Recognition Lett. (2011), doi:10. 1016/j.patrec.2010.12.009. [5] C. Jean, Electrostatics: Principles, Problems and Applications. Adam Higher, Bristol, 1987, pp.16e17. [6] D.F. McGonigle, C.W. Jackson, J.L. Davidon, J. Electrostat. 54 (2002) 167. [7] T. Ficker, J. Phys. D: Appl. Phys. 39 (2006) 410. [8] T. Ficker, J. Electrostat. 64 (2006) 10. [9] K. Takiguchi, T. Wada, S. Toyama, J. Adv. Mech. Design Syst. Manuf. 1 (2007) 294. [10] K. Takiguchi, T. Wada, S. Toyama, J. Adv. Mech. Design Syst. Manuf. 2 (2008) 429. [11] K. Kurita, IEEE Trans. Electr. Electr. 4 (2009) 309.
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577 [12] C.J. Harland, T.D. Clark, R.J. Prance, Appl. Phys. Lett. 81 (2002) 3284. [13] C.J. Harland, T.D. Clark, N.S. Peters, M.J. Everitt, P.B. Stiffel, Physiol. Meas. 26 (2005) 939. [14] W. Gebrial, R.J. Prance, C.J. Harland, T.D. Clark, Rev. Sci. Instrum. 77 (2006) 063708. [15] R.J. Prance, S.T. Beardsome-Rust, P. Watson, C.J. Harland, H. Prance, Appl. Phys. Lett. 93 (2008) 033906. [16] K. Kurita, Rev. Sci. Instrum. 82 (2011) 026105. [17] K. Kurita, Measurement 44 (2011) 1361. [18] K. Kurita, S. Ueta, IEEE Trans. Ind. Appl. 47 (2011) 1022.
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[19] R.S. William, Static and Dynamic Electricity, third ed. Hemisphere Pub Co, New York, 1989, pp. 29. [20] Y. Xiang, J. Electrostat. 64 (2006) 29. [21] Y. Xiang, Commun. Nonlin. Sci. Numer. Simul. 12 (2007) 652. [22] Y. Xiang, J. Electrostat. 66 (2008) 366. [23] O. Marinov, M.J. Deen, J.A.J. Tejada, B. Iniguez, Org. Electron. 12 (2011) 936. [24] R.J. James, G. James, Mathematics Dictionary. Springer, Berlin, 1992, pp.139. [25] L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, fourth ed. Elsevier, Singapore, 2007, pp. 89.
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
Remote monitoring of human hand motion using induced electrostatic signals Wei Zheng a, *, Zhan-zhong Cui a, Zhi Zheng b, Yan Zhang a a b
State Key Lab of Mechatronics Engineering and Control, Beijing Institute of Technology, Beijing 100081, PR China School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350108, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 May 2011 Received in revised form 28 June 2011 Accepted 26 July 2011 Available online 11 August 2011
In this paper, the electrostatic detection equation of moving hand is proposed based on Gauss’ Law and electric field superposition theorem, and experimental results match the theoretical calculation well, which confirms that we can monitor hand motion under non-contact condition effectively. Then we develop an effective non-contact, passive and low cost technique using induced electrostatic signals measurement for determination of the velocity and direction of human hand motion based on the variation tendency in the electric field strength between moving hand and electrodes, which doesn’t require complex data processing even in an open unshielded environment close to sources of power line interference and resistance noise generated by computer and electric iron respectively. Experimental results confirm that hand gesture can be recognized by non-contact electrostatic detection by adopting multiple electrodes array. Ó 2011 Elsevier B.V. All rights reserved.
Keywords: Remote monitoring Electrostatic induction current Hand motion
1. Introduction In this decade, with the rapid development of information technology, increasing interests have been attracted to the field of human motion analysis, the information extracted from which can be used for the purpose of improving the efficiency and comfort of industry applications such as human machine interface, security protection and medical monitoring [1]. Most examples of traditional human motion gesture recognize techniques are based on image recognition method [2], wearable sensors network installation [3] and the fusion of these two techniques [4]. The vision based gesture recognition method with cameras has the advantages of passive sensing and non-attached deployment without discomforting human nor disturbing the normal motion gesture. However, this method is limited in its camera blind area and the complex logic algorithm for image processing to exclude interference caused by varying lighting conditions and cluttered backgrounds. Although adopting wearable sensors can avoid the shortcomings mentioned above, the limitation of requiring attachment of sensors makes it constrained in many situations. The current research focus is on the combination of these techniques, while by contrast, we investigate other suitable method for human motion monitoring with the characteristics of simple and non-
* Corresponding author. Tel.: þ86 13811564898; fax: þ86 01068918503. E-mail address: [email protected] (W. Zheng). 0304-3886/$ e see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2011.07.011
contact deployment, passive detection and low complexity for signal processing, which is electrostatic detection. As moving human bodies will be charged by static electricity in the form of contact and friction charging [5], electrostatic detection technology utilizes the induced charges to achieve the purpose of human motion recognition. Early work concerning electrostatic detection of living creatures was carried out to study the electrification by walking of creeping insects [6]. Inspired by this work, human body potential characters during walking were studied through the electrometer mounted on the object [7,8]. Further improvements of this technique were achieved by adopting noncontact method to achieve the remote sensing of human stepping movement [9e11]. Meanwhile, a set of research achievements on measuring the electrophysiological signals by placing electrodes near the surface of human body based on capacitive coupling method has been reported [12e17], comparing with results obtained by conventional methods such as electrocardiography, the signals of induced electrostatic measurements have the similar waveform characteristics, which confirms its effectiveness in remote sensing of human motion. Although non-contact electrostatic detection has attracted more attention from researchers, there is still lack of relevant research results on monitoring of hand motion revealed until recently [18]. However, the authors focused on qualitative analysis of human hand motion and discussing the moving trend of hand motion without further mathematical quantitative investigation. So in this study, we present a physical model for moving human hand detection, which is based on the measurement of induced electrostatic signals generated by the
572
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
Fig. 3. Simulation results when the hand is moving along the routes with different included angle to electrodes.
Fig. 1. Schematic diagram of the human capacitance.
variation of electric field strength to implement the quantitative analysis of hand motion, and propose a new effective, non-contact, passive and simple construction technique for tracking human hand. 2. Analysis of induced electrostatic signals generated by human hand motion
Q ¼ QB fCr1 ðUB VÞ:
Human capacitance is composed of coupling capacitance Cf between two feet and the floor and the capacitance of the rest of human body Cri (i ¼ 1,2,.) relative to nearby objects on floor. Therefore, the human capacitance can be expressed as the sum of Cf and Cri in parallel:
CB ¼ Cf þ
N X
Cri ;
(1)
i¼1
in which Cf ¼ Cfl þ Cfl ¼ 23 eSe/de, 3 e, Se and de stand for permittivity, area and thickness of shoes sole separately. Schematic diagram of the human capacitance is illustrated in Fig. 1. As human body is a good conductor, we assume the equivalent capacitance between body and electrode is Cr1, then the potential of standing body UB can be expressed as equation (2).
UB ¼ QB = Cf þ Cr1 þ
N X
! Cri ;
i¼2
Fig. 2. Schematic of the interaction between hand and electrode.
where QB is the instantaneous charge on the human body. Assuming that the potential of electrode is V, the equivalent capacitance between body and electrode is Cr1, while the equivalent capacitances between human body and other objects in the environment are expressed as Cri (i ¼ 2,3,.), then the amount of induced charge on electrode can be expressed as:
(2)
(3)
Based on the theories of electrodynamics [19], the capacitance value between electrodes is proportional to the equivalent area 3 hS, permittivity 3 a between them, while inversely proportional to distance dp between two electrodes in their initial positions. So when the person is moving hand perpendicularly to the electrode plane, the capacitance between body and electrode can be determined by: 3a3hS ; Cr1 ¼ dp Dx
(4)
in which Dx is the motion distance in the region between hand and electrode, which is set as the negative value when hand moves away from electrode while becomes positive when hand move toward the electrode. Moreover, the parameter 3 h is inversely proportional to the horizontal distance between hand and electrode that, it is set as 1 when the horizontal distance is 0 between hand and electrode. Then the induced potential on electrode when hand moves vertically to the electrode plane can be obtained by the following equation:
Fig. 4. Schematic diagram of measurement system for measuring the velocity and direction of human hand motion.
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
573
point charges and the electric field generated by the target is composed of the ones generated by numerous point electric charges [24], so we assume that the induced electrostatic signal brought by hand motion is equal to that produced by moving point charge. In Fig. 2, S stands for the charged point target, the horizontal distance and vertical distance between the center of electrode O 0 and S are x and y respectively. Moreover, O is the projection of O on the route of hand motion. Assuming that the quantity of charge on hand is Q, then the normal component of electric field in the position of O is expressed by the following equation [25]:
En ¼
Q cos v : 4p3 0 x2 þ y2
(6)
According to the geometrical relationship in Fig. 2, v can be obtained by:
Fig. 5. Relationship among projection of movement route and electrodes.
v ¼ 90 ð4 þ qÞ:
(7)
Then
dQ dC 3a3hS U ¼ RI ¼ R fRUB r1 fRUB 2 v; dt dt dp Dx
(5)
in which R is the equivalent resistance value of measurement system, and v is the velocity of hand motion. According to equation (5), the induced electrostatic potentials should be determined by effective equivalence area between electrodes, velocity and distance of hand motion as well as the polarity of body electric potential. So it is feasible to recognize the status of hand motion based on the induced electrostatic potentials by analyzing variations of capacitance between body and electrode when the hand is moving perpendicularly to the electrode plane. During the hand motion when moving parallel to the electrode, as the hand is not right against the electrode to form the typical parallel-plate capacitor, the equivalent capacitance can hardly be obtained quantitatively due to the complicated geometry relationship [20e23]. So by analyzing the variation tendency in electric field strength, we study the characteristics of induced electrostatic signals generated by the hand motion parallel to the electrodes. Fig. 2 illustrates the geometrical relationship among the angles of intersection q, v and 4, while q is the angle between human hand motion direction and the plane where electrode is located, v is the angle between the electric field direction and normal direction of electrode surface and 4 represents the angle of intersection between the connection line of hand and electrode surface and the moving route. When the distance between target and electrode is larger than target’s dimension, the charged target can be regarded as a set of
h i cos v ¼ cos 90 ð4 þ qÞ ¼ sin 4 cos q þ cos 4 sin q;
(8)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi in which sin 4 ¼ y= x2 þ y2 , cos 4 ¼ x= x2 þ y2 . By substituting equation (8) into equation (6), we can get
En ¼
Q 3 4p3 0 x2 þ y2 2
ðy cos q þ x sin qÞ:
(9)
In order to simplify the analysis, we focus on the situation that the hand is moving along a straight line approximately. During the period of movement, the electric field strength En varies with different horizontal distance x and vertical distance y. Then we can have the following expression of induced electrostatic current in the form of the change rate of electric field strength [5]:
2 6 6 d6 4
3
7 7 ðy cos q þ x sin qÞ7 3 5 4p x2 þ y2 2 dQE dEn dx i¼ ¼ 30 ¼ dx dt dt dt Q sin q y2 2x2 3xy cos q dx ¼ : 5 4p dt x2 þ y 2 2 Q
0
(10)
If O is set as the origin point of coordinates, the horizontal distance of moving hand can be expressed as:
Fig. 6. Waveforms on electrodes generated during the hand motion perpendicularly to electrodes.
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Fig. 7. Waveforms of induced electrostatic signals generated on electrode when hand was moving at different speeds (a) and in the regions with different distance vertically to the electrode (b).
x ¼ d0 þ vt;
(11)
in which d0 stands for the initial position of human hand and v is the horizontal component of human hand motion velocity. While t 0 represents the time scale, and its values on left side area of O are set to be negative ones. According to equation (11):
dx ¼ v: dt
(12)
By substituting the above expression to equation (10) we can obtain the electrostatic detection equation of human hand motion in the form of induced electrostatic current:
Q v sin q y2 2x2 3xy cos q i ¼ : 5 4p 2 2 x þy 2
(13)
The simulation waveforms obtained when the angle q between human hand motion and the electrodes array plane varies from 0 to 90 are illustrated in Fig. 3. During the simulation, charge amount of hand Q, moving velocity of human hand v and vertical distance y between hand and electrodes array plane are set as 104 C, 2 m/s and 0.2 m separately. According to the simulation results in Fig. 3, it is clear that when q is set as 0 and 90 , the moment when hand is moving pass the nearest position in its motion route between itself and electrode occurs when the waveform is crossing the zero value and
Fig. 8. Induced electrostatic signals generated on 4 electrodes when hand was moving at the direction of 60 .
Fig. 9. Waveforms of induced electrostatic signals on electrodes 1, 3 when hand was moving from down to up at slow speed (a) and from up to down at high speed (b) at the direction of 60 .
reaching the negative peak value respectively. Due to this obvious signal waveform feature, the moment when hand is nearest to electrode can be obtained precisely.
3. Experiment deployment for the hand motion recognition Non-contact human body detection system based on quasielectrostatic field designed in this paper is composed by 4 detection units, D.C. stabilized source and high-speed A/D converter, which is LeCroy WaveRunner 6000A Oscilloscope. The detection unit includes electrode, charge amplifier circuit, IeV converter circuit, notch filter circuit and low pass filter circuit. The analog induced electrostatic signals collected by electrodes are stored in storage space of A/D converter. This detection system has the advantage of simple design. During the experiment, the researcher was wearing cotton T-shirt, shoes with soft rubber sole and jeans standing on marble floor. The temperature and humidity of experiment environment were around 25 C and 40% respectively. Fig. 4 shows a schematic representation of the measurement system for analyzing the status of hand motion based on noncontact electrostatic detection technique. The geometric center of electrodes array is fixed 1.5 m above the floor, and the distance d between centers of the opposite electrodes is 0.5 m.
Fig. 10. Boxplot of measured direction of hand motion.
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577
As the waveform of induced electrostatic signal obtained when the hand is moving along the route with the angle q of 90 is similar to the one generated when hand is implementing perpendicular motion toward electrode, which will cause misjudgment for obtaining the moment when hand is closest to electrode. Moreover, under the circumstance that human hand is charged with large amount of electric charge or the moving velocity is too fast, it is common for electrodes to be charged by the induced electrostatic signals over the measurable range of signal process circuit, which will cause the part of signal waveform near peak value be cut off and leads to the failure of negative peak value judgment. So during
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the verification experiment, we keep moving hands parallel to the electrodes array plane, which means the angle q is set as 0 . Geometric relationship between the projection of human hand movement trajectory on the electrodes array plane and the electrodes is illustrated in Fig. 5. As shown in Fig. 5, O1, O2, O3, O4 are the geometric centers of electrodes 1, 2, 3, 4. The distances between O1, O3 and O2, O4 are both set as d. The electrodes array plane is divided into 4 regions by straight lines O1 O3 and O2 O4 as depicted in Fig. 5. 0 Moreover, O is the geometric centers of electrodes array while O is the point of intersection between the movement route and O2 O4 . O01 ; O02 ; O03 ; O04 are projections of O1, O2, O3, O4 on the movement
Fig. 11. Flow chart of humanecomputer interface system based on remote electrostatic signals measurement.
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route, which means the hand is closest to the corresponding electrodes in these positions separately. According to the former discussion, the induced electrostatic signal waves on electrodes should cross zero in these moments. The angle of intersection a between movement route O02 O01 O0 O03 O04 and O2 O4 is exact the direction of hand motion we want to obtain. ! It’s clear in Fig. 5(b) that jO02 O04 j ¼ d$cos a. Assuming the cross zero moment of induced electrostatic signals on electrodes 2, 4 are tzero2 and tzero4 respectively, then the velocity of hand can be calculated by:
v ¼
d cos a : tzero4 tzero2
(14)
Similarly, the velocity can also be expressed based on the waveform characteristics of signals on electrodes 1, 3 by:
v ¼
d sin a : tzero3 tzero1
(15)
By solving equations (14) and (15) simultaneously, we can obtain the following detection equation for the direction and velocity of human hand motion:
8 tzero3 tzero1 > > a ¼ arctg > < tzero4 tzero2 : d > q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ > > : 2 2 ðtzero3 tzero1 Þ þðtzero4 tzero2 Þ
(16)
In order to verify the effectiveness of non-contact electrostatic detection technique on hand motion monitoring, the hand was moving along different straight lines parallel to the multiple electrodes array plane back and forth repeatedly. During the experiment, we put tips of our fingers together and kept the finger tips pointing to the electrodes plane with the vertical distance of 40 cm between them. 4. Experimental results and discussion Waveforms of induced electrostatic signals on electrodes when hand was moving forth and back perpendicularly to the electrodes array plane are illustrated in Fig. 6, in which the signals in regions I, II, III and IV were generated when hands moved forth and back vertically to electrodes 1, 2, 3 and 4 with the horizontal distance of 0 separately. According to experimental results in Fig. 6, it is obvious that the equivalent area 3 hS between hand and electrode in equation (5), which is decided by the horizontal distance between hand and electrode, determines the amplitude of induced electrostatic signals during the vertical motion to electrodes. Experimental results of hand motion with different velocity in different motion regions are depicted in Fig. 7, from which we can conclude that equation (5) effectively describes the characteristics of the induced electrostatic signals due to the hand motion when people are moving their hands perpendicularly to the electrode. Furthermore, we adopt a group of data generated from electrodes array when hand was moving back and forward along the same route parallel to the electrodes array plane to analysis the accuracy of direction and velocity determination based on induced electrostatic signal measurement. During the experiment, the direction of hand motion was fixed at 60 , and the speed of forward movement was around 3 times than that of back movement. The experiment result is shown in Fig. 8. Signal waveforms obtained on electrodes 1, 3 are illustrated in Fig. 9, from which it is obvious that experiment result shows good agreement with the theoretical analysis in equation (13) for the waveform of induced electrostatic signals generated by hand
motion. According to detection equation (16), the measurement results of moving direction and velocity of hand illustrated in Fig. 9(a) and (b) are ama ¼ 67.3 , vma ¼ 2.86 m/s and amb ¼ 66.9 , vmb ¼ 7.73 m/s respectively. The measurement results match the real situation well, in which the real direction and velocity of hand motion are ar z 60 and vr2 z 3vr1 z7.5 m/s. Furthermore, it is clear that the amplitude of peak value of waveform obtained from electrode 1 is obviously higher than the ones from other electrodes, by which we can conclude that the vertical distance between moving route and electrode 1 was closer than other electrodes. Based on this conclusion, by comparing the signals on different electrodes, we can determine the location of hand motion route in the three dimensional space which will be our future work. Experimental results obtained when hand was moving along different directions parallel to the electrodes array plane at various speeds agree with the real situation, and this experiment has the high repeatability which proves that the moving direction and velocity can be measured effectively by the method of non-contact electrostatic detection based on multiple electrodes array. Due to the characteristic of symmetry of 4 electrodes array, we only list the experimental results obtained when hand was moving along routes with the direction angle between 0 and 90 in Fig. 10, which is within the Region I illustrated in Fig. 5. From experimental results shown in Fig. 10, it is obvious that the non-contact electrostatic detection technique is effective in monitoring the direction of human hand motion. The minor errors exist in the experimental results compared to real situation is probably caused by the slight vibrations of hand when moving parallel to the electrodes array plane. According to the theoretical analysis and experimental results mentioned above, a new humanecomputer interface system based on the electrostatic signals measurements can be implemented as in Fig. 11: 5. Conclusion By measuring the induced electrostatic signals, we proposed an effective non-contact technique for monitoring the hand motion. A principle for the electrostatic induced current flowing through electrode due to the variation in electrostatic field strength generated by the relative movement between hand and electrode has been described. Furthermore, we prove that by comparing differences of signals on electrodes with spatial variability, it is possible to obtain the accurate velocity and direction of hand motion using non-contact electrostatic detection technique. We believe that this technique opens up a new area of remote biometric measurements which can be applied in the field of human machine interface, health care and security. References [1] S. Mitra, T. Acharya, IEEE Trans. Syst. Man Cybern. C Appl. Rev. 37 (2007) 311. [2] M. Vincze, M. Zillich, W. Ponweiser, V. Hlavac, J. Matas, S. Obdrzalek, H. Buxton, J. Howell, K. Sage, A. Argyros, C. Ebert, G. Umgeher, Comput. Vis. Image Und. 113 (2009) 682. [3] J. Liu, Z. Pan, X. Li, ComSIS 7 (2010) 177. [4] J. Cheng, C. Xie, W. Bian, D. Tao, Feature fusion for 3D hand gesture recognition by learning a shared hidden space, Pattern Recognition Lett. (2011), doi:10. 1016/j.patrec.2010.12.009. [5] C. Jean, Electrostatics: Principles, Problems and Applications. Adam Higher, Bristol, 1987, pp.16e17. [6] D.F. McGonigle, C.W. Jackson, J.L. Davidon, J. Electrostat. 54 (2002) 167. [7] T. Ficker, J. Phys. D: Appl. Phys. 39 (2006) 410. [8] T. Ficker, J. Electrostat. 64 (2006) 10. [9] K. Takiguchi, T. Wada, S. Toyama, J. Adv. Mech. Design Syst. Manuf. 1 (2007) 294. [10] K. Takiguchi, T. Wada, S. Toyama, J. Adv. Mech. Design Syst. Manuf. 2 (2008) 429. [11] K. Kurita, IEEE Trans. Electr. Electr. 4 (2009) 309.
W. Zheng et al. / Journal of Electrostatics 69 (2011) 571e577 [12] C.J. Harland, T.D. Clark, R.J. Prance, Appl. Phys. Lett. 81 (2002) 3284. [13] C.J. Harland, T.D. Clark, N.S. Peters, M.J. Everitt, P.B. Stiffel, Physiol. Meas. 26 (2005) 939. [14] W. Gebrial, R.J. Prance, C.J. Harland, T.D. Clark, Rev. Sci. Instrum. 77 (2006) 063708. [15] R.J. Prance, S.T. Beardsome-Rust, P. Watson, C.J. Harland, H. Prance, Appl. Phys. Lett. 93 (2008) 033906. [16] K. Kurita, Rev. Sci. Instrum. 82 (2011) 026105. [17] K. Kurita, Measurement 44 (2011) 1361. [18] K. Kurita, S. Ueta, IEEE Trans. Ind. Appl. 47 (2011) 1022.
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[19] R.S. William, Static and Dynamic Electricity, third ed. Hemisphere Pub Co, New York, 1989, pp. 29. [20] Y. Xiang, J. Electrostat. 64 (2006) 29. [21] Y. Xiang, Commun. Nonlin. Sci. Numer. Simul. 12 (2007) 652. [22] Y. Xiang, J. Electrostat. 66 (2008) 366. [23] O. Marinov, M.J. Deen, J.A.J. Tejada, B. Iniguez, Org. Electron. 12 (2011) 936. [24] R.J. James, G. James, Mathematics Dictionary. Springer, Berlin, 1992, pp.139. [25] L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, fourth ed. Elsevier, Singapore, 2007, pp. 89.