# A Tent Map BasedA/D Conversion Circuit for Robot Tactile Sensor

Authors: Jianxin Liu; Xuan Zhang; Zhiming Li; Xuling Li
Journal: Journal of Sensors
 (2013)

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## Abstract

Force and tactile sensors are basic elements for robot perception and control, which call for large range and high-accuracy amplifier. In this paper, a novelA/D conversion circuit for array tactile sensor is proposed by using nonlinear tent map phenomenon, which is characterized by sensitivity to small signal and nonlinear amplifying function. The tent map based A/D conversion circuits can simultaneously realize amplifying and A/D converting functions. The proposed circuit is not only simple but also easy to integrate and produce. It is very suited for multipath signal parallel sampling and A/D converting of large array tactile sensor.


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## Body

## 1. Introduction

In recent decades, with the rapidly development of robot technology, robot sensors have received much attention as a sensing element for robot. Multiaxis force sensors and array tactile sensors, usually called haptic sensors, especially, have become the major research content in the robot sensor research areas [1, 2]. People hope that robot haptic sensor can be like human perception organs which have high measurement accuracy, with similar hand force and tactile organ of integration, miniaturization, and flexibility characteristics. For instance, Song developed a small four-degree-of-freedom wrist force sensor with high precision, which consists of small cross-elastic beam, compliant beams, and the base of the elastic body. It is a kind of self-decoupling force sensor in mechanical structure [3]. Beyeler et al. designed a six-axis MEMS force sensor with a movable body suspended by flexures which allow deflections and rotations along the x-, y-, and z-axes. And the orientation of this movable body is sensed by seven capacitors based on transverse sensing, resulting in a high sensitivity [4]. Ma et al. proposed a novel nonlinear static decoupling algorithm based on the establishment of a coupling error model for 3-axis force sensor in order to avoid overfitting and minimize the negative effect of random noises in calibration data, which can obtain high precise measurement results of 3-axis force for robot force control [5]. Although robot array tactile sensor can be regarded as a multipoint integrated force sensor, due to flexible and miniaturization requirements of tactile sensor which are high, the measurement principle is more complex than the multiaxis force sensor [6, 7]. Song et al. proposed a novel design of a haptic texture sensor by using PVDF film to fabricate a high-accuracy, high-speed-response texture sensor [8]. Lee and Won developed a novel tactile imaging sensor by using a multilayer polydimethylsiloxane optical waveguide as the sensing probe, which is capable of measuring the elasticity of the touched object with high precision [9]. Based on semiconductor technique, piezoresistive, capacitive, piezoelectric, and other types of robot, array tactile sensors are developing rapidly. Array tactile sensors have a corresponding increase in array size and resolution [10, 11]. Nonetheless, because of measurement mechanism limit, output signal of sensing element of most high-resolution tactile sensors is relatively weak. In addition, as the expansion of tactile array, it hopes that tactile image signal has a fast A/D conversion rate. Sharing the same A/D conversion in small scale tactile sensor cannot meet the real-time requirements of signal acquisition for the large scale array tactile sensor.In recent years, some of the unique properties of nonlinear systems have much in measurement area for their unique character, such as the chaotic system sensitivity to small signal [12], nonlinear mapping [13], nonlinear information storage [14], and resonance stochastic [15]. In this paper, a tent map is sensitive to small signal circuit and nonlinear transform of unique properties. A novel A/D conversion circuit for robot tactile sensor array is proposed to achieve parallel sampling of multichannel tactile signals and A/D conversion with high cost performance, which has a conditioning amplification and A/D conversion function integration advantages in combination, simple circuit, and easy integration to realize.


## 2. Signal Acquisition System for Robot Tactile Sensor

Typical signal acquisition circuit for robot tactile sensor is shown in Figure1, including timing control circuit, line scan circuit, read circuit, and interface circuit. The whole signal acquisition process was controlled and coordinated by timing control circuit. According to the arrangements of the timing control circuit, line scan circuit is ordered in m clock cycles to send the periodic excitation signal to m-line array sensitive element, while the read circuit is ordered in m clock cycles to read the output signal of n column in parallel. Then through interface circuit which consists of signal conditioning and A/D conversion, tactile signals were transferred to the computer for processing and target recognition.Figure 1
Tactile sensor array signal acquisition circuit.Conventional robot array tactile sensor, because of the small array size (about8×8), often uses an A/D conversion in order to complete the analog-digital conversion of output signal of m×n sensitive elements.


## 3. Small Signal Nonlinear Amplifier andA/D Conversion Based on Tent Map

Tent map was a typical one-dimensional chaotic system [16], which was described as
(1)xn+1=T(xn)={2xn,0<xn≤0.5,2(1-xn),0.5<xn<1,
wherexn∈[0,1], n=0,1,2,….This map consisted of two steps: the first step was to uniformly elongate the interval[0,1] to its doubled range; the second step was to fold the elongated interval into the original interval [0,1]. These iterative operations would cause the separation of adjacent points index, eventually to achieve the state of chaos.Tent map on the initial value (the system input signal) amplification was different from the linear amplification method. Linear amplification multiples were a constant and also limited by system operating range. Tent map system in chaotic state amplified the signal doubly and folded the doubled range symmetrically in each iteration, so that the initial small signal could eventually be greatly amplified without beyond range of system operating after several iterations.The initial valuex0, which was corresponding to the input signal of tent map system Vin, could be described as a binary fraction
(2)x0=0.t0t1t2⋯=∑j=0∞tj2j+1.In order to obtain the relationship of the iterative output and the initial signal of discrete tent map, here, this paper would introduce the nonlinear relationship of Bernoulli shift; its kinetic equation was(3)xn+1′=B(xn′)={2xn′,0<xn′≤0.5,2xn′-1,0.5<xn′<1.In each iteration, Bernoulli shift left shifted the binary fractiont1,t2,…one place
(4)x1′=B(x0′)=0.t1t2t3⋯,x2′=B(x1′)=0.t2t3t4⋯.For Bernoulli shift,bn=sgn(xn′-0.5)was defined as the nth iteration output; there bn=tn, and bi, i=0,1,2,…, was a binary sequence. For tent map, if we definegn=sgn(xn-0.5), then the corresponding relationship between gi, i=0,1,2,…, and bi, i=0,1,2,…, was as follows:(1)
when0<xk<0.25, that is, bk=0, thenB(xk)<0.5,bk+1=0,T(xk)<0.5, and gk+1=0;(2)
when0.25<xk<0.5, that is, bk=0, then B(xk)>0.5,bk+1=1,T(xk)>0.5, and gk+1=1;(3)
when0.5<xk<0.75, that is, bk=1, then B(xk)<0.5,bk+1=0,T(xk)>0.5, and gk+1=1;(4)
when0.75<xk<1, that is, bk=1, then B(xk)>0.5,bk+1=1,T(xk)<0.5, and gk+1=0.Therefore, gi, i=0,1,2,…, was a Gray-code sequence of bi, i=0,1,2,…:
(5)gk+1=bk⊕bk+1,k=0,1,2,….According to the above formula and initial timex0=x0′=Vin, we could obtain
(6)bk+1=bk⊕gk+1,k=0,1,2,…,b0=g0.So we designed a tent map iteration output Gray-code sequencegi, i=0,1,2,…, into a binary sequence of Bernoulli mapbi, i=0,1,2,…, and then calculated the initial value through binary fraction sequence as follows:
(7)x0=∑j=0Nbj2j+1,
where gi, i=0,1,2,…, was the needed digital value. Here, tent map completed signal amplification and A/D conversion function.


## 4. Implementation on the Circuit of Tent Map forA/D Conversion

A
/
D circuit basic element was switched capacitor integral circuit shown in Figure 2, where T1 and T2 were analog switches and C1 and C2 were capacitors. The clocks Φ1, Φ2 were in reverse phase with same period T. During the former half period of T, the T1 was on and T2 was off; thus the C1 was charged by input voltage VI. During the latter half period of T, T1 was off and T2 was on, so that the C2 was charged by C1VI. The output voltage of this circuit in a period was
(8)Vo(nt)=Vo((n-1)t)-C1C2VI((n-1)t).Figure 2
Switched capacitor integral circuit.The tent map circuit consisted of the above circuit as shown in Figure3. Parts I and III implemented the function ofy=2x, and parts II and III implemented the function of y=2(1-x). Part IV was a circuit for holding and delay.Figure 3
The circuit of tent map forA/D conversion.Figure4 shows the control logic for A/D conversion. First, start signal got high, and switch J0 connected the input signal with the part I and part II. After delay of t1, D trigger produces a switch instruction; if 0≤Vi≤0.5, then J1 was switched on; if 0.5<Vi<1, then J2 was switched on. At time t1+t2, the control signal e switches were high, so that the charge of C1 or C2 was transferred to C3, due to C3=(1/2)C1=(1/2)C2, so that the input voltage was amplified doubly. In the meantime, C4 was also charged. At the next time 0, the o switches were switched off and e switches were switched on, so that the charge of C4 was transferred to C5 and results in VC5=VC4. At the same time, J0 was disconnected with input signal V0, so that an iterative feedback loop exists in the A/D conversion, and C1, C2 were charged by the same feedback voltage to realizey=2xandy=2(1-x). This circle continuously iterated N times.Figure 4
Circuit logic for theA/D conversion.Hence theN binary bits output of D trigger was the Gray-code sequence of A/D conversion
(9)gk=Q-k(k=1,2,3,…),b0=Q0.The abovegk sequence, the initial condition b0=Q0 into (6), and Bernoulli binary sequence bk  (k=0,1,2,…) could be obtained.


## 5. Array Tactile Sensor Signal Acquisition System Based on Tent Map ofA/D Circuit

The schematic diagram of signal amplification of array tactile sensor analog andA/D conversion based on tent map circuit is shown in Figure 5. According to the arrangements of the timing control circuit, line scan circuit sent the periodic excitation signal to m-line array sensitive element, while the read circuit read the output signal of n column in parallel. The n-column signal was generated by simultaneously signaling nonlinear amplification and analog-digital conversion of n of A/D converters based on tent map. The resulting Gray-code sequence was sent directly to the computer which will complete the conversion of Gray code to binary code. Then, under the control of timing logic, the read n-column signal on the next line, and the completed amplification and A/D conversion, after obtaining an m×n tactile image signal by the computer, we could process tactile signals.Figure 5
The schematic diagram of array tactile sensor signal acquisition system based on tent map ofA/D circuit.We could carry out the amplification andA/D conversion experiments sensitive element signal of 16×16 microarray tactile sensor based on the above circuit. The results of the A/D conversion for eight sensitive elements in the 8th line were shown in Table 1, which indicates that A/D circuits based on the tent map could effectively achieve the amplification and A/D conversion of a small signal.Table 1
Results of the A/D conversion.
Sensitive element
(8, 1)
(8, 2)
(8, 3)
(8, 4)
(8, 5)
(8, 6)
(8, 7)
(8, 8)
Output value (mV)
0
0
0
0
25
80
188
246
Gray codeg0g1g2g3g4g5g6g7
00000000
00000000
00000000
00000000
00000101
00011111
00101000
00100001
Binary codeb0b1b2b3b4b5b6b7
00000000
00000000
00000000
00000000
00000110
00010101
00110000
00111110
Calculated value (mV)
0.0
0.0
0.0
0.0
23.4
82.0
187.5
242.2
Sensitive element
(8, 9)
(8, 10)
(8, 11)
(8, 12)
(8, 13)
(8, 14)
(8, 15)
(8, 16)
Output value (mV)
310
230
170
67
33
0
0
0
Gray codeg0g1g2g3g4g5g6g7
01101000
00100111
00111110
00011001
00001100
00000000
00000000
00000000
Binary codeb0b1b2b3b4b5b6b7
01001111
00111010
00101011
00010001
00001000
00000000
00000000
00000000
Calculated value (mV)
308.5
226.5
168.0
66.4
31.3
0.0
0.0
0.0Figure6 is the output of a 16×16 micro array tactile sensor manufactured by us based on the tent map circuit when a very light hexagon aluminum flake was put on it. The measurement range of each tactile sensing unit was from 0.01 N to 10 N, which shows that the proposed tent map based A/D conversion circuits had the advantages of large amplification range and high resolution. By comparison with the conventional high precision array tactile sensor [17], our method is more cost effective and easier to realize.Figure 6
The output of a16×16 array tactile sensor based on the tent map circuit when a very light hexagon aluminum flake was put on it.


## 6. Conclusion

This paper presents a novelA/D conversion circuit for robot array tactile sensor of unique properties. The circuit makes use of unique advantage for tent map sensitive to small signal circuit and nonlinear transform and has conditioning amplification and A/D conversion function integration advantages, simple circuit, and easy integration to realize. This method can achieve the parallel sampling of multichannel tactile signal and A/D converter, which can meet the real-time requirements of signal acquisition for the large scale array tactile sensor. This experiment gives the effectiveness of this method.



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