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A Jump-U model of echo pattern for a sonar ranging module
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Applied Acoustics 69 (2008) 1299–1307 www.elsevier.com/locate/apacoust
A Jump-U model of echo pattern for a sonar ranging module Bo-Chang Chen *, Jung-Hua Chou
1
Department of Engineering Science, National Cheng Kung University No. 1, University Road, Tainan City 70101, Taiwan, ROC Received 30 March 2007; received in revised form 3 August 2007; accepted 4 September 2007 Available online 22 October 2007
Abstract Sonar is extensively used in robot as a range sensor and the time-of-flight (TOF) information of ultrasonic echo is frequently adopted in sonar applications. This paper proposes a Jump-U model of ultrasonic echo pattern based on TOF data for a sonar ranging module. The model is established through a data regression method, utilizing TOF data and the relation between the delay time and the bearing angle of the sensor as input parameters. Because the proposed model can explain the jump phenomenon of TOF data and the shape of TOF data is similar to character U, the model is named as Jump-U. Moreover, the model includes several parameters, and one of them is intensity factor which can be regard as a relative strength of ultrasonic echo. Experiments are conducted to verify the proposed model by measuring the echo’s TOF data of a plane with distances ranging from 100 to 200 cm. The results show a close agreement between simulation and measurements. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Sonar; Ultrasonic sensor; Time-of-flight; Echo model
1. Introduction Sonar has the advantage of being relatively small, cheap, and easy to use. Therefore it has been used extensively in robots for ranging measurements, obstacle sensing and so on. Sonar can provide environmental information needed for a robot to locate and avoid obstacles [1–3], build the map of the environment [4–7], and identify the shape of an obstacle [8–10] etc. On the other hand, a typical sonar sensor has a wide beam width about 24°. Because of this wide beam angle effect, the exact reflection point on an obstacle cannot be determined precisely. Many methods to overcome this inadequacy have been proposed, such as probability approach [4] or multiple sonar sensors [6,10,11]. If there is a good sonar model which can predict the behavior of sonar, one can perform simulation first to *
Corresponding author. Tel.: +886 6 2757575x63342x37; fax: +886 6 2766549. E-mail addresses: [email protected] (B.-C. Chen), jungchou@ mail.ncku.edu.tw (J.-H. Chou). 1 Tel.: +886 6 2757575x63324; fax: +886 6 2766549. 0003-682X/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2007.09.002
verify whether the proposed design does fulfill the desired requirement. This can save not only a lot of cost but also much time for experiments. In order to understand more about the behavior of sonar, many researchers have devoted efforts into the model developing of sonar. For example, Kuc and Seigel [12] proposed a physically-based simulation model for sonar navigation system for reflecting structures. According to proposed model, an acoustic sensor based robot could be navigated in a CEW environment consisting of corners, edges and walls. Lim and Cho [13] propose a specular reflection probability model, which included two parameters, namely the range confidence factor and orientation probability, and permitted robot to build a high quality probability map of specular environment. In order to reduce the noise presented in TOF to increase the accuracy of sonar ranging system, Sabatini [14] adopted autoregressive-moving average (ARMA) modeling technique to develop a stochastic model to describe the statistical properties of noise, which was decomposed into three components, namely, a deterministic time-varying mean, a correlated random process and an uncorrelated random process. Harris and Recce [15] collected a large quantity of TOF data with a single Polaroid
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ultrasonic rangefinder, and proposed two empirical models of sonar TOF, one was a closed form model for rough brick wall and the other is a probability model for smooth walls, respectively. Because of proposed models, one could understand more the behavior of Polaroid sonar sensor for both rough and smooth walls. Kuc [16] proposed a forward model for the Polaroid 6500 series sonar ranging module connected to a 600 series electrostatic transducer, which configuration is also adopted in this paper. The model could predict the TOF readings from an object at a given range, bearing angle, and reflecting strength. However, this model did not include the jump phenomena of TOF readings, which will be described in later section. Because of its simplicity, time-of-flight (TOF) of a sonar sensor is commonly adopted in ranging applications. In principle, as the distance being the same, the TOF of an ultrasonic wave reflecting from the same reflection point at different bearing angles should be the same. However, due to the situation that the echo intensity decreases as the angle increases, the received TOF will contain certain embedded time delay and the magnitude of the time delay depends on the angle. In this regard, Kuc [16] proposed a sonar echo model utilizing the relation between the echo intensity and the angle. The model was used to differentiate a plane from cylinders of different diameters. However, because the echo of a square wave was assumed, no time delay caused by the reduction of echo intensity was considered and resulted in a difference in time delay between the echo model and actual echo wave near the center angle. It should be noted that echo intensity has adopted in many applications [8–10,16]. However, in order to measure the echo intensity, additional circuits, such as an AD convert circuit or a DAQ card, are needed to acquire the high frequency echo wave. Sometimes, a high-speed signal processor, for example a DSP, is required to handle effectively the huge amount of data acquired [16]. Thus, for simplicity, in most case, the sonar module is operated in the single-echo mode [17,18]. In this paper, a Jump-U sonar echo model is proposed for ranging measurements by a single sonar sensor. The model is based on the measured TOF and the relation between the delay time and angle to obtain the echo model and echo intensity without any additional circuit. The sonar sensor examined is the Polaroid 6500 series sonar ranging module, which is the most common sonar employed in mobile robot [15]. The rest of this paper is organized as follows: In the Section 2, a sonar ranging system, including a basic sonar physical model and soar ranging principles, is briefly reviewed. Thereafter, Section 3 starts with a number of experiments to realize the behavior of sonar for a plane, and so the time delay phenomenon of TOF and its reason are introduced. Furthermore, the proposed Jump-U model of sonar echo is provided. The experimental setup and results are presented in Section 4 to verify the performance of the proposed echo model. Finally, the conclusions of this paper are drawn in Section 5.
2. Sonar ranging system 2.1. Sonar physical model Typically, a sonar beam pattern can be divided into two regions, the near and far regions as shown in Fig. 1 [8]. In the near region, the shape of beam pattern is like a cylinder with a radius a. In the far region, the beam pattern is similar to a cone with angle 2h0 [19]. The half-angle h0 of the cone can be computed from the following equation: 0:61k h0 ¼ sin1 ð1Þ a In Eq. (1), the symbol a is the radius of the sonar transducer, and k is the wavelength of the ultrasound wave. At a room temperature of 25 °C, the speed of sound in air is about 346 m/s. The Polaroid 6500 series sonar ranging module has a firing frequency of 49.4 kHz and a transducer radius of 1.9 cm. The corresponding wavelength and half-beam angle h0 are about 0.7 cm and 13°, respectively. The amplitude of a sonar sensor is a function of the beam angle and can be expressed by a Gaussian function with a standard deviation of h0 =2 [8] as follows: ! h2 AðhÞ ¼ Amax exp 2 2 ð2Þ h0 where Amax is the on-axis amplitude. The corresponding intensity of the sonar sensor based on the Gaussian function model is shown in Fig. 2. Comparing to the actual sonar intensity pattern given in Fig. 3 [17], it can be seen that in addition to the main lobe, the actual sonar intensity pattern also includes the first and second side-lobes. When the angle is close to the intersection of the main and the first side-lobes, the sonar intensity will be affected by the presence of the first side-lobes. In other words, the Gaussian function model only resembles the main lobe portion of the sonar sensor. 2.2. Sonar ranging principle Using a sonar sensor to measure a distance is straightforward. The sensor is fired first and at the same time a counter is triggered to initiate counting. When the sonar signal touches an object, it will be reflected and returned.
Fig. 1. Sonar beam pattern, the near and far regions.
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r¼
Fig. 2. The sonar intensity model corresponding to the Gaussian beam pattern.
Fig. 3. The actual sonar amplitude pattern, including main lobe, and first and second side-lobes.
For convenience, the touch point on the object is referred to as the reflection point in this study. A typical sonar echo pattern is shown in Fig. 4 [8]. Also shown in the figure is a predetermined threshold value s for the registration of the echo. When the intensity of the echo is greater than the threshold value s, the echo is treated as being received by the sonar sensor and at the same time the counting sequence of the counter is stopped. The time interval between starting and stopping of the counter is the commonly used time-of-flight (TOF). The distance r between the sonar module and reflection point can be obtained by the following equation in which c is the speed of sound in air:
Fig. 4. A typical sonar echo pattern.
c TOF 2
1301
ð3Þ
As mentioned above, a Polaroid 6500 series sonar ranging module is adopted in this study. The ranging module will emit 16 pulses continuously at a frequency of 49.4 kHz after it is fired. After that, the internal circuit will delay 2.38 ms in default before starting to receive the echo. Thus, the shortest distance measurable is about 40 cm. If a shorter distance ranging measurement is desired, one needs to change the default time delay. In this paper, the 2.38 ms default delay time is used without any modification. The echo is considered being received by the sensor when its intensity is greater than the threshold value. The ranging module has two operation modes; namely, a single-echo mode and a multiple-echo mode [17]. The single echo mode is adopted in this study to avoid possible pulse interference. Because the intensity of sound wave decays with distance, the internal circuit of the Polaroid 6500 series sonar ranging module has an amplifier with a time varying step gain to compensate the intensity decay caused by distance. With the amplification compensation, the intensity of echo is usually considered to be independent of distance. However, from the experimental results obtained in this study, the echo intensity is still affected by distance. More discussion about this aspect will be presented later. 3. Jump-U echo model 3.1. Plane experiment A plane is a fundamental shape of an object. Therefore, the measured result of a smooth plane is presented below to show the features of TOF. A schematic diagram of the plane measurement setup is shown in Fig. 5. A
Fig. 5. A schematic diagram of the plane distance measurement setup.
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sonar sensor (S) is mounted on the axis of a stepping motor with a step angle of 0.9°. The sonar sensor faces the smooth plane at a distance D, where point A on the plane is the nearest point from the sonar sensor to the plane. A 16-bit MPU Chip PIC16F877 is used to control the stepping motor and carry out the distance measurement. The stepping motor is used to rotate the sonar sensor from 0° to 180° in counterclockwise direction. Correspondingly, the total measured data points are 200. The counting frequency of the PIC16F877 for TOF is 2 MHz. The measured TOF data are sent to a personal computer (PC) with an RS232 RF wireless module for further processing and applications. A typical measured distance result is shown in Fig. 6 for which the distance between the sonar sensor and the plane is 150 cm. In Fig. 6, the Y-axis is TOF in ls, and the X-axis is the bearing angle in degrees. The main lobe is in the range of about ±15°. It can be seen that the measured TOF pattern in the main lobe range resembles the shape of an upward parabola. In addition, there is a short flat portion at the center part of TOF data. This flat portion is larger when the echo intensity is stronger. Because of the particular shape, the upward parabola will be referred to as the U-shape curve. Outside of this range, the TOF pattern is the result of first side-lobe. As shown in Fig. 5, point A is the nearest point from the sensor to the plane. Ideally, if the ultrasound wave can touch the same point A and return to the sensor irrespective of different incident angles, then the measured TOF would be the same. However, as can be observed from Fig. 6, there is a time delay in TOF when the angle is larger. It can be seen that the measured TOF has discontinuous jumps with time intervals with multiples of 20 ls. The time delay phenomenon is caused by the decrease in echo intensity as the angle increases and will be examined in detail in the following sections.
Fig. 6. A typical measured TOF pattern of the plane at 150 cm.
3.2. Time delay of TOF 3.2.1. The excitation After triggering the excitation, the Polaroid 6500 series sonar ranging module will continuously transmit 16 square waves with an amplitude and frequency of 400 V and 49.4 kHz, respectively, as shown in Fig. 7. In other words, the excitation period dt is about 20 ls, and the total excitation time T is 320 ls [17]. 3.2.2. The reflection When the ultrasound waves touch an object and are reflected, the intensities of echo pulses are not identical as shown in Fig. 8 [16], where Fig. 8a shows the overall feature of the echo and Fig. 8b is an expanded view of the time interval between T 0 and T m . The intensities increase gradually until leveling off to a higher value; thereafter, the intensities decrease. In figure, T 0 is the time of the first echo pulse and T m is the time when the intensity of an echo pulse is greater than the threshold value s. Here as usual, T m is called the time-of-flight (TOF). 3.2.3. Time delay phenomenon When the intensity of the first echo pulse is greater than the threshold value s, and the measured time is T 0 , there will be no time delay, namely, T 0 ¼ T m as shown in Fig. 9a. However, as the bearing angle increases, the intensity of first echo pulse can be smaller than the threshold value. When this occurs, the sensor will not count it as a receiving echo. In this situation, if the intensity of the second echo pulse is greater than the threshold value and then it will be registered. Because there is a time interval of 20 ls between the first and second echoes, this will cause a 20 ls time delay as depicted in Fig. 9b. By the same token, if no echo is greater than the threshold value until the pth echo pulse, then the delay time T d will be 20ðp 1Þ ls and the total measured time is T 0 þ T d . This will result in discontin-
Fig. 7. The excitation pattern of Polaroid 6500 series sonar ranging module.
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EðpÞ < s ) TOF ¼ TBD EðpÞ P s ) TOF ¼ T 0 þ T d
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ð4Þ
T d ¼ ðp 1Þ dt where TBD denotes the situation that TOF is yet to be determined and dt ¼ 20 ls. From Eq. (2), it can be seen that the amplitude of ultrasound emission wave A(h) can be represented by a Gaussian normal distribution [8]. Assuming that the relation between E(p) and AðhÞ is EðpÞ ¼ AðhÞAE ðpÞ
ð5Þ
The symbol AE ðpÞ denotes the echo amplitude and can be modeled by the following equation according to the actual echo pattern shown in Fig. 8a: ! p2 ð6Þ AE ðpÞ ¼ 1 exp 2 2rp
3.3. Jump-U echo model
where p is the pth echo pulse, p = 1–16, and rp is the intensity factor. A typical curve with rp ¼ 3 is shown in Fig. 10. It can be seen that it is a normalized model with the maximum value of 1. By letting EðpÞ ¼ s, the following equation can be obtained: !! 2 Amax p2 h 1 exp 2 ð7Þ ¼ exp s 2rp 2r2h
As mentioned above, the delay time of the sonar is caused by the reduction of echo intensity as the bearing angle increases. Assuming that the echo intensity of the pth echo pulse is EðpÞ, then one has the following relations:
From the experimental results obtained in this study, it is evident that when the echo intensity is large enough, the intensity of the first echo can still be greater than s even when the angle is large. This will result in a broadening of the center flat portion of the TOF pattern shown in
Fig. 8. The echo pattern of ultrasound pulses.
uous jumps in TOF with a time interval multiples of 20 ls as show in Fig. 6.
Fig. 9. The time delay phenomenon of echo pulse.
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intensity reduction due to angle takes place, only the pth echo intensity will reach the threshold value. By the assumption of EðpÞ ¼ s adopted in the echo model, for data with the same delay time, the intensity of data point with the largest bearing angle will be closest to the threshold value. Therefore, for data with the same delay time, the most outside data point is chosen as the regression data point. In addition, at the intersection of the main lobe and the first side-lobe, the echo intensity is mingled by the first side-lobe, and results in an outward expansion phenomenon. Thus, the data points in this region are not chosen for regression analysis. In Fig. 11, the Y-axis denotes the delay time in ls while the X-axis is the bearing angle. The rhombus points are the original measured data, and the square points are the regression data points chosen for deducing the echo model. Fig. 10. The echo model of sonar, the intensity has been normalized and rp ¼ 3.
Fig. 6 and make the pattern look more like the U shape. The echo pattern becomes more similar to the U shape and fewer data points can be used to find the echo model. When the bearing angle is near 12°, a slight change in angle will cause a large increase in the delay time, indicating a situation of larger reduction of echo intensity. This will result in large uncertainties in the measured data and cause errors in the corresponding echo model. In order to improve the accuracy of the echo model, a fixed factor k is added to Eq. (6) to compensate this intensity effect as follows: ! p2 AE ðpÞ ¼ 1 k exp 2 ð8Þ 2rp In general, the value of k is close to 1, implying that the echo intensity is not too high. With this modification and using the relationship p ¼ ðT d =dtÞ þ 1, the following equation is obtained: " !# 2 2 ðTdtd þ 1Þ Amax h 1 k exp ¼ exp ð9Þ s 2r2p 2r2h
3.4.2. Regression echo model The echo pattern result from the regression model is shown Fig. 12, where Y-axis is the intensity of echo pulse in dB and X-axis denotes the pulse number. The rhombus symbols are the experimental data, and the square ones represent the data obtained from the regression echo model. It can be seen that the simulation result is in close agreement with the actual data. The quantities of Amax , k and rp are 53.6 dB, 1.0095 and 3.46, respectively. 3.4.3. TOF simulation results of a plane The regression echo model developed above is used to simulate the TOF of the plane at the distance of 150 cm. The simulation results are shown in Fig. 13, where the rhombus symbols are the experimental data, and the square ones are the simulation data from the regression echo model. From the figure, it can be seen that the simulation results are very close to the actual measured data, despite some slight difference between the model and the measurement due to the assumption of EðpÞ ¼ s.
where rh is the standard deviation in Eq. (2) and equal to h0 =2. It can be observed that both quantities of Amax and rp are needed for the echo model. These two quantities are obtained by regression analysis using the experimental results of T d , h and Eq. (9). 3.4. Plane TOF simulation results 3.4.1. Regression data selection As shown in Fig. 6, there are discontinuities in TOF due to echo delays. Thus, data for the regression analysis need to be selected. From Fig. 6, it can be seen that as far as the first echo intensities are greater than s, the values of TOF will be the same. On the other hand, when the effect of
Fig. 11. The regression data of the plane at 150 cm.
B.-C. Chen, J.-H. Chou / Applied Acoustics 69 (2008) 1299–1307
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Fig. 12. The echo model of the plane at 150 cm.
Fig. 14. The experimental results of delay times for planes at distances ranging from 100 to 200 cm.
Fig. 13. TOF simulation results of the plane at 150 cm.
Fig. 15. The trend lines of the experimental results of planes at 100– 200 cm.
4. Experimental results and discussion 4.1. Experimental results The model developed above is used further to simulate the distance measurements for planes at various distances ranging from 100 to 200 cm with an interval of 5 cm. The measured delay times are shown in Fig. 14. It can be seen that the discontinuous jumps of the data are quite obvious as already discussed above. To see more clearly the trend embedded in the data shown in Fig. 14, the data are replaced by their corresponding trend lines as given in Fig. 15. From the figure, it can be observed that as the distance of the plane increases from 100 to 200 cm, the patterns of the delay time will change from a U shape to a V shape. This trend
indicates that even with a time variable gain embedded in the ranging module to compensate distance effect, the reduction of the echo intensity with increasing distance still occurs. It is also evident that when the angle is greater than about ±15°, the delay times will decrease drastically, instead of increasing further. This is due to intensity contribution from the first side-lobe to increase the overall intensity of the echoes. It is obvious that the echo intensity is stronger for the plane at a shorter distance. Thus, the main lobe at 100 cm is about ±15°. This range of angle tends to decrease as the plane is at a farther distance away. However, for the distances of 100 and 200 cm, the decrease in the range of angles of the main lobe is only about 0.5°. Furthermore, the maximum amplitude Amax for the 200 cm case is close to 50 dB.
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about 0.6 and rp is about 1.7. Fig. 18 shows the simulated TOF results of the echo model of the plane at the distance of 125 cm. At this distance, the echo intensity is still strong but not as strong as that for the 100 cm case. Therefore, the extent of flat portion reduces slightly. Furthermore, as the echo intensity decreases with increasing distance, the effect of the first side-lobe also reduces. In other words, the range of agreement between the simulated and the measured results extends outwards slightly. For the plane at the distance of 180 cm, the parameters of the echo model are Amax is about 52 dB, k is about 0.99, very close to 1, and rp is about 4.1. Fig. 19 is the simulated TOF results of the echo model of the plane at the distance of 180 cm. As shown in the figure, because of the obvious increase in distance and reduction in intensity, the pattern has changed from a U shape to a V shape. Furthermore, Fig. 16. The echo model of the plane at 100 cm.
4.2. Simulation results The echo models are deduced by the regression analysis of the measured delay times. Fig. 16 is the echo model of the plane at the distance of 100 cm. Assuming s ¼ 1, then the maximum amplitude Amax is about 50 dB. Furthermore, k is about 0.55 and rp ¼ 1:5. Fig. 17 is TOF simulation results corresponding to Fig. 16 for the plane at the distance of 100 cm. The echo intensity is stronger because the distance is relatively short. Thus, the flat portion ranges from 10° to +10°. From about 13° to +13°, the agreement between the simulated results and the measured ones is good. But beyond these two angles, there are large discrepancies. These discrepancies are due to the effects of the first side-lobe. Their effects are not considered in the present echo model. When the plane is at the distance of 125 cm, the values of parameters of the echo model are Amax ¼ 52 dB, k is
Fig. 18. TOF Simulation results of the plane at 125 cm.
Fig. 17. TOF Simulation results of the plane at 100 cm.
Fig. 19. TOF Simulation results of the plane at 180 cm.
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both sides of the TOF pattern rise rapidly as the intensities are not affected by the first side-lobe. The experimental results show that when the distance increases from 100 to 200 cm, the variations of the maximum amplitude Amax , the fixed factor k and the intensity factor rp are from 50 to 55 dB, 0.5 to 1, and 1.5 to 4.5, respectively. 5. Conclusions The most often used information of a sonar sensor is the time-of-flight (TOF). On the other hand, there are numerous situations that will need the information of echo intensity. In order to measure the echo intensity, an ADC circuit or a DAQ card is usually required and may need a high speed processor such as a DSP to process the huge amount of measured data. In this paper, a simple Jump-U sonar echo model is proposed for Polaroid 6500 series sonar ranging module utilizing TOF data only. From the measured TOF data of the sonar sensor, and the relation between delay time and bearing angle, an echo model is obtained by data regression calculation. The experiments show that the simulation result is very close to the measured data. In other words, the model is very accurate and can be used to replace the actual echo intensity measurement for obstacle avoiding or map building of robots. References [1] Borenstein J, Koren Y. Obstacle avoidance with ultrasonic sensors. IEEE Trans Robot Autom 1988;4:213–8. [2] Barshan B, Kuc R. A bat-like sonar system for obstacle localization. IEEE Trans Syst Man Cyb 1992;22:636–46.
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[3] Sekmen AS, Barshan B. Estimation of object location and radius of curvature using ultrasonic sonar. Appl Acoust 2001;62:841–65. [4] Elfes A. Sonar-based real world mapping and navigation. IEEE Trans Robot Autom 1987;RA-3:249–65. [5] Bozma O, Kuc R. Building a sonar map in a specular environment using a single mobile sensor. IEEE Trans Pattern Anal Mach Intell 1991;13:1260–9. [6] Jeon HJ, Kim BK. A study on world map building for mobile robots with tri-aural ultrasonic sensor system. IEEE Int Conf Robot Autom 1995:2907–12. [7] Chong KS, Kleeman L. Sonar based map building for a mobile robot. IEEE Int Conf Robot Autom 1997:1700–5. [8] Barshan B, Kuc R. Differentiating sonar reflections from corners and planes by employing an intelligent sensor. IEEE Trans Pattern Anal Machine Intell 1990;12:560–9. [9] Barshan B, Ayrulu B, Utete SW. Neural network-based target differentiation using sonar for robotics applications. IEEE Trans Robot Autom 2000;16:435–42. [10] Oufroukh NA, Barat C, Colle E. Ultrasonic multi-transducer processing for pattern recognition. Sensor, Proc IEEE 2002:1329–34. [11] Wijk O, Jensfelt P, Christensen HI. Triangulation based fusion of ultrasonic sensor data. In: IEEE international conference on robotics and automation. Leuven, Belgium; 1998, p. 3419–24. [12] Kuc R, Siegel MW. Physically-based simulation model for acoustic sensor robot navigation. IEEE Trans Pattern Anal Mach Intell 1987;9:766–78. [13] Lim JH, Cho DW. Physically based sensor modeling for a sonar map in a specular environment. In: IEEE international conference on robotics and automation. Nice, France; 1992. p. 1714–19. [14] Sabatini AM, Stochastic A. Model of the time-of-flight noise in airborne sonar ranging systems. IEEE Trans Ultrason Ferroelectr Freq Control 1997;44:606–14. [15] Harris KD, Recce M. Experimental modelling of time-of-flight sonar. Robot Auton Syst 1998:2433–42. [16] Kuc R. Forward model for sonar maps produced with the polaroid ranging module. IEEE Trans Robot Autom 2003;19:358–62. [17] Polaroid, Technical Specifications for 6500 Series Sonar Ranging Module, 1999. [18] T. Instruments, Tl852 Sonar Ranging Receiver, 1998. [19] Wells PNT. Biomedical ultrasonic. New York: Academic; 1977.
Applied Acoustics 69 (2008) 1299–1307 www.elsevier.com/locate/apacoust
A Jump-U model of echo pattern for a sonar ranging module Bo-Chang Chen *, Jung-Hua Chou
1
Department of Engineering Science, National Cheng Kung University No. 1, University Road, Tainan City 70101, Taiwan, ROC Received 30 March 2007; received in revised form 3 August 2007; accepted 4 September 2007 Available online 22 October 2007
Abstract Sonar is extensively used in robot as a range sensor and the time-of-flight (TOF) information of ultrasonic echo is frequently adopted in sonar applications. This paper proposes a Jump-U model of ultrasonic echo pattern based on TOF data for a sonar ranging module. The model is established through a data regression method, utilizing TOF data and the relation between the delay time and the bearing angle of the sensor as input parameters. Because the proposed model can explain the jump phenomenon of TOF data and the shape of TOF data is similar to character U, the model is named as Jump-U. Moreover, the model includes several parameters, and one of them is intensity factor which can be regard as a relative strength of ultrasonic echo. Experiments are conducted to verify the proposed model by measuring the echo’s TOF data of a plane with distances ranging from 100 to 200 cm. The results show a close agreement between simulation and measurements. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Sonar; Ultrasonic sensor; Time-of-flight; Echo model
1. Introduction Sonar has the advantage of being relatively small, cheap, and easy to use. Therefore it has been used extensively in robots for ranging measurements, obstacle sensing and so on. Sonar can provide environmental information needed for a robot to locate and avoid obstacles [1–3], build the map of the environment [4–7], and identify the shape of an obstacle [8–10] etc. On the other hand, a typical sonar sensor has a wide beam width about 24°. Because of this wide beam angle effect, the exact reflection point on an obstacle cannot be determined precisely. Many methods to overcome this inadequacy have been proposed, such as probability approach [4] or multiple sonar sensors [6,10,11]. If there is a good sonar model which can predict the behavior of sonar, one can perform simulation first to *
Corresponding author. Tel.: +886 6 2757575x63342x37; fax: +886 6 2766549. E-mail addresses: [email protected] (B.-C. Chen), jungchou@ mail.ncku.edu.tw (J.-H. Chou). 1 Tel.: +886 6 2757575x63324; fax: +886 6 2766549. 0003-682X/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2007.09.002
verify whether the proposed design does fulfill the desired requirement. This can save not only a lot of cost but also much time for experiments. In order to understand more about the behavior of sonar, many researchers have devoted efforts into the model developing of sonar. For example, Kuc and Seigel [12] proposed a physically-based simulation model for sonar navigation system for reflecting structures. According to proposed model, an acoustic sensor based robot could be navigated in a CEW environment consisting of corners, edges and walls. Lim and Cho [13] propose a specular reflection probability model, which included two parameters, namely the range confidence factor and orientation probability, and permitted robot to build a high quality probability map of specular environment. In order to reduce the noise presented in TOF to increase the accuracy of sonar ranging system, Sabatini [14] adopted autoregressive-moving average (ARMA) modeling technique to develop a stochastic model to describe the statistical properties of noise, which was decomposed into three components, namely, a deterministic time-varying mean, a correlated random process and an uncorrelated random process. Harris and Recce [15] collected a large quantity of TOF data with a single Polaroid
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ultrasonic rangefinder, and proposed two empirical models of sonar TOF, one was a closed form model for rough brick wall and the other is a probability model for smooth walls, respectively. Because of proposed models, one could understand more the behavior of Polaroid sonar sensor for both rough and smooth walls. Kuc [16] proposed a forward model for the Polaroid 6500 series sonar ranging module connected to a 600 series electrostatic transducer, which configuration is also adopted in this paper. The model could predict the TOF readings from an object at a given range, bearing angle, and reflecting strength. However, this model did not include the jump phenomena of TOF readings, which will be described in later section. Because of its simplicity, time-of-flight (TOF) of a sonar sensor is commonly adopted in ranging applications. In principle, as the distance being the same, the TOF of an ultrasonic wave reflecting from the same reflection point at different bearing angles should be the same. However, due to the situation that the echo intensity decreases as the angle increases, the received TOF will contain certain embedded time delay and the magnitude of the time delay depends on the angle. In this regard, Kuc [16] proposed a sonar echo model utilizing the relation between the echo intensity and the angle. The model was used to differentiate a plane from cylinders of different diameters. However, because the echo of a square wave was assumed, no time delay caused by the reduction of echo intensity was considered and resulted in a difference in time delay between the echo model and actual echo wave near the center angle. It should be noted that echo intensity has adopted in many applications [8–10,16]. However, in order to measure the echo intensity, additional circuits, such as an AD convert circuit or a DAQ card, are needed to acquire the high frequency echo wave. Sometimes, a high-speed signal processor, for example a DSP, is required to handle effectively the huge amount of data acquired [16]. Thus, for simplicity, in most case, the sonar module is operated in the single-echo mode [17,18]. In this paper, a Jump-U sonar echo model is proposed for ranging measurements by a single sonar sensor. The model is based on the measured TOF and the relation between the delay time and angle to obtain the echo model and echo intensity without any additional circuit. The sonar sensor examined is the Polaroid 6500 series sonar ranging module, which is the most common sonar employed in mobile robot [15]. The rest of this paper is organized as follows: In the Section 2, a sonar ranging system, including a basic sonar physical model and soar ranging principles, is briefly reviewed. Thereafter, Section 3 starts with a number of experiments to realize the behavior of sonar for a plane, and so the time delay phenomenon of TOF and its reason are introduced. Furthermore, the proposed Jump-U model of sonar echo is provided. The experimental setup and results are presented in Section 4 to verify the performance of the proposed echo model. Finally, the conclusions of this paper are drawn in Section 5.
2. Sonar ranging system 2.1. Sonar physical model Typically, a sonar beam pattern can be divided into two regions, the near and far regions as shown in Fig. 1 [8]. In the near region, the shape of beam pattern is like a cylinder with a radius a. In the far region, the beam pattern is similar to a cone with angle 2h0 [19]. The half-angle h0 of the cone can be computed from the following equation: 0:61k h0 ¼ sin1 ð1Þ a In Eq. (1), the symbol a is the radius of the sonar transducer, and k is the wavelength of the ultrasound wave. At a room temperature of 25 °C, the speed of sound in air is about 346 m/s. The Polaroid 6500 series sonar ranging module has a firing frequency of 49.4 kHz and a transducer radius of 1.9 cm. The corresponding wavelength and half-beam angle h0 are about 0.7 cm and 13°, respectively. The amplitude of a sonar sensor is a function of the beam angle and can be expressed by a Gaussian function with a standard deviation of h0 =2 [8] as follows: ! h2 AðhÞ ¼ Amax exp 2 2 ð2Þ h0 where Amax is the on-axis amplitude. The corresponding intensity of the sonar sensor based on the Gaussian function model is shown in Fig. 2. Comparing to the actual sonar intensity pattern given in Fig. 3 [17], it can be seen that in addition to the main lobe, the actual sonar intensity pattern also includes the first and second side-lobes. When the angle is close to the intersection of the main and the first side-lobes, the sonar intensity will be affected by the presence of the first side-lobes. In other words, the Gaussian function model only resembles the main lobe portion of the sonar sensor. 2.2. Sonar ranging principle Using a sonar sensor to measure a distance is straightforward. The sensor is fired first and at the same time a counter is triggered to initiate counting. When the sonar signal touches an object, it will be reflected and returned.
Fig. 1. Sonar beam pattern, the near and far regions.
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r¼
Fig. 2. The sonar intensity model corresponding to the Gaussian beam pattern.
Fig. 3. The actual sonar amplitude pattern, including main lobe, and first and second side-lobes.
For convenience, the touch point on the object is referred to as the reflection point in this study. A typical sonar echo pattern is shown in Fig. 4 [8]. Also shown in the figure is a predetermined threshold value s for the registration of the echo. When the intensity of the echo is greater than the threshold value s, the echo is treated as being received by the sonar sensor and at the same time the counting sequence of the counter is stopped. The time interval between starting and stopping of the counter is the commonly used time-of-flight (TOF). The distance r between the sonar module and reflection point can be obtained by the following equation in which c is the speed of sound in air:
Fig. 4. A typical sonar echo pattern.
c TOF 2
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ð3Þ
As mentioned above, a Polaroid 6500 series sonar ranging module is adopted in this study. The ranging module will emit 16 pulses continuously at a frequency of 49.4 kHz after it is fired. After that, the internal circuit will delay 2.38 ms in default before starting to receive the echo. Thus, the shortest distance measurable is about 40 cm. If a shorter distance ranging measurement is desired, one needs to change the default time delay. In this paper, the 2.38 ms default delay time is used without any modification. The echo is considered being received by the sensor when its intensity is greater than the threshold value. The ranging module has two operation modes; namely, a single-echo mode and a multiple-echo mode [17]. The single echo mode is adopted in this study to avoid possible pulse interference. Because the intensity of sound wave decays with distance, the internal circuit of the Polaroid 6500 series sonar ranging module has an amplifier with a time varying step gain to compensate the intensity decay caused by distance. With the amplification compensation, the intensity of echo is usually considered to be independent of distance. However, from the experimental results obtained in this study, the echo intensity is still affected by distance. More discussion about this aspect will be presented later. 3. Jump-U echo model 3.1. Plane experiment A plane is a fundamental shape of an object. Therefore, the measured result of a smooth plane is presented below to show the features of TOF. A schematic diagram of the plane measurement setup is shown in Fig. 5. A
Fig. 5. A schematic diagram of the plane distance measurement setup.
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sonar sensor (S) is mounted on the axis of a stepping motor with a step angle of 0.9°. The sonar sensor faces the smooth plane at a distance D, where point A on the plane is the nearest point from the sonar sensor to the plane. A 16-bit MPU Chip PIC16F877 is used to control the stepping motor and carry out the distance measurement. The stepping motor is used to rotate the sonar sensor from 0° to 180° in counterclockwise direction. Correspondingly, the total measured data points are 200. The counting frequency of the PIC16F877 for TOF is 2 MHz. The measured TOF data are sent to a personal computer (PC) with an RS232 RF wireless module for further processing and applications. A typical measured distance result is shown in Fig. 6 for which the distance between the sonar sensor and the plane is 150 cm. In Fig. 6, the Y-axis is TOF in ls, and the X-axis is the bearing angle in degrees. The main lobe is in the range of about ±15°. It can be seen that the measured TOF pattern in the main lobe range resembles the shape of an upward parabola. In addition, there is a short flat portion at the center part of TOF data. This flat portion is larger when the echo intensity is stronger. Because of the particular shape, the upward parabola will be referred to as the U-shape curve. Outside of this range, the TOF pattern is the result of first side-lobe. As shown in Fig. 5, point A is the nearest point from the sensor to the plane. Ideally, if the ultrasound wave can touch the same point A and return to the sensor irrespective of different incident angles, then the measured TOF would be the same. However, as can be observed from Fig. 6, there is a time delay in TOF when the angle is larger. It can be seen that the measured TOF has discontinuous jumps with time intervals with multiples of 20 ls. The time delay phenomenon is caused by the decrease in echo intensity as the angle increases and will be examined in detail in the following sections.
Fig. 6. A typical measured TOF pattern of the plane at 150 cm.
3.2. Time delay of TOF 3.2.1. The excitation After triggering the excitation, the Polaroid 6500 series sonar ranging module will continuously transmit 16 square waves with an amplitude and frequency of 400 V and 49.4 kHz, respectively, as shown in Fig. 7. In other words, the excitation period dt is about 20 ls, and the total excitation time T is 320 ls [17]. 3.2.2. The reflection When the ultrasound waves touch an object and are reflected, the intensities of echo pulses are not identical as shown in Fig. 8 [16], where Fig. 8a shows the overall feature of the echo and Fig. 8b is an expanded view of the time interval between T 0 and T m . The intensities increase gradually until leveling off to a higher value; thereafter, the intensities decrease. In figure, T 0 is the time of the first echo pulse and T m is the time when the intensity of an echo pulse is greater than the threshold value s. Here as usual, T m is called the time-of-flight (TOF). 3.2.3. Time delay phenomenon When the intensity of the first echo pulse is greater than the threshold value s, and the measured time is T 0 , there will be no time delay, namely, T 0 ¼ T m as shown in Fig. 9a. However, as the bearing angle increases, the intensity of first echo pulse can be smaller than the threshold value. When this occurs, the sensor will not count it as a receiving echo. In this situation, if the intensity of the second echo pulse is greater than the threshold value and then it will be registered. Because there is a time interval of 20 ls between the first and second echoes, this will cause a 20 ls time delay as depicted in Fig. 9b. By the same token, if no echo is greater than the threshold value until the pth echo pulse, then the delay time T d will be 20ðp 1Þ ls and the total measured time is T 0 þ T d . This will result in discontin-
Fig. 7. The excitation pattern of Polaroid 6500 series sonar ranging module.
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EðpÞ < s ) TOF ¼ TBD EðpÞ P s ) TOF ¼ T 0 þ T d
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ð4Þ
T d ¼ ðp 1Þ dt where TBD denotes the situation that TOF is yet to be determined and dt ¼ 20 ls. From Eq. (2), it can be seen that the amplitude of ultrasound emission wave A(h) can be represented by a Gaussian normal distribution [8]. Assuming that the relation between E(p) and AðhÞ is EðpÞ ¼ AðhÞAE ðpÞ
ð5Þ
The symbol AE ðpÞ denotes the echo amplitude and can be modeled by the following equation according to the actual echo pattern shown in Fig. 8a: ! p2 ð6Þ AE ðpÞ ¼ 1 exp 2 2rp
3.3. Jump-U echo model
where p is the pth echo pulse, p = 1–16, and rp is the intensity factor. A typical curve with rp ¼ 3 is shown in Fig. 10. It can be seen that it is a normalized model with the maximum value of 1. By letting EðpÞ ¼ s, the following equation can be obtained: !! 2 Amax p2 h 1 exp 2 ð7Þ ¼ exp s 2rp 2r2h
As mentioned above, the delay time of the sonar is caused by the reduction of echo intensity as the bearing angle increases. Assuming that the echo intensity of the pth echo pulse is EðpÞ, then one has the following relations:
From the experimental results obtained in this study, it is evident that when the echo intensity is large enough, the intensity of the first echo can still be greater than s even when the angle is large. This will result in a broadening of the center flat portion of the TOF pattern shown in
Fig. 8. The echo pattern of ultrasound pulses.
uous jumps in TOF with a time interval multiples of 20 ls as show in Fig. 6.
Fig. 9. The time delay phenomenon of echo pulse.
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intensity reduction due to angle takes place, only the pth echo intensity will reach the threshold value. By the assumption of EðpÞ ¼ s adopted in the echo model, for data with the same delay time, the intensity of data point with the largest bearing angle will be closest to the threshold value. Therefore, for data with the same delay time, the most outside data point is chosen as the regression data point. In addition, at the intersection of the main lobe and the first side-lobe, the echo intensity is mingled by the first side-lobe, and results in an outward expansion phenomenon. Thus, the data points in this region are not chosen for regression analysis. In Fig. 11, the Y-axis denotes the delay time in ls while the X-axis is the bearing angle. The rhombus points are the original measured data, and the square points are the regression data points chosen for deducing the echo model. Fig. 10. The echo model of sonar, the intensity has been normalized and rp ¼ 3.
Fig. 6 and make the pattern look more like the U shape. The echo pattern becomes more similar to the U shape and fewer data points can be used to find the echo model. When the bearing angle is near 12°, a slight change in angle will cause a large increase in the delay time, indicating a situation of larger reduction of echo intensity. This will result in large uncertainties in the measured data and cause errors in the corresponding echo model. In order to improve the accuracy of the echo model, a fixed factor k is added to Eq. (6) to compensate this intensity effect as follows: ! p2 AE ðpÞ ¼ 1 k exp 2 ð8Þ 2rp In general, the value of k is close to 1, implying that the echo intensity is not too high. With this modification and using the relationship p ¼ ðT d =dtÞ þ 1, the following equation is obtained: " !# 2 2 ðTdtd þ 1Þ Amax h 1 k exp ¼ exp ð9Þ s 2r2p 2r2h
3.4.2. Regression echo model The echo pattern result from the regression model is shown Fig. 12, where Y-axis is the intensity of echo pulse in dB and X-axis denotes the pulse number. The rhombus symbols are the experimental data, and the square ones represent the data obtained from the regression echo model. It can be seen that the simulation result is in close agreement with the actual data. The quantities of Amax , k and rp are 53.6 dB, 1.0095 and 3.46, respectively. 3.4.3. TOF simulation results of a plane The regression echo model developed above is used to simulate the TOF of the plane at the distance of 150 cm. The simulation results are shown in Fig. 13, where the rhombus symbols are the experimental data, and the square ones are the simulation data from the regression echo model. From the figure, it can be seen that the simulation results are very close to the actual measured data, despite some slight difference between the model and the measurement due to the assumption of EðpÞ ¼ s.
where rh is the standard deviation in Eq. (2) and equal to h0 =2. It can be observed that both quantities of Amax and rp are needed for the echo model. These two quantities are obtained by regression analysis using the experimental results of T d , h and Eq. (9). 3.4. Plane TOF simulation results 3.4.1. Regression data selection As shown in Fig. 6, there are discontinuities in TOF due to echo delays. Thus, data for the regression analysis need to be selected. From Fig. 6, it can be seen that as far as the first echo intensities are greater than s, the values of TOF will be the same. On the other hand, when the effect of
Fig. 11. The regression data of the plane at 150 cm.
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Fig. 12. The echo model of the plane at 150 cm.
Fig. 14. The experimental results of delay times for planes at distances ranging from 100 to 200 cm.
Fig. 13. TOF simulation results of the plane at 150 cm.
Fig. 15. The trend lines of the experimental results of planes at 100– 200 cm.
4. Experimental results and discussion 4.1. Experimental results The model developed above is used further to simulate the distance measurements for planes at various distances ranging from 100 to 200 cm with an interval of 5 cm. The measured delay times are shown in Fig. 14. It can be seen that the discontinuous jumps of the data are quite obvious as already discussed above. To see more clearly the trend embedded in the data shown in Fig. 14, the data are replaced by their corresponding trend lines as given in Fig. 15. From the figure, it can be observed that as the distance of the plane increases from 100 to 200 cm, the patterns of the delay time will change from a U shape to a V shape. This trend
indicates that even with a time variable gain embedded in the ranging module to compensate distance effect, the reduction of the echo intensity with increasing distance still occurs. It is also evident that when the angle is greater than about ±15°, the delay times will decrease drastically, instead of increasing further. This is due to intensity contribution from the first side-lobe to increase the overall intensity of the echoes. It is obvious that the echo intensity is stronger for the plane at a shorter distance. Thus, the main lobe at 100 cm is about ±15°. This range of angle tends to decrease as the plane is at a farther distance away. However, for the distances of 100 and 200 cm, the decrease in the range of angles of the main lobe is only about 0.5°. Furthermore, the maximum amplitude Amax for the 200 cm case is close to 50 dB.
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about 0.6 and rp is about 1.7. Fig. 18 shows the simulated TOF results of the echo model of the plane at the distance of 125 cm. At this distance, the echo intensity is still strong but not as strong as that for the 100 cm case. Therefore, the extent of flat portion reduces slightly. Furthermore, as the echo intensity decreases with increasing distance, the effect of the first side-lobe also reduces. In other words, the range of agreement between the simulated and the measured results extends outwards slightly. For the plane at the distance of 180 cm, the parameters of the echo model are Amax is about 52 dB, k is about 0.99, very close to 1, and rp is about 4.1. Fig. 19 is the simulated TOF results of the echo model of the plane at the distance of 180 cm. As shown in the figure, because of the obvious increase in distance and reduction in intensity, the pattern has changed from a U shape to a V shape. Furthermore, Fig. 16. The echo model of the plane at 100 cm.
4.2. Simulation results The echo models are deduced by the regression analysis of the measured delay times. Fig. 16 is the echo model of the plane at the distance of 100 cm. Assuming s ¼ 1, then the maximum amplitude Amax is about 50 dB. Furthermore, k is about 0.55 and rp ¼ 1:5. Fig. 17 is TOF simulation results corresponding to Fig. 16 for the plane at the distance of 100 cm. The echo intensity is stronger because the distance is relatively short. Thus, the flat portion ranges from 10° to +10°. From about 13° to +13°, the agreement between the simulated results and the measured ones is good. But beyond these two angles, there are large discrepancies. These discrepancies are due to the effects of the first side-lobe. Their effects are not considered in the present echo model. When the plane is at the distance of 125 cm, the values of parameters of the echo model are Amax ¼ 52 dB, k is
Fig. 18. TOF Simulation results of the plane at 125 cm.
Fig. 17. TOF Simulation results of the plane at 100 cm.
Fig. 19. TOF Simulation results of the plane at 180 cm.
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both sides of the TOF pattern rise rapidly as the intensities are not affected by the first side-lobe. The experimental results show that when the distance increases from 100 to 200 cm, the variations of the maximum amplitude Amax , the fixed factor k and the intensity factor rp are from 50 to 55 dB, 0.5 to 1, and 1.5 to 4.5, respectively. 5. Conclusions The most often used information of a sonar sensor is the time-of-flight (TOF). On the other hand, there are numerous situations that will need the information of echo intensity. In order to measure the echo intensity, an ADC circuit or a DAQ card is usually required and may need a high speed processor such as a DSP to process the huge amount of measured data. In this paper, a simple Jump-U sonar echo model is proposed for Polaroid 6500 series sonar ranging module utilizing TOF data only. From the measured TOF data of the sonar sensor, and the relation between delay time and bearing angle, an echo model is obtained by data regression calculation. The experiments show that the simulation result is very close to the measured data. In other words, the model is very accurate and can be used to replace the actual echo intensity measurement for obstacle avoiding or map building of robots. References [1] Borenstein J, Koren Y. Obstacle avoidance with ultrasonic sensors. IEEE Trans Robot Autom 1988;4:213–8. [2] Barshan B, Kuc R. A bat-like sonar system for obstacle localization. IEEE Trans Syst Man Cyb 1992;22:636–46.
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