Acoustical Localization in Schools of Submersibles

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1 Oceans 6, Singapore (authors manuscript o not istribute) Acoustical Localization in Schools of Submersibles Navina Kottege & Uwe R. Zimmer Research School of Information Sciences an Engineering Autonomous Unerwater Robotics Research Group The Australian National University, ACT, Australia 1 navina.kottege@anu.eu.au uwe.zimmer@ieee.org Most forms of swarm coorination require frequently upate relative position an posture information about at least all near neighbours. The Serafina project [1][2] consiers comparatively small submersibles (4cm in lengths) but in large numbers. This imposes constraints in terms of size an energy consumption of the components. It also requires high egrees of flexibility as the school configuration changes frequently an fast. This article suggests a lowcost localization metho which involves the communication system [3] an fuses information on the longwave raio ban with wieban acoustic reaings in orer to generate range, bearing, an posture estimates of all surrouning submersibles, i.e. all submersibles in sensing range. (maximum lengths sequence) signals are employe for high interference robustness an eployability even in cluttere environments which usually impose multiple specular reflections an possible resonance effects. A number of physical experiments are iscusse which tests for precision, sensing range, interference robustness, an motion sensitivity. All those experiments refer to interschool localization. Absolute localization (with respect to external, global lanmarks) nee only to be solve for one of the submersibles in the school (as all internal, relative locations are known) an is not iscusse in this article. 1. Introuction In robot swarming each iniviual nees to know the positions an orientations of at least its near neighbours. The Serafina project ([1], [2]) aims to have many small submersibles (about 4 cm in length) in large schools. While the small size imposes constraints in terms of size an energy consumption of the components the swarming behavior require 1. Parts of this project are supporte by Avance Technology Systems Australia (ats, Newcastle, NSW, Australia high egrees of flexibility as the spatial configuration changes frequently an fast. The research is motivate by the nee for a small, lowcost unerwater localization, an posture estimation system for the Serafina submersibles. In swarm context, localization usually refers to relative localization an the propose system estimates relative bearing an can be extene to estimate relative posture as well. 2. Bearing an Posture Estimation Bearing Estimation The propose metho uses wieban acoustic signals which are transmitte from the small Serafina submersibles an receive on up to six miniature hyrophones on each neighbouring submersible enabling estimation of bearing an posture as seen from those neighbouring Serafinas. The relative bearing of the sening submersible can be calculate by measuring the phase shift of the receive signal channels. The phase shift δ is obtaine by crosscorrelating the receive signal channels (figure 5) an etecting the peak in the correlation curve. The relative bearing estimate θ e of the soun source is given by: ( 4r θ 2 δ 2 )( 2 δ 2 ) e = ±atan (1) δ 4r δ 2 where enotes the istance between receivers, r the raial istance to the source. When r» (for practical purposes r 2 satisfies this conition) the above equation can be approximate by the much simpler form below: δ θ e = ±atan (2) 2 δ 2 The ± sign in (1) an (2) enotes the front/back ambiguity arising in a two (omniirectional) receiver setup. This problem can be overcome using multiple

2 2 Section: CrossCorrelation of signals y 2 x 2 y 1 R 2 θ r Projectors θ 1 θ 2 x 1 R 1 Hyrophones Autonomous Submersibles (Serafina mark II) figure 2: Serafina school of autonomous submersibles receiver pairs, or (more biologically motivate) by employing irectional hyrophones an tracking soun sources. While crosscorrelation of receive signals will eliver the relative bearing, there is still no estimation of ranges. In fact, for very near neighbors (when r < 2 ), accoring to (1) the range r is require in orer to prouce the bearing estimate. However, in most cases (2) is sufficient to obtain the bearing estimate. Range Estimation: Fusing LongWave Raio with Acoustic Reaings One way of obtaining range information woul be to go back to common methos of reflective measurements which woul require significantly higher energies. If on the other han the actual sening point in time (on a ifferent submersible) coul be etecte by some other means then the simple ifference between sening an receiving time gives a linear measurement of range. Fortunately this is supplie by other moules of the Serafina communication system which inclues longwave raio an optical communication channels. Synchronizing the acoustical with the optical an longwave raio transucers results not only in a precise range measurement, but also reuces (or eliminates) crosstalk as the communication channels (while having similar broacast ranges) are controlle by a locally collision free scheule. This is implemente by means of the ynamical istribute omnicast routing metho as introuce in [3]. Posture Estimation figure 1: Bearing an range efinition By consecutively sening signals from the projectors at the bow an aft ens of the submersible an separately crosscorrelating the receive signal pairs to obtain the relevant phase ifferences will provie two bearing estimates for the two ens of the vehicle. Combining the range information with this gives the posture/orientation of the sening submersible. The main bearing measurement can be erive from of the two en bearing measurements using a simple weighte average epening on the actual positioning of the receivers on the submersible. 3. CrossCorrelation of signals Maximum Length Sequence () signals are employe to prouce the wie ban acoustic signals. It has high interference robustness an provies eployability even in cluttere environments which usually impose multiple specular reflections an possible resonance effects. The theoretical characteristics of maximum length sequences () are well known an explore since the early 6 s [4]. However the resulting characteristics of mixe multiple signals unerwater, transmitte with highly nonlinear transucers in moving water with many specular reflections from the environment can still not be fully theoretically aresse. Signals of arbitrary egree can be generate using a computer program evelope by us. The egree n of the signal governs the length l of the sequence as l = 2 n The length of the sequence an the employe sampling rate of the igital to analog converter etermines the uration of the outgoing signal. Even though longer signals give better resolution of the crosscorrelation peak resulting in higher precision of the estimate bearing, the longer uration has its rawbacks. They are: unesirable echoes in cluttere or enclose environments, higher processing overhea, smaller frequency of estimates ( f E ). As a compromise signals of egree 6 (length 7) are employe which gives a choice of 18 ifferent signal forms of which some show a specifically small maximal crosscorrelation.

3 Section: Experiments 3 4. Experiments Experimental Setup Our current experimental setup employs two Benthos AQ hyrophones as receivers an two Auiowell AU555 piezoelectric transucers as the projectors. Two Serafina hulls with acoustic transucers are mounte on a gantry with an arm that can be rotate (figure 3). The whole gantry is place on top of our circular outoor pool (iameter: 4.2 m, epth: 1.5 m, meium: freshwater) immersing the Serafina hulls 1m unerwater. This setup restricts the motion to one plane an therefore two receiving hyrophones separate by a istance =.36 m are sufficient. With the hyrophones mounte on the Serafina hull on the centre, the transucers on the Serafina hull mounte on the gantry arm sens out a continuous acoustic pulse train while being rotate aroun the centre axis a 1. The pulse train consists of length 7 signals an 3kHz marker signals (figure 4). The signals arriving at the hyrophones are capture an recore for offline analysis. The igitaltoanalog conversion for the outgoing signals an analogtoigital conversion for the incoming signals are implemente on a synchronize bit 96 khz sampling evice connecte to a notebook computer. This sampling frequency gives a signal uration of approximately 1.3ms an a gap of about ms between the pulses an the marker signals is employe to ensure that all the reverberations off the pool walls have sufficient time to ecay. Two consecutive pulses have a gap of aroun 8ms which translates to a maximum estimate sampling rate of f E = 4.8 Hz. A geare DC electric motor attache to the sie wall of the pool is use to move the gantry arm with a constant angular velocity such that the transmitting Serafina makes a arc aroun the stationary receiving Serafina. Using this setup, the raial istance a 1 AQ Hyrophones AU555 Transucers θ a 2 figure 3: Experimental setup r (within constraints impose by the size of the pool) between the sener an the receiver as well as the angular velocity ω at which the gantry is rotate can be varie. As the gantry is rotate ( θ : 1 17 ) the inuce phase shift δ at the receiving hyrophone pair is given by: δ = ( rsinθ ) 2 + rcosθ + (3) 2 2 ( rsinθ ) 2 + rcosθ 2 2 where is the istance between the receiving hyrophones an r is the raial istance between the sener an the receiver. Equation (3) is the inverse function of (1). The receive signals were recore an the 3kHz marker signal was use to slice the pulse train in to segments containing only the pulse. Each of the two channel pulses were crosscorrelate using the algorithm given in [6]. The phase shift between the channels is obtaine by searching for the peak in the crosscorrelation plot (figure 5). A cubic spline interpolation is use to interpolate peaks which lie in between sample points. By using an interpolation step of.1 samples the minimum achievable resolution coul be improve close to.35 (for static measurements). In general the minimum achievable angular resolution (in the ynamical case moving submersibles) R min is given by: ω R min = (4) f E The position x (in sample points) of the peak in the correlation plot is relate to the actual phase shift δ (in metres) by: xv δ = (5) f S where f S is the sampling frequency (96kHz in our experiments) an v is the spee of soun in water ( ms 1 as calculate by Mackenzie s [5] nineterm equation with parameters T = 18 C, D = 1. m an S =.73 ). Experimental Results A number of experiments with ifferent r values an ifferent angular velocities were conucte. For comparison, results obtaine in two ifferent experimental runs are inclue. Figure 7.b shows the phase shift x vs. samples an figure 7.a bearing estimate vs. samples for r = 1.4 m, ω = 3.2 s 1 which gives R min =.67. Figure 8 shows the same measurements for r = 1. m, ω = 6. s 1 which gives R min = 1.25.

4 4 Section: Conclusions.9 ms 1.3 ms (1)); δ = ±.1 m, δr = ±.1 m, δv = ± 1ms 1, δ f S = ±. Hz the following error formula for the estimate bearing is obtaine: c) 3kHz khz 3kHz 13 ms 8 ms 13 ms 3kHz 3kHz 3kHz figure 4: Employe outgoing pulse train structure figure 5: an c) represent the receive signals normalize amplitues over the samples; shows the crosscorrelation result over the sampleshift, corresponing to bearing θ = 1 (actual bearing estimation θ e = in this measurement; an in general θ < 8 ). θ e c δθ 1 + c 2 x 2.18 e = ± c 3 c 4 x 2 π with c 1 = c 2 = c 3 = c 4 = (7) This translates to a maximum nominal error boun of ± 8 for 6 θ e 1. In figure 7.b an figure 8.b the soli re curve epicts the ieal variation of x as θ is varie. In figure 7.a an figure 8.a the ashe blue line epicts the ieal variation of θ e while the two ashe re curves enote the maximum error boun corresponing to θ e ± δθ e. As can be observe from these plots, the resulting bearing estimates lie well within the error bouns for most of the range. The eviations at the two extremes of the range can be explaine as follows; The hyrophones use in this experiment are irectional with an approximate forwar opening angle of 1 within the operating range. When the sening projectors reach the sensitivity bounary of the receiving hyrophones, the probability of one or both of them etecting a signal bounce off the pool wall instea of the irect signal increases. 5. Conclusions From the obtaine results we conclue that this approach can be successfully implemente to measure relative bearing an posture of unerwater vehicles even with highly nonlinear projectors an hyrophones. While it seems obvious that the achieve resolution an precision can be improve by the employment of more wieban, omniirectional transucers, an higher sampling rates, it is alreay sufficient for the problem at han: relative spatial es (6) Analysis of Results The nonlinearity of the sening an receiving transucers seem to have a etrimental effect on original signals introucing a high pass filtering with f C 32 khz (figure 6). However, still the crosscorrelation of the receive signals provies the bearing information with lowere precision. The introuce frequency filtering results in an uncertainty of x ( δx ) of approximately ±3 samples. By consier the uncertainties for all quantities involve (substituting (3) in c) ) signals (outgoing) signals (incoming) figure 6: Actual signal sent out an the corresponing signals receive by the hyrophones

5 Section: Conclusions figure 7: r = 1.4 m ; estimate bearings with error margin; measure phase shift x over samples set figure 8: r = 1. m ; estimate bearings with error margin; measure phase shift x over samples set timations in ynamical schools of submersibles. However the extension to three imensional measurements, i.e. the utilization of more than two microphones still nees to be one. Other experiments an extensions which will be implemente in close future inclue: Measurement of the ratio of employe energy to achievable minimum error an maximal range with respect to bearing as well as the control of a boune range for the acoustical base estimations. A boune range is in fact essential for scaling up to larger schools of vehicles as otherwise multiple measurements in the same school coul not take place without interference. The Serafina project will incorporate the results presente here an integrate these estimates into the existing an further evelope control an communication concepts. Specifically the close integration between communication an position estimation layers into more spatially oriente forms of communication will be essential for future large submersible school applications. References [1] Shahab Kalantar, Uwe R. Zimmer; Control of Open Contour Formations of Autonomous Unerwater Vehicles; International Journal of Avance Robotic Systems, Dec. 5 [2] Shahab Kalantar, Uwe R. Zimmer; Distribute Shape Control of Homogeneous Swarms of Autonomous Unerwater Vehicles; to appear in Autonomous Robots (journal) 6 [3] Felix Schill, Uwe R. Zimmer; Distribute Dynamical Omnicast Routing; to appear in Intl. Journal of Complex Systems 6 [4] W. Wesley Peterson, E.J. Welon, Jr.; ErrorCorrecting Coes; MIT Press, secon eition, 1972 [5] K. V. Mackenzie, Nineterm Equation for Soun Spee in the Oceans; Journal of the Acoustical Society of America, vol. 7(3), pp. 878, September [6] J. G. Proakis, D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, an Applications, 3 r e., New Jersey: Prentice Hall, 1996, pp