MLS based Distributed, Bearing, Range and Posture Estimation for Schools of Submersibles

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1 ISER 6, Brazil (authors manuscript o not istribute) base Distribute, Bearing, Range an Posture Estimation for 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 Continuous relative localization among all local members of a school of submarines is an essential pre-conition for istribute motion control. Exploiting the short-range, unerwater electromagnetic as well as the acoustical channel, the propose approach elivers sufficient bearing, range an posture estimations base on local sensing in small, autonomous submersibles with limite energy capacities an computational resources. This research is part of the Serafina project at the Australian National University, aiming for large schools of autonomous unerwater vehicles. Results of a number of physical experiments are presente which tests for precision, sensing range, interference robustness, an motion sensitivity. 1. Motivation In orer for unerwater vehicles to behave as a swarm each member nees to know the positions an orientations of at least its near neighbours. The Serafina project ([1], [2], [1]) aims to have many small submersibles (about 5 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 requires a high egree of flexibility as the spatial configuration changes frequently an fast. The research is motivate by the nee for a small, low-cost unerwater localization an posture estimation system for the Serafina submersibles. The initial experiments presente in [7] showe that it is feasible to use an acoustic base system in orer to achieve this objective. In this paper we further refine the techniques use an present results of more real worl experiments conucte in the outoor testing pool an in the Lake Burley Griffin Parts of this project are supporte by Avance Technology Systems Australia (ats, Newcastle, NSW, Australia 2. Technical approach Bearing Estimation figure 1: Serafina MkII The metho introuce in [7] uses wie-ban acoustic signals which are transmitte from small Serafina submersibles an receive on multiple 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 cross-correlating the receive signal channels (figure 7) an etecting the peak in the correlation curve. The relative bearing estimate of the soun source is given by: θ e θ 2 δ 2 e = ±atan δ 2. Lake Burley Griffin is a lake with an approximate surface area of 6.64 km 2 situate in the centre of Canberra. (1)

2 2 Section: Technical approach y 2 x 2 a weighte average epening on the actual positioning of the receivers on the submersible. R 1 y 1 where enotes the istance between receivers. The ± sign in (1) enotes the front/back ambiguity arising in a two (omniirectional) receiver setup. This problem is overcome by using multiple receiver pairs, or as in the presente experiments, employing irectional hyrophones. Range Estimation The information receive from the long wave an optical communication moules of the Serafina [3] is fuse with the acoustic measurements to calculate the range information. The pulses of the acoustic localization system are synchronise to the omnicast scheule introuce in [3] an simultaneously transmitte with the long wave raio packets. On the receiving vehicles, the arrival time of the electromagnetic signal t e an the acoustic signal t a gives the ifference in the arrival times as t r : t r = t a t e (2) Consiering the acoustical propagation spee v a an electromagnetic propagation spee v e unerwater, the istance to the sening vehicle r can be calculate as follows: r Posture Estimation t r v e v = a v e v a 1 2 x 1 Consecutively sening acoustic pulses from the projectors at the bow an aft ens of the submersible an separately cross-correlating the receive signal pairs to obtain the relevant phase ifferences provies 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 the two en bearing measurements using r figure 2: Bearing an range efinition R 2 (3) Signals In an unerwater environment, acoustic signals are subject to many unesirable phenomena such as noise, faing, reflections, reverberations an multipath propagation [8][9]. However in the setup uner consieration, some problems face by conventional unerwater acoustic communication oes not have an effect ue to the very short ranges an low power use for transmission. After experimenting with a number of ifferent types of acoustic signals, the most esirable characteristics were exhibite by Maximum Length Sequence () signals. signals have a quasi-flat frequency spectrum up to the Nyquist frequency. These signals can be classifie as a type of white noise but are eterministic. Therefore it can be reprouce accurately. The most attractive feature of this type of signals is that they have a single sharp peak at zero in the auto-correlation graph. The theoretical characteristics of maximum length sequences () are well known an explore since the early s [4]. Using ifferent generating polynomials will result in signals of ifferent length an there also can be ifferent signals of the same length. 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 cross-correlation 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 ). signals of egree 6 (length 127) are employe as a compromise which gives a choice of 18 ifferent signal forms of which some show a specifically small maximal cross-correlation. System Overview Figure 3 shows the main components of the bearing, range an posture estimation system. Even though each submersible woul be equippe with both the sening an receiving system, for any given sen-receive event, the sener an the receiver woul be two ifferent vehicles. The lower block represents the sener while the upper block represents the receiver. The longwave raio communication moule is represente as one block an is not iscusse in etail in this paper.

3 Section: Experiments & results Longwave Raio Communication System Hyrophones Preamplification A/D Conversion Crosscorrelation 3 Range Estimation Range Estimate Posture Estimation Posture Estimate Bearing Estimation Bearing Estimate Acoustic Signals D/A Conversion Amplification Longwave Raio Signals Longwave Raio Communication System Signal Generation Projectors figure 3: The main components of the bearing, range an 3. Experiments & results Experimental Setup Our current experimental setup employs four Benthos AQ hyrophones, two as receivers an another two as the projectors. Two Serafina mock hulls with acoustic transucers are mounte on a gantry with two arms as shown in figure 4. The gantry is either place on top of the outoor testing pool (iameter: 4.2m, epth: 1.5m, meium: freshwater) immersing the hulls 1m unerwater or connecte to the en of a pier on the Lake Burley Griffin. This setup restricts the motion to one plane an therefore one pair of receiving hyrophones separate by a istance =.3 m is sufficient. can rotate at constant low velocities (.5-1.rpm). Varying the supply voltage of the motor varies the angular velocity ω.the Serafina hull with the sening hyrophones can is also connecte to the gantry arm with a shaft that can be arbitrarily oriente on the plane to suit the experiment. The istance r between the sening an receiving apparatus can be ajuste. The maximum separation for the experiments conucte so far have been limite by the physical size of the testing pool an the with of the pier on the lake. The mock hulls use in this setup is shown in figure 5. A acoustic pulse train is sent out repeately from the projectors while the receiving hyrophones are being rotate aroun its shaft axis a 1. The pulse train consists of length 127 signals an khz marker signals (figure 6). The signals arriving at the hyrophones are capture an recore for off-line analysis. The frequency of the marker signal is selecte to be the resonance frequency of the hyrophones. This provies istinct markers for slicing the long recore signal in to many small signal segments containing one pulse per channel. These signal segments are use as inputs for the cross-correlation using the algorithm given in [6]. The Serafina mock hull with the receiving hyrophones is connecte to the gantry arm with a shaft that is mounte on a geare DC electric motor which a1 a2 Receivers Seners figure 4: Experimental setup figure 5: Serafina mock hulls with the acoustic transucers

4 4 Section: Experiments & results.9 ms 1.3 ms 1. khz. 13 ms 8 ms 13 ms khz khz khz khz khz 1. figure 6: Employe outgoing pulse train structure The igital-to-analog conversion for the outgoing signals an analog-to-igital conversion for the incoming signals are implemente on a synchronize 24-bit 96kHz sampling evice connecte to a notebook computer. This sampling frequency gives a signal uration of approximately 1.3ms an a gap of about 12ms 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. As the receiving hull is rotate ( θ : 1 ) the inuce phase shift δ at the receiving hyrophone pair is given by: δ = ( rsinθ ) 2 + rcosθ ( rsinθ ) 2 + rcosθ where is the istance between the receiving hyrophones an r is the istance between the sener an the receiver. The phase shift (in sample points) between the channels is obtaine by searching for the peak in the cross-correlation plot (figure 7). 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 is improve to.35 (for static measurements). In general the minimum achievable angular resolution (in the ynamical case moving submersibles) R min is given by: R min = ω f E (5) Where ω is the angular velocity of the rotating receiver an the estimate sampling rate. f E (4) c) figure 7: an c) represent the receive signals normalize amplitues over the samples; shows the cross-correlation result over the sample-shift, corresponing to bearing θ = 1 (actual bearing estimation θ e = in this measurement; an in general θ < 8 ). θ e The position on the x-axis (in sample points) which correspons to the peak in the correlation plot is relate to the actual phase shift δ (in metres) by: xv δ = a (6) f S where f S is the sampling frequency (96kHz in the current experiments) an v a is the spee of soun in water ( ms 1 as calculate by Mackenzie s [5] nine-term equation with parameters T = 18 C, D = 1. m an S =.73 ). Experimental Results Many experiments with ifferent r values an ifferent angular velocities were conucte both in the test pool an the lake. Each cross-correlation of the two channels in a signal segment constitutes a measurement an yiels one bearing estimate. Each experiment consists of a series of such measurements obtaine while the receiving hull is rotate at a uniform angular velocity proucing a series of such bearing estimates. The presente graphs plot the calculate bearing estimate against the series of measurements. Figure 8 an 9 shows plots of two experimental runs

5 Section: Experiments & results Sample points Sample points Estimete bearing (egrees) 1 1 Estimete bearing (egrees) figure 8: r =.8 m, Clockwise rotation; measure phase shift x over the series of measurements; estimate bearings with error margin over the series of measurements figure 9: r =.8 m, Anti-clockwise rotation; measure phase shift x over the series of measurements; estimate bearings with error margin over the series of measure- in the test pool with r =.8 m for clockwise an anti-clockwise rotation. The top graphs show the phase shift x (in sample points) over the series of measurements while the bottom graphs shows the estimate bearings over the series of measurements. Figure 1 gives another pair of graphs which plots the estimate bearings over the series of measurements showing clockwise an anti-clockwise rotation in the test pool with r = 2.4 m. Figure 11 gives a pair of graphs which plots the estimate bearings over the series of measurements showing clockwise an anti-clockwise rotation in the lake Burley Griffin with r = 1.5 m an r = 2.2 m. In all the test pool experiments, the receiving hull was rotate by 1 while the rotation was only in the lake experiment presente in figure 11. This was ue to obstruction by the pier. The symmetry of the clockwise an anti-clockwise plots isplays the repeatability of measurements an also reveals some features of the environment. The breaking off of the almost linear plots at certain points suggests strong reflections off the environment. In the test pool, the reflections are suspecte to be off the pool wall while in the lake figure 11.a shows a strong reflection off the pier while figure 11.b shows soft reflections which are probably ue to the unerwater plants in close proximity to the pier. Analysis of Results The non-linearity of the sening an receiving transucers seem to have a etrimental effect on original signals introucing a high pass filtering with (figure 12) ue to the resonance of the AQ hyrophones. As receivers, these hyrophones have a flat frequency response from DC to approximately 1kHz, but as projectors, they are most efficient near its resonance frequency ( f C khz ). However, still the cross-correlation 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 consiering the uncertainties for all quantities involve an substituting (6) in (1); δ = ±.1 m, δr = ±.1 m, δv a = ± 1ms 1, δ f S = ±. Hz the

6 6 Section: Conclusions Estimete bearing (egrees) Estimete bearing (egrees) Estimete bearing (egrees) Estimete bearing (egrees) figure 1: Estimate bearings over the series of measurements obtaine at the test pool; r = 2.4 m, Clockwise rotation; Anti-clockwise rotation; figure 11: Estimate bearings over the series of measurements obtaine at the lake; Clockwise rotation with r = 1.5 m ; Anti-clockwise rotation with r = 2.2 m ; following error formula for the estimate bearing is obtaine: x δθ e = ± (7) x 2 π This translates to a maximum nominal error boun of ± 8 for θ e 1. In figure 8.a an 9.a the soli re curve epicts the ieal variation of x as θ is varie. In figure 8.b an 9.b 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 it can be observe from these plots, the resulting bearing estimates lie well within the error bouns for most of the measurements. The eviations at the two extremes of can be explaine by examining (1); when δ approaches the uncertainty of θ e approaches ± 1. Furthermore the hyrophones use in this experiment are irectional with an approximate forwar opening angle of 1 within the operating range an frequency. When the arriving signals 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. 4. Conclusions From the results of the presente experiments it can be conclue that this approach can be successfully implemente to measure relative bearing an posture of unerwater vehicles even with the frequency filtering introuce by the sening an receiving hyrophones. While it seems obvious that the achieve resolution an precision can be improve by the employment of more wie-ban, omni-irectional transucers, an higher sampling rates, it is alreay sufficient for the problem at han. In all the experiments, it was note that the bearing estimate plot showe a linear variation with the measurements for at least an opening angle of ( θ e 1 ). Since more than one pair of receivers woul be utilise in the actual implementation on the Serafina vehicle, this result showsjust two pairs of receiving hyrophones coul cover the full fiel of 3 aroun each vehicle on a plane. Three pairs woul exten measurements to cover all three imensions. Furthermore, in this experimental setup the receiver hyrophones were constantly moving while the measurements were taken in contrast to the stationary hyrophones in the experiments presente in [7].

7 Section: Conclusions 7 This suggests the bearing estimation system is not sensitive to motion. The experimental results obtaine in the lake suggests that the system is robust enough to perform well in a real unerwater environment. 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 which woul be utilise in implementing swarming behavior in schools of submersibles. 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.; Error-Correcting Coes; MIT Press, secon eition, 1972 [5] K. V. Mackenzie, Nine-term Equation for Soun Spee in the Oceans; Journal of the Acoustical Society of America, vol. 7(3), pp , September [6] J. G. Proakis, D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, an Applications, 3 r e., New Jersey: Prentice Hall, 1996, pp [7] Navina Kottege, Uwe R. Zimmer; Acoustic Localization in Schools of Submersibles; Proceeings of the IEEE Oceans 6, Singapore, May 6. [8] Ethem M. Sozer, Milica Stojanovic, an John G. Proakis, Unerwater acoustic networks; IEEE Journal of Oceanic Engineering, vol. 25(1), pp , January. [9] Daniel B. Kilfoyle, Arthur B. Baggeroer; The State of the Art in Unerwater Acoustic Telemetry; IEEE Journal of Oceanic Engineering, vol. 25(1), pp. 4-27, January. [1] b ) c) ) si gnals (outgoing) si gnals (incoming) figure 12: Actual signal sent out an the corresponing signals receive by the hyrophones