O AUV +a <VIC>- sign (a <VIC>)-900 '<VIC> = p<VIC>. sin(a <VIC> )
Where: x ' t<VIC>, y' t<VIC> - object position on the video camera image; AxVIC, AyVIC - onboard camera position; G(^) - turn-matrix of coordinate system to an angle
It is necessary to note that video recognition system does not guarantee reliable results due to noisy objects can be present on images (starfishes, alga, stones, sea garbage and so on) or inspected object can be invisible (buried or hidden by other objects). The probability pt<vic> of correct recognition depends on identified length and direction of the line on the image. If line is long and lies down in appropriate direction then probability is high. Video imaging complex contacts and cable existence probability function during object inspection mission are shown on fig. 2.
2.2 Electromagnetic searcher for metallic cable and pipeline recognition
Metallic communications (e.g. cables and pipelines) can be detected on the basis of electromagnetic methods.
EMS operation is based on electromagnetic field excitation in a water column and environment reaction measurement on this field (Kukarskih & Pavin, 2008). Electromagnetic Searcher (fig. 3) consists of three pairs of transmitting Ao, Ai, A2 and receiving Bo, Bi, B2 dipole antennas (TX- and RX- antennas) formed by corresponding electrodes A1A2 '-A1A2", Ai '-Ai", A2 '-A2" and Bi B2 '-Bi'BJ', Bi -Bi", B2 '-B2" (electrodes of antennas Ao and Bo are paired).
TX-dipole antennas directed at a sharp angles a0, ai, a2 with AUV longitudinal axis. Angles of RX-antennas (Po, Pi, P2) fitted so that transmitting electromagnetic field do not influence to corresponding RX-dipoles (mutual TX- and RX- antennas angles differ from 90° because of the field distortions by AUV shape). Such approach allows metallic object detection at any attack angle of the vehicle and the object.
Fig. 3. Electrodes arrangement of EMS
Fig. 3. Electrodes arrangement of EMS
Thus, alternately excite dipoles An (n=0,1,2) the current In will be induced in the object:
Where: y - angle between AUV longitudinal axis and lengthy metallic object; p - distance from the center of electrode system up to object; RAn(p) - function of dependence of the current induced in a metallic object (by antenna An) from distance up to it; IAn - the current in dipole An; KAn - the constant coefficient dependent on AUV constructive properties, antenna An and electromagnetic properties of metallic object.
RX-antenna Bn measure potential difference Un during transmitting of corresponding antenna An. Electrical field lines (induced in a metallic object) are directed along the lengthy object, because of this the potential difference Un on antenna Bn depend on the following laws:
Where: RBn(p) - potential difference function for antenna Bn (depend of distance from object); KBn - the constant coefficient characterizes antenna Bn.
Metallic object detection problem consist of calculation next two values: 9 - object direction angle (fig. 3) and v - object vicinity to AUV (object existence probability assessment near the underwater vehicle). Value 9 obtained by adding AUV heading (in absolute coordinate system) 9AUV and AUV-object mutual angle y: 9 = 9AUV + y. Using (5) & (7) and replace Rn(p) = lAn ■ RAn(p) ■ RBn(p) (n=0,1,2) the next system of equations can be obtained for synchronous detected potential difference Un:
Using equation (9) with n=1,2 and the fact that Ri(p)^R2(p)^R(p) (because Aj-Bj and A2-B2 is symmetrical, see fig. 3) the next solving relatively y can be obtained:
Where: a = U1 • (sin a2 • sin p2) - U2 • (sin a1 • sin p1), b = U1 • (sin a2 • cos p2 + cos a2 • sin p2) - U2 • (sin a1 • cos p1 + cos a1 • sin p1), c = U1 • (cos a2 • cos p2) - U2 • (cos a1 • cos p1). The next situations can be during calculating (11):
1. Equation (11) haven't real roots. It means that lengthy metallic object does not exist near the AUV (v=0).
2. Equation (11) have one or two real roots. The root Rn(p)>0 (n=0,1,2) will be chosen. Object vicinity v can be estimated basing on Rn(p) values calculated from (9). Each Rn(p) (n=0,1,2) has maximum value when AUV situated over the metallic object. Besides, sensitivity of each transmitting-receiving electrode system An-Bn depends of angle y (11). Using weighted sum of Rn(p) with corresponding weights | cos(y-an)-cos(y-pn) | for v calculation, the next equation is produced:
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