CN104820430B - A kind of AUV based on dipole potential field returns depressed place guidance system and guidance method - Google Patents

Abstract

Depressed place guidance system and guidance method are returned the present invention relates to a kind of AUV based on dipole potential field, it is characterised in that the head of AUV is provided with USBL transceivers, two USBL transponders are installed in the both sides of recycle bin；AUV is using the measurable transponder of transceiver in AUV body coordinate systems x_Bo_By_BUnder distance and bearing；Coordinates of the AUV in the case where coordinate system xoy is reclaimed is calculated according to distance and bearing, and based on dipole potential field principle, obtains the desired course angle instruction that AUV goes back to depressed place；AUV is navigated by water using self adaptation non-singular terminal sliding-mode control control AUV with desired course angle, realizes back that depressed place guides.The method can directly calculate coordinates of the AUV in the case where coordinate system is reclaimed.Then enter recycle bin along recycle bin axis direction using the dipole potential field guiding AUV for setting up, the method is simple, and amount of calculation is smaller so that the error very little during time depressed place between actual heading angle and command heading angle, return depressed place effect and return depressed place algorithm better than other.

Description

A kind of AUV based on dipole potential field returns depressed place guidance system and guidance method

Technical field

Docking technique field is reclaimed the invention belongs to submarine navigation device, and in particular to a kind of AUV based on dipole potential field is returned Depressed place guidance system and guidance method.

Background technology

AUV (Autonomous Underwater Vehicle) as a kind of delivery vehicle autonomous under water, by itself institute The energy navigation of carrying, can complete the tasks such as subaqueous survey, article delivery, in military ocean surveillance, marine environmental monitoring, oil field The fields such as exploration play the role of important.AUV performs the limited energy carried during task, for the AUV of long working, it is necessary to AUV is laid and reclaimed by operation lash ship in the region of the task of execution, to complete the supplement energy, reading information, dimension The work such as shield guarantee.In order to improve operating efficiency, there has been proposed the voluntary recall system under water of AUV, voluntary recall is controlled Through one of study hotspot as current ocean engineering field.

At present, AUV returns depressed place guidance method and mainly has：

(1) depressed place guidance method is returned based on horizontal tracing control.The axis that the method is reclaimed firstly the need of one AUV of definition Line, then AUV controlled AUV to be navigated by water along axis according to the distance between current location and axis deviation, finally realize AUV Recovery.The major defect of the method is the situation for being not suitable for initial position in side or rear, is not also suitable for the dynamic of AUV Reclaim.

(2) depressed place guidance method is returned based on Artificial Potential Field.The method uses traditional Artificial Potential Field Method, and producing one can arrive Nothing up to recycle bin touches air route, then controls AUV to navigate by water down an airway, so as to realize the recovery of AUV.The major defect of the method is There is a problem that local minimum point, i.e. AUV are subject to gravitation and repulsion simultaneously when near recycle bin, may be with joint efforts zero, one Denier AUV is absorbed in local minimum point and the unreachable problem of recycle bin just occurs, and the phenomenons such as path jitter easily occur in narrow zone.

(3) AUV based on fuzzy theory reclaims movement technique.It is according to the basis of fuzzy control theory and right according to controlling As the characteristics of, formulate fuzzy control rule, design fuzzy controller, the recovery motion process to AUV is controlled.The method Major defect be fuzzy control rule acquisition and input fuzzy variable domain and membership function establish a capital really be experiment point Analysis collects with operating personnel's experience, is influenceed larger by artificial subjective factor.

The content of the invention

The technical problem to be solved

In order to avoid the deficiencies in the prior art part, the present invention proposes that a kind of AUV based on dipole potential field goes back to depressed place guiding system System and guidance method.

Technical scheme

A kind of AUV based on dipole potential field returns depressed place guidance system, it is characterised in that including USBL transceivers and two USBL Transponder；USBL transceivers are arranged on the central axis of the head of AUV, and two USBL transponders are arranged at the two of recycle bin Side；Described two USBL transponders are electric dipole.

AUV based on dipole potential field described in a kind of utilization claim 1 returns the method that depressed place guidance system guiding AUV goes back to depressed place, It is characterized in that step is as follows：

Step 1：AUV is in the case where coordinate system xoy is reclaimed from initial point X (0)=［ x0 y0 ］^TStarted with initial heading angle ψ (0) Carry out back depressed place guiding；Wherein：X, y are position coordinateses of the AUV in the case where coordinate system is reclaimed, and (x (0), y (0)) is in the advance of AUV navigation Row setting；The recovery coordinate system xoy is the two USBL transponders B installed with the both sides of recycle bin₁And B₂Center for original Point, two USBL transponders B₁And B₂Between line be y-axis, horizontal vertical is in y-axis and to cross origin be x-axis；

Step 2：The USBL transceivers and the transponder B of recycle bin both sides installed on AUV₁And B₂Communicated, measuring should Answer device B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder apart from L_iAnd orientation μ (i=1,2)_i(i=1,2)；

Step 3：Calculate transponder B₁And B₂In position coordinates B_i(x_Ti,y_Ti), i=1,2：

Step 4：According to electric dipole principle of electric field, electric dipole moment vector is definedResponse The position coordinates at device midpoint isDue to the entry vector of recycle binWithVertically, then

Step 5：Calculate AUV body coordinate systems x_Bo_By_BAnd the angle between AUV recovery coordinate systems xoy：

B_i(x_Ti,y_Ti) i=1,2 is transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates；

Step 6：Calculate position coordinateses of the AUV in the case where coordinate system xoy is reclaimed：

Step 7：Define dipole potential fieldIt is one to locate in addition to origin Locate the two-dimentional vector field of non-zero, wherein, constant λ >=2, p=[p_x p_y]^ΤIt is the electric dipole moment of dipole potential field, n is dipole potential field Position vector.The characteristics of dipole potential field is maximum is motion the cutting all along potential field line at any point in dipole potential field space Line direction；

Position coordinates of two transponders in the case where coordinate system xoy is reclaimed is respectively p₁=p_1x,p_1yAnd p₂=p_2x,p_2y, then it is electric Dipole moment p=p_2x-p_1x,p_2y-p_1y ^T；

Because position vectors of the AUV in dipole potential field is n=[x y]^Τ, then dipole potential field be

F_nx=(λ -1) (p_2x-p_1x)x²+λ(p_2y-p_1y)xy-(p_2x-p_1x)y²

F_ny=(λ -1) (p_2y-p_1y)y²+λ(p_2x-p_1x)xy-(p_2y-p_1y)x²；

Step 8：According to the dipole potential field that step 7 is defined, formula determines that the course angle instruction that AUV is reclaimed is：

Step 9：Course angle instruction ψ according to step 8_d, using self adaptation non-singular terminal sliding-mode control to course Angle is tracked control, and selection rudder angle is：

Wherein,U, v, ω are respectively the forward direction speed of AUV under body coordinate system Degree, side velocity and course angular speed, m₁₁、m₂₂And m₃₃It is inertia coeffeicents of the AUV comprising additional mass, d₁₁、d₂₂And d₃₃It is AUV Hydrodynamic damping coefficient, N_σIt is AUV yawing moment coefficients.β, η are for constant and η ＞ 0, β ＞ 0, p ＞ q ＞ 0 and for strange Number,x₀It is the modeling indeterminate upper bound,It is x₀Estimate, q₀＞ 0 is adaptive gain；

Step 10：If AUV is less than given acceptable error with the distance of recovery point, next step is gone to；It is no Then return to step 2；

Step 11：AUV has arrived at recovery point, goes back to depressed place and terminates.

Beneficial effect

A kind of AUV based on dipole potential field proposed by the present invention returns depressed place guidance system and guidance method, USBL transceivers peace Two transponders are mounted with mounted in the head of AUV, on recycle bin, it is easy to obtain coordinate of the transponder under body coordinate system, no Coordinates of the AUV in the case where coordinate system is reclaimed directly is calculated by needing other measurement means again.Then using the dipole set up Potential field guides AUV and enters recycle bin along recycle bin axis direction, and the method is simple, and amount of calculation is smaller so that return during depressed place Error very little between actual heading angle and command heading angle, returns depressed place effect and returns depressed place algorithm better than other.

Brief description of the drawings

Fig. 1：The removal process schematic diagram of AUV

Fig. 2：AUV recovery system figures with double response device

Fig. 3：Coordinate system transition diagram

Fig. 4：AUV navigates by water the ship trajectory figure of process

Fig. 5：Course angle variation diagram during AUV navigation

Fig. 6：The variation diagram of vertical rudder angle during AUV navigation

Fig. 7：Different initial points returns depressed place ship trajectory figure

Fig. 8：Time depressed place ship trajectory figure of different λ values

Specific embodiment

In conjunction with embodiment, accompanying drawing, the invention will be further described：

The present invention proposes that a kind of AUV based on dipole potential field returns depressed place guidance method, as shown in Figure 1, it is characterised in that AUV's Head is provided with USBL transceivers, and two USBL transponders B are installed in the both sides of recycle bin₁And B₂；AUV is measurable using transceiver Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), as shown in Figure 2；Root According to apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), can calculate coordinates of the AUV in the case where coordinate system xoy is reclaimed, and based on idol Pole potential field principle, obtains the desired course angle instruction that AUV goes back to depressed place；Then AUV utilizes self adaptation non-singular terminal sliding formwork control side Method control AUV is navigated by water with desired course angle, final to realize back that depressed place guides.Step is as follows：

Step 1：AUV is in the case where coordinate system xoy is reclaimed from initial point X (0)=[x0 y0]^TStarted with initial heading angle ψ (0) Carry out back depressed place guiding.Wherein, x, y are position coordinateses of the AUV in the case where coordinate system is reclaimed, and (x (0), y (0)) can be before AUV navigation Set.

Step 2：On AUV install transceiver by with recycle bin on transponder B₁And B₂Communicated, can be measured Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), as shown in Figure 2.

Step 3：AUV according to measurement obtain apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), can be calculated using following formula Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti,y_Ti) i=1,2.

In formula, l is distance of the transceiver to AUV centre of buoyancys.

Step 4：As shown in Fig. 2 according to electric dipole principle of electric field, defining electric dipole moment vector The position coordinates at transponder midpoint isDue to the entry vector of recycle binWithVertically, i.e.,

Step 5：As shown in figure 3, according to transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti, y_Ti) i=1,2, AUV body coordinate systems x can be calculated_Bo_By_BAnd the angle between AUV recovery coordinate systems xoy.

Step 6：Position coordinateses of the AUV in the case where coordinate system xoy is reclaimed can be calculated using following formula.

Step 7：Under the inspiration of electric dipole electric field line, dipole potential field is defined

It is a vector field for two dimension, the non-zero everywhere in addition to origin, Wherein, constant λ >=2, p=[p_x p_y]^ΤIt is the electric dipole moment of dipole potential field, n is the position vector of dipole potential field.Dipole potential field is most Big the characteristics of is the tangential direction of the motion all along potential field line at any point in dipole potential field space.Two transponders are in idol Position and electric dipole position consistency in the electric field in the potential field of pole.It is assumed that two transponders are reclaiming coordinate on recycle bin It is the position coordinates respectively p under xoy₁=p_1x,p_1yAnd p₂=p_2x,p_2y, then electric dipole moment p=p_2x-p_1x,p_2y-p_1y ^T.Due to Position vectors of the AUV in dipole potential field is n=[x y]^Τ, then dipole potential field be

F_nx=(λ -1) (p_2x-p_1x)x²+λ(p_2y-p_1y)xy-(p_2x-p_1x)y²

F_ny=(λ -1) (p_2y-p_1y)y²+λ(p_2x-p_1x)xy-(p_2y-p_1y)x²

Step 8：According to the dipole potential field that step 7 is defined, can determine that AUV reclaims the course angle instruction of guiding with following formula.

Step 9：Course angle instruction ψ according to step 8_d, using self adaptation non-singular terminal sliding-mode control to course Angle is tracked control, selects rudder angle

Wherein,U, v, ω are respectively the forward direction speed of AUV under body coordinate system Degree, side velocity and course angular speed, m₁₁、m₂₂And m₃₃It is inertia coeffeicents of the AUV comprising additional mass, d₁₁、d₂₂And d₃₃It is AUV Hydrodynamic damping coefficient, N_σIt is AUV yawing moment coefficients.β, η are for constant and η ＞ 0, β ＞ 0, p ＞ q ＞ 0 and for strange Number,x₀It is the modeling indeterminate upper bound,It is x₀Estimate, q₀＞ 0 is adaptive gain.

Step 10：If AUV is less than given acceptable error with the distance of recovery point, next step is gone to；It is no Then return to step 2.

Step 11：AUV has arrived at recovery point, goes back to depressed place and terminates.

Embodiment one：AUV based on dipole potential field returns depressed place guided procedure：

Step 1：Returning the depressed place stage, AUV carries out go back to depressed place and leads from starting point coordinate (- 100, -100) with 0 ° of initial heading angle Draw, forward speed is u=1m/s.

Step 2：On AUV install transceiver by with recycle bin on transponder B₁And B₂Communicated, can be measured Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), as shown in Figure 2.

Step 3：AUV according to measurement obtain apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), can be calculated using following formula Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti,y_Ti) i=1,2.

In formula, l=3m.

Step 4：As shown in Fig. 2 according to electric dipole principle of electric field, defining electric dipole moment vector The position coordinates at transponder midpoint isDue to the entry vector of recycle binWithVertically, i.e.,

Step 5：As shown in figure 3, according to transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti, y_Ti) i=1,2, AUV body coordinate systems x can be calculated_Bo_By_BAnd the angle between AUV recovery coordinate systems xoy.

Step 6：Position coordinateses of the AUV in the case where coordinate system xoy is reclaimed can be calculated using following formula.

Step 7：λ=2 are taken, the coordinate of two transponders is respectively (0, -0.5) and (0,0.5) on recycle bin, so p= [0 1]^Τ.N=[x y]^ΤIt is the position coordinates of AUV, then dipole potential field is

F_nx=2xy

F_ny=y²-x²

Step 8：According to the dipole potential field that step 7 is defined, can determine that the course angle that AUV is reclaimed is instructed with following formula.

Step 9：Course angle instruction ψ according to step 8_d, using self adaptation non-singular terminal sliding-mode control to course Angle is tracked control, selects rudder angle

Wherein, α₀=-0.524v s^-2,α₁=-2.848s^-1,α₂=-50s², what s was represented is unit second.β=0.5, η= 0.1,x₀It is the modeling indeterminate upper bound,It is x₀Estimate, q₀＞ 0 is adaptive gain.

Step 10：If AUV is less than 0.1 with the distance of recovery point, next step is gone to；Otherwise return to step 2.

Step 11：AUV has arrived at recovery point, goes back to depressed place and terminates.

The ship trajectory figure of AUV navigation processes as shown in figure 4, AUV from initial point (- 100, -100) with 0 ° of initial heading angle Start navigation, recycle bin is entered along recycle bin axis direction using the dipole potential field guiding AUV for setting up.Can from figure Arrive, AUV can be with more smooth track, shorter time navigation to recycle bin under self adaptation non-singular terminal sliding formwork control. The depressed place stage is returned, AUV enters recycle bin along axis.

AUV navigation during course angle variation diagram as shown in figure 5, the error between actual heading angle and command heading angle very Small, error only has 3 degree or so, can complete back depressed place task.

The variation diagram of vertical rudder angle is as shown in fig. 6, the vertically change of rudder angle during depicting navigation during AUV navigation Situation, between ± 20 degree that as can be seen from the figure vertical rudder angle is being limited always, is only proceeding by back when depressed place guides The degree of hard over angle -20 is reached in very short time.

Embodiment two：Consider to enter back the depressed place stage to returning the influence of depressed place process from different initial positions

Step 1：AUV enters back depressed place rank with different initial points (- 20, -20), (20, -20), (- 20,20) and (20,20) Section, initial heading angle is 0 °, and forward speed is u=1m/s.

Step 2：On AUV install transceiver by with recycle bin on transponder B₁And B₂Communicated, can be measured Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), as shown in Figure 2.

Step 3：AUV according to measurement obtain apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), can be calculated using following formula Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti,y_Ti) i=1,2.

In formula, l=3m.

Step 4：As shown in Fig. 2 according to electric dipole principle of electric field, defining electric dipole moment vector The position coordinates at transponder midpoint isDue to the entry vector of recycle binWithVertically, i.e.,

Step 5：As shown in figure 3, according to transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti, y_Ti) i=1,2, AUV body coordinate systems x can be calculated_Bo_By_BAnd the angle between AUV recovery coordinate systems xoy.

Step 6：Position coordinateses of the AUV in the case where coordinate system xoy is reclaimed can be calculated using following formula.

Step 7：λ=2 are taken, the coordinate of two transponders is respectively (0, -0.5) and (0,0.5) on recycle bin, so p= [0 1]^Τ.N=[x y]^ΤIt is the position coordinates of AUV, then dipole potential field is

F_nx=2xy

F_ny=y²-x²

Step 8：According to the dipole potential field that step 7 is defined, can determine that the course angle that AUV is reclaimed is instructed with following formula.

Step 9：Course angle instruction ψ according to step 8_d, using self adaptation non-singular terminal sliding-mode control to course Angle is tracked control, selects rudder angle

Wherein, α₀=-0.524v s^-2,α₁=-2.848s^-1,α₂=-50s², what s was represented is unit second.β=0.5, η= 0.1,x₀It is the modeling indeterminate upper bound,It is x₀Estimate, q₀＞ 0 is adaptive gain.

Step 10：If AUV is less than 0.1 with the distance of recovery point, next step is gone to；Otherwise return to step 2.

Step 11：AUV has arrived at recovery point, goes back to depressed place and terminates.

AUV returns depressed place ship trajectory figure as shown in fig. 7, as seen from the figure with different initial points, although AUV enters back depressed place navigation Initial point it is different, but AUV can enter recycle bin under the guiding of dipole potential field along the direction of recycle bin axis.Thus test The correctness of the algorithm for proposing is demonstrate,proved.

Embodiment three：Consider the different λ values of selection to build dipole potential field to returning the influence of depressed place process

Step 1：AUV enters back the depressed place stage with identical initial point (- 20, -20), and initial heading angle is 0 °, forward speed It is 1m/s.

Step 2：On AUV install transceiver by with recycle bin on transponder B₁And B₂Communicated, can be measured Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), as shown in Figure 2.

Step 3：AUV according to measurement obtain apart from L_iAnd orientation μ (i=1,2)_i(i=1,2), can be calculated using following formula Transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti,y_Ti) i=1,2.

In formula, l=3m.

Step 4：As shown in Fig. 2 according to electric dipole principle of electric field, defining electric dipole moment vector The position coordinates at transponder midpoint isDue to the entry vector of recycle binWithVertically, i.e.,

Step 5：As shown in figure 3, according to transponder B₁And B₂In AUV body coordinate systems x_Bo_By_BUnder position coordinates B_i(x_Ti, y_Ti) i=1,2, AUV body coordinate systems x can be calculated_Bo_By_BAnd the angle between AUV recovery coordinate systems xoy.

Step 6：Position coordinateses of the AUV in the case where coordinate system xoy is reclaimed can be calculated using following formula.

Step 7：The coordinate of two transponders is respectively (0, -0.5) and (0,0.5) on recycle bin, so p=[0 1]^Τ。n =[x y]^ΤIt is the position coordinates of AUV, then dipole potential field is

F_nx=λ xy F_ny=(λ -1) y²-x²

Step 8：According to the dipole potential field that step 7 is defined, can determine that the course angle that AUV is reclaimed is instructed with following formula.

In order that AUV can enter recycle bin along axis as soon as possible, and when nearer apart from recycle bin, ψ_dValue should be smaller Better.Dipole potential parameters λ is considered to returning the influence of depressed place guiding, byUnderstand, ψ_dIt is parameter lambda Monotonically increasing function, to cause ψ_dSmaller, dipole potential parameters λ should select smaller value, therefore the value of selection λ is 2.

Step 9：λ is taken respectively₁=2, λ₂=2.5, λ₃=3, λ₄=5 and λ₅=10 build dipole potential field, are tested by emulation Demonstrate,prove the correctness for discussing.

F_nx1=2xy F_ny1=y²-x²

F_nx2=2.5xy F_ny2=1.5y²-x²

F_nx3=3xy F_ny3=2y²-x²

F_nx4=5xy F_ny4=4y²-x²

F_nx5=10xy F_ny5=9y²-x²

Step 10：Course angle instruction ψ according to step 8_d, using self adaptation non-singular terminal sliding-mode control to course Angle is tracked control, selects rudder angle

Wherein, α₀=-0.524v s^-2,α₁=-2.848s^-1,α₂=-50s², what s was represented is unit second.β=0.5, η= 0.1,x₀It is the modeling indeterminate upper bound,It is x₀Estimate, q₀＞ 0 is adaptive gain.

Step 11：If AUV is less than 0.1 with the distance of recovery point, next step is gone to；Otherwise return to step 2.

Step 12：AUV has arrived at recovery point, goes back to depressed place and terminates.

Time depressed place ship trajectory figure of different λ values is as shown in figure 8, as seen from the figure, λ takes 2 optimal values for being dipole potential field.Although λ value is bigger, and the dipole potential field of foundation makes AUV more fast-forward into recycle bin, but it is increasing to work as taken λ value, and such as λ takes 5 and 10, During into recycle bin, it is more and more remote that AUV deviates axis.So λ should choose 2 so that AUV enters recycle bin along axis. Also the correctness discussed λ value before demonstrating.

Claims (1)

1. it is a kind of to return the method that depressed place guidance system guiding AUV goes back to depressed place using the AUV based on dipole potential field, it is described based on dipole gesture The AUV of field returns depressed place guidance system：Including USBL transceivers and two USBL transponders；USBL transceivers are arranged at the head of AUV Central axis on, two USBL transponders are arranged at the both sides of recycle bin；Described two USBL transponders are electric dipole, its It is characterised by that step is as follows：

Step 1：AUV is in the case where coordinate system xoy is reclaimed from initial point X (0)=[x (0) y (0)]_TWith initial heading angle ψ (0) start into Go back depressed place guiding；Wherein：X, y are position coordinateses of the AUV in the case where coordinate system is reclaimed, and (x (0) y (0)) was carried out before AUV navigation Setting；The recovery coordinate system xoy is the two USBL transponders B installed with the both sides of recycle bin₁And B₂Center be origin, Two USBL transponders B₁And B₂Between line be y-axis, level upwards perpendicular to y-axis and to cross origin be the positive direction axle of x, B₁Positioned at B₂The left side, B₁Point to B₂Direction for y-axis positive direction；

Step 2：The USBL transceivers and the transponder B of recycle bin both sides installed on AUV₁And B₂Communicated, measured transponder B₁And B₂In AUV body axis systems x_Bo_By_BUnder apart from L_iWith orientation μ_i, wherein i=1,2；

Step 3：Calculate transponder B₁And B₂In AUV body axis systems x_Bo_By_BUnder position coordinates B_i(x_Ti,y_Ti), i=1,2：

$\left[\begin{array}{c}{x}_{Ti}\\ y_{Ti}\end{array}\right]=\left[\begin{array}{c}{\mathrm{cos\μ}}_i\\ {\mathrm{sin\μ}}_i\end{array}\right]\[L_i\]+\left[\begin{array}{c}l\\ 0\end{array}\right]$

Step 4：According to electric dipole principle of electric field, electric dipole moment vector is definedThe position at transponder midpoint Coordinate isDue to the entry vector of recycle binWithVertically, theno To reclaim the origin of coordinate system xoy, l is transponder B₁And B₂The distance between；

Step 5：Calculate AUV body axis systems x_Bo_By_BAnd the angle between AUV recovery coordinate systems xoy：

$\mathrm{\ψ}=arctan\left(\frac{x_{T2}-x_{T1}}{y_{T2}-y_{T1}}\right)$

B_i(x_Ti,y_Ti) it is transponder B₁And B₂In AUV body axis systems x_Bo_By_BUnder position coordinates, i=1,2；

Step 6：Calculate position coordinateses of the AUV in the case where coordinate system xoy is reclaimed：

$\left[\begin{array}{c}x\\ y\end{array}\right]=-\left[\begin{array}{cc}cos\mathrm{\ψ}& -\sin \mathrm{\ψ}\\ \sin \mathrm{\ψ}& \cos \mathrm{\ψ}\end{array}\right]{(\frac{x_{T1}+x_{T2}}{2},\frac{y_{T1}+y_{T2}}{2})}^T$

Step 7：Define dipole potential field F (n)=λ (p^Tn)n-p(n^Tn),It is a non-zero everywhere in addition to origin Two-dimentional vector field, wherein, constant λ >=2, p=[p_x p_y]^ΤIt is the electric dipole moment of dipole potential field, n is the position of dipole potential field The characteristics of vector, dipole potential field maximum is the tangent line side of the motion all along potential field line at any point in dipole potential field space To；

Position coordinates of two transponders in the case where coordinate system xoy is reclaimed is respectively p₁=(p_1x,p_1y) and p₂=(p_2x,p_2y), then it is electric Dipole moment p=(p_2x-p_1x,p_2y-p_1y)^Τ；

Because position vectors of the AUV in dipole potential field is n=[x y]^Τ, then dipole potential field be

F_nx=(λ -1) (p_2x-p_1x)x²+λ(p_2y-p_1y)xy-(p_2x-p_1x)y²

F_ny=(λ -1) (p_2y-p_1y)y²+λ(p_2x-p_1x)xy-(p_2y-p_1y)x²；

Step 8：According to the dipole potential field that step 7 is defined, determine that the course angle instruction that AUV is reclaimed is：

${\mathrm{\ψ}}_d=arctan\left(\frac{F_{ny}}{F_{nx}}\right)-arctan\left(\frac{v}{u}\right)$

Step 9：Course angle instruction ψ according to step 8_d, course angle is carried out using self adaptation non-singular terminal sliding-mode control Tracing control, selection rudder angle be：

${\mathrm{\δ}}_r=-{\mathrm{\α}}_2({\mathrm{\α}}_0+{\mathrm{\α}}_1\mathrm{\ω}+\mathrm{\β}\frac{q}{p^{\′}}{\mathrm{\ω}}^{2-p^{\′}/q}+({\hat{x}}_0+\mathrm{\η}\left)sgn\right(s\left)\right)$

${\mathrm{\δ}}_{r1}=-{\mathrm{\α}}_2({\mathrm{\α}}_0+{\mathrm{\α}}_{1}w+\mathrm{\β}\frac{q}{p^{\′}}{w}^{2-p/q}+({\hat{x}}_0+\mathrm{\η}\left)\mathrm{sgn}\right(s\left)\right)$

Wherein,U, v, ω be respectively the forward speed of AUV under body axis system, Side velocity and course angular speed, m₁₁、m₂₂And m₃₃It is inertia coeffeicents of the AUV comprising additional mass, d₁₁、d₂₂And d₃₃It is AUV's Hydrodynamic damping coefficient, N_σIt is AUV yawing moment coefficients, β, η are constant and η>0, β>0, p '>q>0 and be odd number,x⁰It is the modeling indeterminate upper bound,It is x₀Estimate, q₀>0 is adaptive gain, and s is sliding-mode control law；

Step 10：If AUV is less than given acceptable error with the distance of recovery point, next step is gone to；Otherwise return Return to step 2；

Step 11：AUV has arrived at recovery point, goes back to depressed place and terminates.