CN104820430A - AUV back-to-dock guidance system and AUV back-to-the-dock guidance method based on dipole potential field - Google Patents

Abstract

The invention relates to an AUV back-to-the-dock guidance system and an AUV back-to-the-dock guidance method based on a dipole potential field. The AUV back-to-the-dock guidance system and the AUV back-to-the-dock guidance method are characterized in that the head of an AUV is equipped with a USBL transceiver, and two USBL transponders are installed at the two sides of a recycling station; the AUV can use the transceiver to measure the distances and the azimuths of the transponders in an AUV body coordinate system xBoByB; the coordinates of the AUV in a recycling coordinate system xoy can be calculated according to the distances and the azimuths, and an AUV back-to-the-dock expected course angle instruction can be obtained based on the principle of dipole potential field; and the AUV controls the AUV to sail at an expected course angle by an adaptive nonsingular terminal sliding mode control method to realize back-to-the-dock guidance. By adopting the method, the coordinates of the AUV in the recycling coordinate system xoy can be calculated directly. Then, the AUV is guided by an established dipole potential field to enter the recycling station along the central axis of the recycling station. The method is simple, only needs a small amount of calculation, makes the error between the actual course angle and the course angle specified by the instruction in the back-to-the-dock process very small, and has a better back-to-the-dock effect than other back-to-the-dock algorithms.

Description

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

Technical field

The invention belongs to submarine navigation device and reclaim docking technique field, be specifically related to a kind of AUV based on dipole potential field and return depressed place guidance system and guidance method.

Background technology

AUV (Autonomous Underwater Vehicle) is as one autonomous delivery vehicle under water, the energy entrained by self is relied on to navigate by water, the task such as underwater survey, article delivery can be completed, have important effect in fields such as military ocean surveillance, marine environmental monitoring, oil field explorations.The limited energy of carrying when AUV executes the task, for the AUV of long working, must be laid AUV by operation lash ship in the region of executing the task and reclaim, to complete the work such as the supplementary energy, reading information, Support.In order to improve operating efficiency, there has been proposed the voluntary recall system under water of AUV, voluntary recall controls to have become one of the study hotspot in current oceanographic engineering field.

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

(1) what control based on horizontal tracing returns depressed place guidance method.The axis that first the method needs definition AUV to reclaim, then AUV navigates by water along axis according to the range deviation control AUV between current location and axis, finally realizes the recovery of AUV.The major defect of the method is not suitable for initial position in side or situation below, is not also suitable for the dynamic recovery of AUV.

(2) based on time depressed place guidance method of Artificial Potential Field.The method adopts traditional Artificial Potential Field Method, and produce a nothing that can arrive recycle bin and touch air route, then control AUV navigates by water down an airway, thus realizes the recovery of AUV.The major defect of the method is the problem that there is local minimum point, namely AUV is subject to gravitation and repulsion when near recycle bin simultaneously, may be zero with joint efforts, be absorbed in local minimum point once AUV and just there will be the unreachable problem of recycle bin, and easily the phenomenons such as path jitter occur at narrow zone.

(3) AUV based on fuzzy theory reclaims movement technique.According to the basis of fuzzy control theory, and according to the feature of control object, formulate fuzzy control rule, design fuzzy controller, the recovery motion process of AUV is controlled.The major defect of the method is that the acquisition of fuzzy control rule and input fuzzy variable domain and subordinate function establish a capital really is gathering of experimental analysis and operating personnel's experience, and the impact by artificial subjective factor is larger.

Summary of the invention

The technical matters solved

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

Technical scheme

AUV based on dipole potential field returns a depressed place guidance system, it is characterized in that comprising USBL transceiver and two USBL transponders; USBL transceiver is arranged on the central axis of the head of AUV, and two USBL transponders are arranged at the both sides of recycle bin; Described two USBL transponders are electric dipole.

Utilize described in claim 1 and return based on the AUV of dipole potential field 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 reclaiming under coordinate system xoy from initial point X (0)=［ x0 y0 ］ ^tstart to carry out back depressed place guiding with angle, initial heading ψ (0); Wherein: x, y are that AUV is reclaiming the position coordinates under coordinate system, and (x (0), y (0)) set before AUV navigation; Described recovery coordinate system xoy is two the USBL transponder B installed with the both sides of recycle bin ₁and B ₂center be initial point, two USBL transponder B ₁and B ₂between line be y-axis, horizontal vertical in y-axis and cross initial point be x-axis;

The USBL transceiver that step 2:AUV installs and the transponder B of recycle bin both sides ₁and B ₂communicate, measure transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2);

Step 3: calculate transponder B ₁and B ₂at position coordinates B _i(x _ti, y _ti), i=1,2:

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

Step 4: according to electric dipole principle of electric field, definition electric dipole moment vector the position coordinates of transponder mid point is due to the entry vector of recycle bin with vertically, then $\stackrel{\→}{\mathrm{OE}}={(y_{T2}-y_{T1},x_{T1}-x_{T2})}^T;$

Step 5: calculate AUV body coordinate system x _bo _by _bwith AUV reclaims the angle between coordinate system xoy:

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

B _i(x _ti, y _ti) i=1,2 is transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates;

Step 6: calculate AUV and reclaiming the position coordinates under coordinate system xoy:

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

Step 7: definition dipole potential field the vector field of a two dimension for non-zero everywhere except initial point, wherein, constant λ>=2, p=[p _xp _y] ^Τfor the electric dipole moment of dipole potential field, n is the position vector of dipole potential field.The maximum feature of dipole potential field is that the motion of any point in dipole potential field space is all along the tangential direction of potential field line;

The position coordinates of two transponders under recovery coordinate system xoy is respectively p ₁=p _1x, p _1yand p ₂=p _2x, p _2y, then electric dipole moment p=p _2x-p _1x, p _2y-p _1y ^t;

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

F _nx＝(λ-1)(p _2x-p _1x)x ²+λ(p _2y-p _1y)xy-(p _2x-p _1x)y ²

F _ny＝(λ-1)(p _2y-p _1y)y ²+λ(p _2x-p _1x)xy-(p _2y-p _1y)x ²；

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

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

Step 9: according to the course angle instruction ψ of step 8 _d, adopt self-adaptation non-singular terminal sliding-mode control to carry out tracing control to course angle, selection rudder angle is:

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

${\stackrel{\·}{\hat{x}}}_0={q_0}^{-1}\left|\frac{1}{\mathrm{\β}}\frac{p}{q}{\mathrm{\ω}}^{p/q-1}\right|\left|s\right|$

Wherein, u, v, ω are the forward speed of AUV under body coordinate system, side velocity and course angle speed respectively, m ₁₁, m ₂₂and m ₃₃for AUV comprises the inertial coefficient of additional mass, d ₁₁, d ₂₂and d ₃₃for the hydrodynamic damping coefficient of AUV, N _σfor AUV yawing moment coefficient.β, η are constant and η > 0, β > 0, p > q > 0 and be odd number, x ₀the modeling indeterminate upper bound, x ₀estimated value, q ₀> 0 is adaptive gain;

Step 10: if when the distance of AUV and recovery point is less than given acceptable error, then forward next step to; Otherwise turn back to step 2;

Step 11:AUV arrives recovery point, goes back to depressed place and terminates.

Beneficial effect

A kind of AUV based on dipole potential field that the present invention proposes returns depressed place guidance system and guidance method, USBL transceiver is arranged on the head of AUV, recycle bin is installed two transponders, be easy to obtain the coordinate of transponder under body coordinate system, no longer need other measurement means directly can calculate AUV and reclaiming the coordinate under coordinate system.Then utilize the dipole potential field of foundation to guide AUV and enter recycle bin along direction, recycle bin axis, the method is simple, and calculated amount is less, makes back the error in the process of depressed place between actual heading angle and command heading angle very little, returns depressed place effect and is better than other time depressed place algorithm.

Accompanying drawing explanation

The removal process schematic diagram of Fig. 1: AUV

Fig. 2: the AUV recovery system figure with double response device

Fig. 3: ordinate transform schematic diagram

The ship trajectory figure of Fig. 4: AUV navigation process

Course angle variation diagram in Fig. 5: AUV navigation process

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

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

Fig. 8: time depressed place ship trajectory figure of different λ value

Embodiment

Now in conjunction with the embodiments, the invention will be further described for accompanying drawing:

The present invention proposes a kind of AUV based on dipole potential field and returns depressed place guidance method, as shown in Figure 1, it is characterized in that the head of AUV is provided with USBL transceiver, and two USBL transponder B are installed in the both sides of recycle bin ₁and B ₂; AUV utilizes transceiver can measure transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2), as shown in Figure 2; According to distance L _i(i=1,2) and orientation μ _i(i=1,2), can calculate AUV and reclaim the coordinate under coordinate system xoy, and based on dipole potential field principle, obtain the desired course angle instruction that AUV goes back to depressed place; Then AUV utilizes self-adaptation non-singular terminal sliding-mode control control AUV with the course angle expected navigation, finally realizes back depressed place guiding.Step is as follows:

Step 1:AUV is reclaiming under coordinate system xoy from initial point X (0)=[x0 y0] ^tstart to carry out back depressed place guiding with angle, initial heading ψ (0).Wherein, x, y are that AUV is reclaiming the position coordinates under coordinate system, and (x (0), y (0)) can set before AUV navigation.

On step 2:AUV install transceiver by with the transponder B on recycle bin ₁and B ₂communicate, transponder B can be measured ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2), as shown in Figure 2.

Step 3:AUV is according to measuring the distance L obtained _i(i=1,2) and orientation μ _i(i=1,2), can adopt following formula to calculate transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2.

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

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

Step 4: as shown in Figure 2, according to electric dipole principle of electric field, definition electric dipole moment vector the position coordinates of transponder mid point is due to the entry vector of recycle bin with vertically, namely $\stackrel{\→}{\mathrm{OE}}={(y_{T2}-y_{T1},x_{T1}-x_{T2})}^T.$

Step 5: as shown in Figure 3, according to transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2, AUV body coordinate system x can be calculated _bo _by _bwith AUV reclaims the angle between coordinate system xoy.

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

Step 6: utilize following formula can calculate AUV and reclaiming the position coordinates under coordinate system xoy.

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

Step 7: under the inspiration of electric dipole electric field line, definition dipole potential field

a two-dimentional vector field, non-zero everywhere except initial point, wherein, constant λ>=2, p=[p _xp _y] ^Τfor the electric dipole moment of dipole potential field, n is the position vector of dipole potential field.The maximum feature of dipole potential field is that the motion of any point in dipole potential field space is all along the tangential direction of potential field line.Position in dipole potential field of two transponders and electric dipole position consistency in the electric field.Suppose, on recycle bin, the position coordinates of two transponders under recovery coordinate system xoy is respectively p ₁=p _1x, p _1yand p ₂=p _2x, p _2y, then electric dipole moment p=p _2x-p _1x, p _2y-p _1y ^t.Because the position vector of AUV in dipole potential field is n=[x y] ^Τ, then dipole potential field is

F _nx＝(λ-1)(p _2x-p _1x)x ²+λ(p _2y-p _1y)xy-(p _2x-p _1x)y ²

F _ny＝(λ-1)(p _2y-p _1y)y ²+λ(p _2x-p _1x)xy-(p _2y-p _1y)x ²

Step 8: the dipole potential field defined according to step 7, available following formula determines that AUV reclaims the course angle instruction of guiding.

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

Step 9: according to the course angle instruction ψ of step 8 _d, adopt self-adaptation non-singular terminal sliding-mode control to carry out tracing control to course angle, select rudder angle

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

${\stackrel{\·}{\hat{x}}}_0={q_0}^{-1}\left|\frac{1}{\mathrm{\β}}\frac{p}{q}{\mathrm{\ω}}^{p/q-1}\right|\left|s\right|$

Wherein, u, v, ω are the forward speed of AUV under body coordinate system, side velocity and course angle speed respectively, m ₁₁, m ₂₂and m ₃₃for AUV comprises the inertial coefficient of additional mass, d ₁₁, d ₂₂and d ₃₃for the hydrodynamic damping coefficient of AUV, N _σfor AUV yawing moment coefficient.β, η are constant and η > 0, β > 0, p > q > 0 and be odd number, x ₀the modeling indeterminate upper bound, x ₀estimated value, q ₀> 0 is adaptive gain.

Step 10: if when the distance of AUV and recovery point is less than given acceptable error, then forward next step to; Otherwise turn back to step 2.

Step 11:AUV arrives recovery point, goes back to depressed place and terminates.

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

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

On step 2:AUV install transceiver by with the transponder B on recycle bin ₁and B ₂communicate, transponder B can be measured ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2), as shown in Figure 2.

Step 3:AUV is according to measuring the distance L obtained _i(i=1,2) and orientation μ _i(i=1,2), can adopt following formula to calculate transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2.

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

In formula, l=3m.

Step 4: as shown in Figure 2, according to electric dipole principle of electric field, definition electric dipole moment vector the position coordinates of transponder mid point is due to the entry vector of recycle bin with vertically, namely $\stackrel{\→}{\mathrm{OE}}={(y_{T2}-y_{T1},x_{T1}-x_{T2})}^T.$

Step 5: as shown in Figure 3, according to transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2, AUV body coordinate system x can be calculated _bo _by _bwith AUV reclaims the angle between coordinate system xoy.

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

Step 6: utilize following formula can calculate AUV and reclaiming the position coordinates under coordinate system xoy.

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

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

F _nx＝2xy

F _ny＝y ²-x ²

Step 8: the dipole potential field defined according to step 7, available following formula determines the course angle instruction that AUV reclaims.

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

Step 9: according to the course angle instruction ψ of step 8 _d, adopt self-adaptation non-singular terminal sliding-mode control to carry out tracing control to course angle, select rudder angle

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

${\stackrel{\·}{\hat{x}}}_0={q_0}^{-1}\left|\frac{1}{\mathrm{\β}}\frac{p}{q}{\mathrm{\ω}}^{p/q-1}\right|\left|s\right|$

Wherein, α ₀=-0.524v s ^-2, α ₁=-2.848s ^-1, α ₂=-50s ², what s represented is unit second.β=0.5, η=0.1, x ₀the modeling indeterminate upper bound, x ₀estimated value, q ₀> 0 is adaptive gain.

Step 10: if when the distance of AUV and recovery point is less than 0.1, then forward next step to; Otherwise turn back to step 2.

Step 11:AUV arrives recovery point, goes back to depressed place and terminates.

As shown in Figure 4, AUV starts navigation from initial point (-100 ,-100) with 0 °, angle, initial heading to the ship trajectory figure of AUV navigation process, utilizes the dipole potential field guiding AUV set up to enter recycle bin along direction, recycle bin axis.As we can see from the figure, self-adaptation non-singular terminal sliding formwork controls lower AUV and can navigate by water recycle bin with more smooth track, shorter time.Returning the depressed place stage, AUV enters recycle bin along axis.

In AUV navigation process, course angle variation diagram as shown in Figure 5, and the error between actual heading angle and command heading angle is very little, and error only has about 3 degree, can complete back depressed place task.

In AUV navigation process, the variation diagram of vertical rudder angle as shown in Figure 6, depict the situation of change of vertical rudder angle in navigation process, as can be seen from the figure vertical rudder angle limit always ± 20 degree between, only starting to carry out back reaching hard over angle-20 degree in very short time when depressed place is guided.

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

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

On step 2:AUV install transceiver by with the transponder B on recycle bin ₁and B ₂communicate, transponder B can be measured ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2), as shown in Figure 2.

Step 3:AUV is according to measuring the distance L obtained _i(i=1,2) and orientation μ _i(i=1,2), can adopt following formula to calculate transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2.

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

In formula, l=3m.

Step 4: as shown in Figure 2, according to electric dipole principle of electric field, definition electric dipole moment vector the position coordinates of transponder mid point is due to the entry vector of recycle bin with vertically, namely $\stackrel{\→}{\mathrm{OE}}={(y_{T2}-y_{T1},x_{T1}-x_{T2})}^T.$

Step 5: as shown in Figure 3, according to transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2, AUV body coordinate system x can be calculated _bo _by _bwith AUV reclaims the angle between coordinate system xoy.

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

Step 6: utilize following formula can calculate AUV and reclaiming the position coordinates under coordinate system xoy.

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

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

F _nx＝2xy

F _ny＝y ²-x ²

Step 8: the dipole potential field defined according to step 7, available following formula determines the course angle instruction that AUV reclaims.

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

Step 9: according to the course angle instruction ψ of step 8 _d, adopt self-adaptation non-singular terminal sliding-mode control to carry out tracing control to course angle, select rudder angle

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

${\stackrel{\·}{\hat{x}}}_0={q_0}^{-1}\left|\frac{1}{\mathrm{\β}}\frac{p}{q}{\mathrm{\ω}}^{p/q-1}\right|\left|s\right|$

Wherein, α ₀=-0.524v s ^-2, α ₁=-2.848s ^-1, α ₂=-50s ², what s represented is unit second.β=0.5, η=0.1, x ₀the modeling indeterminate upper bound, x ₀estimated value, q ₀> 0 is adaptive gain.

Step 10: if when the distance of AUV and recovery point is less than 0.1, then forward next step to; Otherwise turn back to step 2.

Step 11:AUV arrives recovery point, goes back to depressed place and terminates.

AUV returns depressed place ship trajectory figure as shown in Figure 7 with different initial points, and as seen from the figure, although the initial point that AUV enters back depressed place navigation is different, AUV can enter recycle bin in the direction along recycle bin axis under the guiding of dipole potential field.Demonstrate the correctness of the algorithm of proposition thus.

Embodiment three: consider to select different λ value to build dipole potential field to the impact of returning depressed place process

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

On step 2:AUV install transceiver by with the transponder B on recycle bin ₁and B ₂communicate, transponder B can be measured ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2), as shown in Figure 2.

Step 3:AUV is according to measuring the distance L obtained _i(i=1,2) and orientation μ _i(i=1,2), can adopt following formula to calculate transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2.

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

In formula, l=3m.

Step 4: as shown in Figure 2, according to electric dipole principle of electric field, definition electric dipole moment vector the position coordinates of transponder mid point is due to the entry vector of recycle bin with vertically, namely $\stackrel{\→}{\mathrm{OE}}={(y_{T2}-y_{T1},x_{T1}-x_{T2})}^T.$

Step 5: as shown in Figure 3, according to transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates B _i(x _ti, y _ti) i=1,2, AUV body coordinate system x can be calculated _bo _by _bwith AUV reclaims the angle between coordinate system xoy.

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

Step 6: utilize following formula can calculate AUV and reclaiming the position coordinates under coordinate system xoy.

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

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

F _nx＝λxy F _ny＝(λ-1)y ²-x ²

Step 8: the dipole potential field defined according to step 7, available following formula determines the course angle instruction that AUV reclaims.

${\mathrm{\ψ}}_d=\arctan \left(\frac{F_{\mathrm{ny}}}{F_{\mathrm{nx}}}\right)-\arctan \left(\frac{v}{u}\right)=\arctan (\frac{y^2}{\mathrm{xy}}-\frac{1}{\mathrm{\λ}}\·\frac{x^2+y^2}{\mathrm{xy}})-\arctan \left(\frac{v}{u}\right)$

In order to make AUV can enter recycle bin along axis as soon as possible, when distance recycle bin is nearer, ψ _dvalue should be the smaller the better.Consider that dipole potential parameters λ is on the impact of returning depressed place guiding, by known, ψ _dbe the monotonically increasing function of parameter lambda, ψ made _dless, dipole potential parameters λ should select smaller value, therefore selects the value of λ to be 2.

Step 9: get λ respectively ₁=2, λ ₂=2.5, λ ₃=3, λ ₄=5 and λ ₅=10 build dipole potential field, the correctness discussed by simulating, verifying.

F _nx1＝2xy F _ny1＝y ²-x ²

F _nx2＝2.5xy F _ny2＝1.5y ²-x ²

F _nx3＝3xy F _ny3＝2y ²-x ²

F _nx4＝5xy F _ny4＝4y ²-x ²

F _nx5＝10xy F _ny5＝9y ²-x ²

${\mathrm{\ψ}}_{d1}=\arctan \left(\frac{y^2-x^2}{2\mathrm{xy}}\right)-\arctan \left(v\right)$

${\mathrm{\ψ}}_{d2}=\arctan \left(\frac{1.5y^2-x^2}{2.5\mathrm{xy}}\right)-\arctan \left(v\right)$

${\mathrm{\ψ}}_{d3}=\arctan \left(\frac{{2y}^2-x^2}{3\mathrm{xy}}\right)-\arctan \left(v\right)$

${\mathrm{\ψ}}_{d4}=\arctan \left(\frac{4y^2-x^2}{5\mathrm{xy}}\right)-\arctan \left(v\right)$

${\mathrm{\ψ}}_{d5}=\arctan \left(\frac{{9y}^2-x^2}{10\mathrm{xy}}\right)-\arctan \left(v\right)$

Step 10: according to the course angle instruction ψ of step 8 _d, adopt self-adaptation non-singular terminal sliding-mode control to carry out tracing control to course angle, select rudder angle

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

${\stackrel{\·}{\hat{x}}}_0={q_0}^{-1}\left|\frac{1}{\mathrm{\β}}\frac{p}{q}{\mathrm{\ω}}^{p/q-1}\right|\left|s\right|$

Wherein, α ₀=-0.524v s ^-2, α ₁=-2.848s ^-1, α ₂=-50s ², what s represented is unit second.β=0.5, η=0.1, x ₀the modeling indeterminate upper bound, x ₀estimated value, q ₀> 0 is adaptive gain.

Step 11: if when the distance of AUV and recovery point is less than 0.1, then forward next step to; Otherwise turn back to step 2.

Step 12:AUV arrives recovery point, goes back to depressed place and terminates.

As shown in Figure 8, as seen from the figure, λ gets the optimal value that 2 are dipole potential field to time depressed place ship trajectory figure of different λ value.Although λ value is larger, the dipole potential field of foundation makes AUV more fast-forward into recycle bin, works as got λ value increasing, and as λ gets 5 and 10, when entering recycle bin, it is more and more far away that AUV departs from axis.So λ should choose 2, AUV is made to enter recycle bin along axis.Also to the correctness that λ value is discussed before demonstrating.

Claims (2)

1. the AUV based on dipole potential field returns a depressed place guidance system, it is characterized in that comprising USBL transceiver and two USBL transponders; USBL transceiver is arranged on the central axis of the head of AUV, and two USBL transponders are arranged at the both sides of recycle bin; Described two USBL transponders are electric dipole.

2. utilize described in claim 1 and return based on the AUV of dipole potential field 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 under recovery coordinate system xoy from initial point X (0)=x0 y 0] ^tstart to carry out back depressed place guiding with angle, initial heading ψ (0); Wherein: x, y are that AUV is reclaiming the position coordinates under coordinate system, and (x (0), y (0)) set before AUV navigation; Described recovery coordinate system xoy is two the USBL transponder B installed with the both sides of recycle bin ₁and B ₂center be initial point, two USBL transponder B ₁and B ₂between line be y-axis, horizontal vertical in y-axis and cross initial point be x-axis;

The USBL transceiver that step 2:AUV installs and the transponder B of recycle bin both sides ₁and B ₂communicate, measure transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder distance L _i(i=1,2) and orientation μ _i(i=1,2);

Step 3: calculate transponder B ₁and B ₂at position coordinates B _i(x _ti, y _ti), i=1,2:

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

Step 4: according to electric dipole principle of electric field, definition electric dipole moment vector the position coordinates of transponder mid point is due to the entry vector of recycle bin with vertically, then $\stackrel{\→}{\mathrm{OE}}={(y_{T2}-y_{T1},x_{T1}-x_{T2})}^T;$

Step 5: calculate AUV body coordinate system x _bo _by _bwith AUV reclaims the angle between coordinate system xoy:

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

B _i(x _ti, y _ti) i=1,2 is transponder B ₁and B ₂at AUV body coordinate system x _bo _by _bunder position coordinates;

Step 6: calculate AUV and reclaiming the position coordinates under coordinate system xoy:

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

Step 7: definition dipole potential field F (n)=λ (p ^tn) n-p (n ^tn), the vector field of a two dimension for non-zero everywhere except initial point, wherein, constant λ>=2, p=[p _xp _y] ^Τfor the electric dipole moment of dipole potential field, n is the position vector of dipole potential field.The maximum feature of dipole potential field is that the motion of any point in dipole potential field space is all along the tangential direction of potential field line;

The position coordinates of two transponders under recovery coordinate system xoy is respectively p ₁=p _1x, p _1yand p ₂=p _2x, p _2y, then electric dipole moment p=p _2x-p _1x, p _2y-p _1y ^t;

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

F _nx＝(λ-1)(p _2x-p _1x)x ²+λ(p _2y-p _1y)xy-(p _2x-p _1x)y ²

F _ny＝(λ-1)(p _2y-p _1y)y ²+λ(p _2x-p _1x)xy-(p _2y-p _1y)x ²；

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

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

Step 9: according to the course angle instruction ψ of step 8 _d, adopt self-adaptation non-singular terminal sliding-mode control to carry out tracing control to course angle, selection rudder angle is:

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

${\stackrel{.}{\hat{x}}}_0={q_0}^{-1}\left|\frac{1}{\mathrm{\β}}\frac{p}{q}{\mathrm{\ω}}^{p/q-1}\right|\left|s\right|$

Wherein, u, v, ω are the forward speed of AUV under body coordinate system, side velocity and course angle speed respectively, m ₁₁, m ₂₂and m ₃₃for AUV comprises the inertial coefficient of additional mass, d ₁₁, d ₂₂and d ₃₃for the hydrodynamic damping coefficient of AUV, N _σfor AUV yawing moment coefficient.β, η are constant and η > 0, β > 0, p > q > 0 and be odd number, x ₀the modeling indeterminate upper bound, x ₀estimated value, q ₀> 0 is adaptive gain;

Step 10: if when the distance of AUV and recovery point is less than given acceptable error, then forward next step to; Otherwise turn back to step 2;

Step 11:AUV arrives recovery point, goes back to depressed place and terminates.