Underwater Acoustically Guided Docking Method Based on Multi-Stage Planning

: Autonomous underwater vehicles (AUVs) are important in areas such as underwater scientiﬁc research and underwater resource collection. However, AUVs suffer from data portability and energy portability problems due to their physical size limitation. In this work, an acoustic guidance method for underwater docking is proposed to solve the problem of persistent underwater operation. A funnel docking station and an autonomous remotely operated vehicle (ARV) are used as the platform for designing the guidance algorithms. First, the underwater docking guidance is divided into three stages: a long-range approach stage, a mid-range adjustment stage and a short-range docking stage. Second, the relevant guidance strategy is designed for each stage to improve the docking performance. Third, a correction method based on an ultra-short baseline (USBL) system is proposed for the ARV’s estimate of the depth, relative position and orientation angle of the docking station. To verify the feasibility of the docking guidance method, in this work, tests were performed on a lake and in a shallow sea. The success rate of autonomous navigation docking on the lake was 4 out of 7. The success rate of acoustic guidance docking on the lake and in the shallow sea were 11 out of 14 and 6 out of 8, respectively. The experimental results show the effectiveness of the docking guidance method in lakes and shallow seas.


Introduction
With the continuous deepening of ocean exploration in various countries, autonomous underwater vehicles (AUVs) have become an important tool for exploring the marine environment [1][2][3][4].AUVs have important applications in areas such as underwater rescue, military reconnaissance, resource exploration and marine scientific research [5,6].The small size of the AUV makes it highly concealable during operation, however, the small size of the AUV also limits its range of motion, resulting in an inability to operate underwater for extended periods of time [7][8][9][10].In addition, the low transmission rate of underwater acoustic data prevents the AUV from uploading the data in a timely manner [11].Therefore, the AUV requires multiple manual recoveries and deployments, which greatly reduces efficiency, increases costs and is less concealable [12,13].
To enable the AUV to stay underwater for long periods, a docking station for data and power transmission has been deployed underwater [14].After the mission, the AUV can navigate autonomously to the underwater docking station and perform operations such as energy replenishment and data upload [15,16].Underwater docking technology greatly improves the concealment, continuity and mobility of AUV underwater operations and is a key research direction in the future [17][18][19].
Underwater docking guidance methods can be divided into three methods depending on the used sensor: acoustic guidance [20], optical guidance [21] and electromagnetic guidance [22].Underwater acoustic guidance refers to the application of acoustic equipment such as long baseline (LBL) systems, short baseline (SBL) systems and ultra-short baseline (USBL) systems for guidance.The advantage of acoustic guidance is that it works over long distances, up to 3 km, and can be omnidirectional [23,24].The disadvantage is that the positioning accuracy is low, the real-time performance is poor and it is easily exposed [25,26].The following are typical results of docking using acoustic guidance: Stokey et al. proposed a funnel docking scheme based on the REMUS AUV [20].They designed an acoustic localisation method based on a USBL, a clamp and contact motors for locking, charging and communication circuits.Tests were performed in the summer of 1997.Allen et al. proposed a second generation of the REMUS docking system as an improvement on the original docking scheme [23].In their work, they adopted a low-profile, bottom-mounted docking station and upgraded the sensors of the docking station and the docking vehicle.They also successfully performed docking tests in 2005.
Singh et al. proposed a pole docking scheme based on the Odyssey IIB AUV [27].They used acoustic guidance and divided the docking into five stages: homing, docking, core alignment, power transfer and undocking.Tests were conducted at Cape Hatteras in May 1997 to demonstrate the reliability of the docking system.
Kawasaki et al. proposed a platform-based underwater docking solution based on the Marine Bird AUV [28,29].They used a super short base line (SSBL) for acoustic guidance and divided the docking process into six stages: approaching the transponder service area, approaching the base, holding the guide, connecting to the base, recharging the batteries and undocking.In 2001-2003, trials were carried out at a dock and at sea to demonstrate the performance of the docking system.
McEwen et al. proposed a docking method for the Bluefin-21 AUV and a fixed cone docking station [30,31].In their work, the docking process is as follows: use pure pursuit guidance while homing to within USBL range of the beacon, then use the USBL for positioning and sail along the centreline of the cone, when the AUV is close to the dock, slow down and complete the final alignment and then latch.Docking tests were performed in 2005-2006 in a seawater test tank and in Monterey Bay.
Hayato et al. proposed a docking method using acoustic guidance and optical guidance [32].They used passive acoustic guidance to guide the vehicle into a docking cage from a long distance and used optical guidance at short distance to provide high positioning accuracy during terminal guidance.Due to the limitations of the experimental conditions, they tested the optical guidance system to demonstrate the validity of the proposed method.
Maki et al. proposed a docking method for a hovering Tri-TON AUV at a seafloor station [33].In their work, an acoustic localisation and communication device (ALOC) was used to estimate the rough position of the AUV at long distance, while, at short distance, image processing was used to measure the precise relative position of the AUV.Tests were performed in a tank, and the docking success rate was 50%.Sato et al. conducted acousticoptical docking tests with a Tri-TON 2 AUV [34,35].Compared to the Tri-TON AUV, the maximum depth of the Tri-TON 2 was extended from 800 m to 2000 m.The performance of the docking method was verified through a series of tank and sea trials in 2015.
Vallicrosa et al. proposed a combined acoustic-optical-based guidance method using the Sparus II AUV and conducted tests in a water tank and in a shallow sea [36][37][38][39][40].In their work, the docking procedure is as follows: (1) Estimate the position and orientation of the docking station and guide the AUV to a location 40 m in front of the docking station.(2) If the range is available, use an acoustic localisation algorithm to estimate the position of the docking station.(3) If the docking station is detected, navigate the AUV to a location 10 m in front of the docking station.(4) Follow the track towards the docking station until light beacons are detected.Otherwise, return to (3). ( 5) Navigate the AUV to the entrance of the docking station.
Existing acoustic guidance docking methods mostly rely on pre-positioning the AUV within the range of acoustic equipment and then using the acoustic equipment to obtain the precise position of the docking station and then homing.However, these studies focus on the design of the docking structure and the selection of the docking sensors, and the docking guidance process is not studied enough.During the docking process, as the AUV approaches the docking station, the docking accuracy requirement also increases.Therefore, the docking process needs to be divided into several stages according to the distance from the AUV to the docking station, and guidance strategies need to be designed for each stage in order to improve the docking success rate.To address these issues, this paper proposes a docking method based on acoustic guidance for autonomous remotely operated vehicles (ARV).First, the docking process is divided into three stages according to the distance from the ARV to the docking station.Second, the corresponding guidance algorithm for each docking stage is designed.Third, an acoustic-based method is proposed to update the ARV's perception of the docking station, including the depth, relative position and orientation angle of the docking station.
The paper is organised as follows: Section 2 describes the parameters, structure and functions of the ARV for docking and the docking station.Section 3 presents the docking procedure, describes the specific methods for each stage of docking and proposes a method for correcting the ARV's perception of the docking station.Section 4 presents lake and shallow sea tests and analyses the results of the tests.Section 5 outlines the conclusions and future work.

Underwater Docking ARV
An ARV is a composite underwater robot that combines the features of a remotely operated vehicle (ROV) and an AUV, which can operate either remotely or autonomously for underwater tasks [41].The ARV used for underwater docking is shown in Figure 1.The dimensions of the ARV are 2.980 (L) × 0.697 (W) × 0.779 (H) (m), the weight is 350 kg and it is equipped with 6 underwater cameras, 6 lights, a USBL beacon terminal, a doppler velocity log (DVL), a wi-fi module, an altimeter, a depth gauge, an inertial navigation system (INS), a global positioning system (GPS), an attitude sensor and other modules.The ARV can realise motion states such as forward and backward, transverse, in situ rotation, surfacing and diving, its speed can reach 3 knots, the radius of its turning circle is 5 m and the working water depth is 0-4500 m.The ARV can be divided into two types of path planning mode: waypoint path mode and heading path mode [42].The structure of the ARV autonomous docking module is shown in Figure 2. The docking module is an NVIDIA Jetson Nano, which is used to receive status information and optical guidance video information from the ARV main controller and store them into a shared data area.The acoustic guidance module and the optical guidance module generate ARV control commands by processing the shared data and send them to the ARV to realise ARV docking control.

Underwater Docking Station
The docking station used for underwater docking is shown in Figure 3.The overall outline of the docking station consists of two main parts: the base and the dock, where the dock can be divided into two parts: the frame and the guide funnel.The overall dimensions of the dock are 2.067 (L) × 2.065 (W) × 2.065 (H) (m) and the weight is 210 kg, where the guide funnel has a length of 1.17 m, a maximum inner diameter of 1.82 m, a minimum inner diameter of 0.86 m and a weight of 66 kg.The dock is installed on top of the base so that it can be suspended in the water.The internal structure of the docking station includes 8 guide lights, a USBL host terminal, an underwater camera, an altimeter, a depth gauge, an electronic compass and other equipment.

Docking Method
The docking flowchart is shown in Figure 4. Due to the limitation of the entrance nozzle angle of the docking station, it is necessary to reduce the error of the docking attitude angle and the position of the ARV.In addition, during the docking process, the actual depth, orientation angle and position may deviate due to ocean currents or other reasons.Therefore, it needs to be continuously corrected during the docking process.To overcome the above problems, the docking guidance process is designed to be divided into three stages: a long-range approach stage, a mid-range adjustment stage and a short-range docking stage.In the long-range approach stage, the ARV approaches a position on the centreline of the docking station, which is far from its entrance nozzle, to make adjustments with sufficient distance; in the mid-range adjustment stage, the ARV gradually approaches the docking station at a slow speed along its centreline to reduce the lateral deviation during navigation; in the short-range docking stage, the ARV uses inertial navigation to sail directly to the docking station or uses optics for more precise guidance.

Long-Range Approach Stage
When the ARV receives the docking command, it begins the remote docking procedure.The purpose of the long-range approach stage is to allow the ARV to approach the centreline of the docking station, at a heading angle approximately towards its entrance nozzle, to adjust to a more suitable position and heading angle and then enter the mid-range adjustment stage.
In the long-range approach stage, the ARV will descend to the preset depth of the docking station and perform fixed-depth navigation mode so that the ARV and the docking station are at the same level.It selects several points between 80 m and 300 m away from the docking station along the centreline of the docking station (the last point is the 80 m point), and performs a waypoint path mode from far to near.Once the ARV has reached the target position at 80 m, it enters the mid-range adjustment stage.
The method for controlling the ARV to reach the target position during waypoint path mode is shown in Figure 5.The ARV starts from the start position p s and sails towards the target position p e .The formula for calculating the coordinates of p e is as follows: where x e and y e are the along-axis and lateral coordinates of p e , x d and y d are the along-axis and lateral coordinates of the docking station p d , l de is the distance between p d and p e and ϕ d is the orientation angle of p d in the geodetic coordinate system.If the distance between p e and the current ARV position p v is less than or equal to 5 m, or if the ARV sails past L e , which is a vertical plane perpendicular to p s p e that passes through p e (as shown in the shaded part of Figure 5), it can be determined that the ARV has reached the target position.The judgement formula is as follows: where x v and y v are the horizontal and vertical coordinates of p v and ϕ se and ϕ ve are the azimuth angles of p e relative to p s and p v in the geodetic coordinate system.
To prevent the ARV from being unable to reach the target position due to obstacles and other reasons during waypoint path mode, set the maximum time limit for ARV waypoint path mode: where t max is the maximum time limit of waypoint path mode, x s and y s are the horizontal and vertical coordinates of p s and v is the ARV forward speed in waypoint path mode.

Mid-Range Adjustment Stage
The purpose of the mid-range adjustment stage is to adjust the position and heading angle of the ARV.Compared to [20], to enter the short-range docking stage with a better attitude, a lateral deviation adjustment algorithm is added to stabilise the ARV near the centreline of the docking station with a heading angle towards the entrance nozzle of the docking station.
In the mid-range adjustment stage, the start position and the target position are respectively 80 m and 5 m in front of the entrance nozzle of the docking station, and heading path mode is used.Once the ARV has reached the target position, it enters the short-range docking stage.
The path tracking method in the mid-range adjustment stage is shown in Figure 6.When the distance l 3 between ARV current position p v and the docking station centreline L is less than or equal to 1 m, the ARV will dock with the heading angle ϕ t1 of the target position p 1 .Otherwise, the ARV will dock with the heading angle ϕ t2 of the target position p 2 , which is the midpoint between p 1 and the projection point p 3 of p v on L. The judgment formula is as follows: where the distance l 3 is between p v and L, the target heading ϕ t1 and ϕ t2 can be calculated by the following formula: where x 1 and y 1 are the horizontal and vertical coordinates of the target point p 1 : l 1 is the distance between p v and p 1 : ϕ 1 is the angle between p v p 1 and L: x 2 and y 2 are the horizontal and vertical coordinates of p 2 , which is the midpoint of p 1 and p 3 : If the distance between p v and p 1 is less than or equal to 2 m, or if the ARV sails past L 1 , which is the vertical plane perpendicular to L that passes through p 1 , it can be determined that the ARV has reached the p 1 point and enters the short-range docking stage.

Short-Range Docking Stage
The purpose of the short-range docking stage is to control the ARV to navigate accurately to the docking station.The short-range docking stage can be appoached using an optical guidance method, or an autonomous navigation guidance method.In this paper, the autonomous navigation guidance method is used.
In the short-range docking stage, a heading path mode is used, the ARV sails from 5 m in front of the entrance nozzle of the docking station and the direction of the entrance nozzle of the docking station is used as the heading angle for docking.As the ARV approaches the docking station, the influence of the docking station positioning error on the heading angle increases.To avoid the above problem, the ARV will use a fixed-heading mode if the distance between the ARV and the docking station is less than 1.5 m.
As the docking system does not have a capture mechanism, it is impossible to judge whether the docking is in place by hardware.To stop the ARV after it has been guided to the docking station, it is necessary to calculate the sailing time through actual tests.

Correction of Docking Station Status Information
During the docking process, as the ARV approaches the docking station, it receives status information from the docking station measured by the USBL and the depth gauge through a hydroacoustic communicator.The docking station status information includes its depth, relative position and orientation angle, and the ARV uses this information to correct its docking strategy in real time.
The docking station depth correction method is as follows: if the difference between the received docking station depth and the docking station depth before update is less than 5 m, update the depth information.
The correction of the docking station relative position and orientation angle is obtained by the positioning information measured by the USBL.The method is shown in Figure 7: If the difference between the depth of the ARV and the preset depth of the docking station is less than 0.5 m, the ARV and the docking station are considered to be in the same horizontal plane.The formula for calculating the relative position of the docking station is as follows: where l r is the distance between the ARV and the docking station measured by USBL, ϕ v is the heading angle of the ARV and ϕ a is the azimuth angle of the docking station in the ARV coordinate system measured by USBL.If the distance between the new docking station position and the docking station position before update is less than 15 m, update the position information.
The formula for calculating the orientation angle of the docking station is as follows: where ϕ h is the azimuth angle of the ARV in the docking station coordinate system measured by the USBL.If the difference between the new docking station orientation angle and the docking station orientation angle before update is less than 15 degrees, update the orientation angle information.
The method for updating the position and orientation angle is shown in

Test Verification and Analysis
To verify the feasibility of the guidance method, tests on lakes and shallow seas are performed from July 2022 to August 2022.The tests include autonomous navigation docking tests and acoustic guidance docking tests.

Autonomous Navigation Docking Tests on the Lake
Autonomous navigation docking uses only position information provided by inertial navigation for guidance without using USBL to correct the docking station depth, position and orientation angle.The ARV starts the docking task at a random position between 20 m and 50 m away from the docking station and a random initial heading angle.The longguidance waypoints are set at 100 m and 80 m in front of the docking station, and the sailing speed is set at 2 knots for the first waypoint path mode and 0.3 m/s for the remaining stages.
The docking station is deployed 1.5 m underwater, and the position and the orientation angle of the docking station are measured and input to the ARV autonomous docking module as the preset docking station position and the preset orientation angle.
Real images and video screenshots of the autonomous docking tests on the lake are shown in Figure 9.A total of seven autonomous navigation docking tests were performed, of which four docking tests were successful.The records of the docking tests are shown in Table 1, where the lateral control error is the distance between the ARV position when docking is complete and the vector, which is in the direction of the docking station orientation angle through the docking station position.A positive value means that the ARV is to the right side of the vector, and a negative value means that the ARV is to the left side of the vector.Table 1 shows that the lateral deviation of the docking control using the position information provided by the inertial navigation has reached the accuracy required for docking.However, the large positioning error of inertial navigation causes the actual arrival position of the AUV to deviate, resulting in docking failure.The track and the deviation curve of the sixth autonomous navigation docking test are shown in Figure 10.It can be seen that as the ARV sails from the 100 m waypoint to the 80 m waypoint, there is some fluctuation in the lateral deviation at this stage due to the change in target heading.As the ARV approaches the 80 m waypoint, the lateral deviation has stabilised around 0, that is, the ARV has been adjusted to be close to the centreline of the docking station.As the ARV sails from the 80 m waypoint to the docking station, the track is always stable on the centreline of the docking station.When entering the docking station, the lateral deviation is −0.061 m.

Acoustic Guidance Docking Tests on the Lake
Acoustic guidance docking uses inertial navigation position for guidance and uses underwater acoustic communication to correct the docking station depth, position and orientation angle in real time.The ARV starts the docking task at a random position between 20 m and 50 m away from the docking station and starts the docking task with a random initial heading angle.The long-guidance waypoints are set at 120 m and 80 m in front of the docking station, and the navigation speed at each stage is the same as that of the autonomous navigation docking tests.
The docking station is deployed 1.5 m underwater, and the position and the orientation angle of the docking station are measured and input to the ARV autonomous docking module as preset values.
The acoustic guidance docking tests are divided into three stages: acoustic guidance performance tests, docking station orientation angle adjustment tests and docking station position adjustment tests.

Acoustic Guidance Performance Tests
In this stage, the USBL functioned only to adjust the position of the docking station, the method for updating the docking station orientation angle mentioned in Section 3.4 is not used, and the orientation angle of the docking station is kept at the preset value.
In the first stage of acoustic guidance docking, a total of 10 tests were performed, of which 8 docking tests were successful.The records of the docking tests are shown in Table 2.
The track and the deviation curve of the ninth acoustic guidance docking test is shown in Figure 11.The apparent position of the docking station after several updates has some deviation from the preset position because the inertial navigation of the ARV has a cumulative error during its navigation, resulting in some offset in its self-estimated position.As the ARV navigates from the 80 m waypoint to the docking station, its track is gradually corrected as the position of the docking station is continuously updated.When the docking is complete, the lateral deviation of the ARV relative to the updated docking station position is −0.909 m.It can be seen that the acoustic guidance docking algorithm has sufficient adjustment capability in the case of drift in autonomous navigation.Figure 11 shows that when the ARV is successfully docked, its position has not reached the updated docking station position that it has estimated using data provided by the USBL.After analysis, due to reasons such as data delay caused by ARV movement and the USBL operating mechanism, the estimated docking station position is directly behind the actual docking station position after multiple adjustments.This error affects the lateral deviation and the success rate of acoustic guidance docking.

Docking Station Orientation Angle Adjustment Tests
At this stage, the orientation angle of the docking station received by the USBL is used to update the docking strategy in real time and control the docking of the ARV.
In the second stage of acoustic guidance docking, a total of two tests were performed, both of which were successful.The records of the docking tests are shown in Table 3.
The track and heading angle update curve of the first acoustic guidance docking test are shown in Figure 12.The orientation angle of the docking station will fluctuate to some extent due to factors such as water flow.The ARV successfully used the updated docking station orientation angle to modify the docking path in real time, and the docking can still be successful.The lateral deviation of the ARV when it reaches the docking station was 0.023 m, which meets the accuracy requirements for docking.This proves that the ARV docking strategy can overcome fluctuations in the orientation angle of the docking station.

Docking Station Position Adjustment Tests
At this stage, the preset position of the docking station was altered so that there was a certain deviation from the actual measured position, forcing the ARV to correct its estimate of the position of the docking station in real time according to the information from the USBL.
In the third stage of acoustic guidance docking, a total of two tests were performed, of which one docking test was successful.The records of the docking tests are shown in Table 4.The track of the first acoustic guidance docking test is shown in Figure 13.The preset docking station position is 2.608 m east of the measured docking station position, so the ARV adjusts the relative position and the orientation angle of the docking station using the positioning information from the USBL and finally successfully completes the docking.The lateral deviation is 0.956 m when the docking is complete.

Acoustic Guidance Docking Tests in the Shallow Sea
In the shallow sea acoustic guidance docking tests, the ARV started the docking task with a random initial heading angle at a random position between 20 m and 500 m from the docking station.The long-guidance waypoints were set at 220 m, 180 m, 120 m and 80 m ahead of the docking station, and the sailing speed was set at 2 knots for the first waypoint path mode and 1 knot for the remaining stages.
The docking station was deployed 1.5 m to 2.5 m underwater, and the position and the orientation angle of the docking station were measured and input to the ARV autonomous docking module as preset values.
Real images and video screenshots of the autonomous docking tests in the shallow sea are shown in Figure 14.A total of eight acoustic guidance docking tests were performed, of which six docking tests were successful.The records of the docking tests are shown in Table 5.The track and the deviation curve of the seventh acoustic guidance docking test are shown in Figure 15.To overcome the influence of the complex underwater environment on ARV navigation and USBL reception, more waypoints were set in the long-range approach stage, adjustments were made from a longer distance to reduce lateral deviation during docking and more USBL positioning information was received to locate the relative position of the docking station more accurately.It can be seen that the ARV has tracked to the centreline of the docking station when it sailed to 180 m ahead of the docking station.During the approach, as the position and orientation angle of the docking station are updated, the centreline of the docking station will also change, resulting in an increase in the lateral deviation of the ARV.Through continuous adjustment, the ARV can track the centreline of the docking station in real time and complete the docking successfully.We have compared the success rates of some classical docking tests in the sea, as shown in Table 6.It can be seen that the docking algorithm in this paper has improved the docking success rate, demonstrating the reliability of the docking algorithm.The heading adjustment algorithm in the mid-range adjustment stage effectively reduced the lateral deviation during docking.The real-time adjustment of the depth, relative position and orientation of the docking station using USBL effectively overcame the depth and orientation changes of the docking station in the water as well as the cumulative errors generated by the ARV inertial navigation.All these were helpful for the improvement of docking success rate.After analysis, the following reasons are summarised for the failures of the acoustic guidance docking tests in the shallow sea: 1.
The ocean environment is complex and changing; sea currents and waves will also affect the navigation of the ARV, resulting in docking failure.

2.
There is a drift in autonomous navigation; if the ARV has a long continuous underwater navigation distance, the inertial navigation will accumulate significant error; if the error is large, it will be difficult for the ARV to adjust to the centreline of the docking station after it begins to receive information from the USBL, resulting in docking failure.

3.
If the ARV does not receive a sufficient amount of docking station status information, it may not be able to locate the correct position of the docking station, resulting in docking failure.

Conclusions
Aiming at persistent operation of autonomous underwater vehicles, this paper proposes an underwater docking method based on acoustic guidance.According to the structural properties of the funnel docking station, the underwater docking is divided into three stages.To solve the problem of autonomous navigation deviation in underwater docking, a USBL-based correction method for the docking station depth, relative position and orientation angle is proposed.Autonomous navigation docking tests on a lake were first performed, with a docking success rate of 4 out of 7. Next, acoustic guidance docking tests on the lake were performed, and the docking success rate was 11 out of 14.Finally, through shallow sea tests, acoustic guidance docking tests were performed, with a docking success rate of 6 out of 8.The following conclusions can be drawn from the analysis of the test data: the average lateral error of the autonomous navigation docking was 0.077 m, which met the required accuracy for docking, however, due to the cumulative error of inertial navigation, the docking success rate was low; acoustic guidance docking tests on the lake improved the docking success rate by 17.9% by correcting the ARV's estimate of the depth, relative position and orientation angle of the docking station, verifying the reliability of the acoustic guidance algorithm on the lake; finally, in acoustic guidance docking tests in a shallow sea, due to the complexity of the ocean environment, the success rate of the docking was reduced.Therefore, improving the docking success rate of acoustic guidance in the sea and increasing the stability of the docking guidance algorithm are the focus of future research.

Figure 2 .
Figure 2. Structure diagram of the docking control module.

Figure 5 .
Figure 5. Judgment of reaching the target position.

Figure 6 .
Figure 6.Path tracking method in the mid-range adjustment stage.

Figure 7 .
Figure 7. Correction of the relative position and orientation angle of the docking station.
Figure 8. DP . . .and DO . . .are the currently stored docking station positions and orientation angles, 5 groups are stored in total and the initial values are the preset position and orientation angle of the docking station.DP and DO are the new status information measured by USBL, DP mean and DO mean are the average docking station position and orientation angle.If DP and DO satisfy the conditions for updating the position and orientation angle of the docking station, they are pushed into the array and DP 0 and DO 0 are pushed out of the array.The ARV uses the updated position and orientation angle of the docking station DP mean and DO mean .

Figure 8 .
Figure 8. Method of updating the position and orientation angle.

Figure 9 .
Figure 9. Autonomous docking tests on the lake.

Figure 10 .
Figure 10.(a) Track of autonomous navigation docking test on the lake.(b) Deviation curve of autonomous navigation docking test on the lake.

Figure 11 .
Figure 11.(a) Track of acoustic guidance docking test on the lake (stage 1).(b) Deviation curve of acoustic guidance docking test on the lake (stage 1).

Figure 12 .
Figure 12.(a) Track of acoustic guidance docking test on the lake (stage 2).(b) Orientation angle update curve of acoustic guidance docking test on the lake (stage 2).

Figure 13 .
Figure 13.Track of acoustic guidance docking test on the lake (stage 3).

Figure 14 .
Figure 14.Autonomous docking tests in the shallow sea.

Figure 15 .
Figure 15.(a) Track of acoustic guidance docking test in the shallow sea.(b) Deviation curve of acoustic guidance docking test in the shallow sea.

Table 1 .
Records of autonomous navigation docking tests on the lake.

Table 2 .
Records of acoustic guidance docking tests on the lake (stage 1).

Table 3 .
Records of acoustic guidance docking tests on the lake (stage 2).

Table 4 .
Records of acoustic guidance docking tests on the lake (stage 3).

Table 5 .
Records of acoustic guidance docking tests in the shallow sea.

Table 6 .
Comparison of success rates of sea docking tests.