Alternating landmark navigation of multiple AUVs for wide seafloor survey: Field experiment and performance verification

This paper reports the results of the sea experiments and the performance verification of a navigation method for wide area surveys of the seafloor using multiple autonomous underwater vehicles (AUVs). In the method, AUVs alternately land on the seafloor to act as landmarks for each other, and all AUVs can observe a wide area with accurate positioning relative to the landmark AUV. For self‐localization, AUVs are typically supported by long base line (LBL) or super short base line (SSBL) of the support system. Thanks to the proposed method, AUVs can perform near‐seafloor surveys requiring real‐time and accurate positioning, such as seafloor imaging and sampling, without these support systems. The method was implemented on two AUVs: “Tri‐Dog 1” and “Tri‐TON.” The performance of the method was verified using these AUVs through sea experiments and postprocessing simulation using experimental data. In addition, it was also verified that the performance of the method is comparable to high‐grade conventional navigation methods, such as LBL or SSBL, through simulations of long distance navigation.


INTRODUCTION
This paper reports the results of sea experiments of the navigation method of multiple autonomous underwater vehicles (AUVs). In the method, each AUV alternately becomes a landmark AUV, which remains stationary on the seafloor, enabling all other AUVs to navigate over a wide area with high positioning accuracy based on the landmark AUV. For self-localization, AUVs are typically supported by long base line (LBL) or super short base line (SSBL) of the support system. The proposed method realizes stable navigation using only AUVs. Our aim is to realize surveys near the seafloor using only AUVs without any surface aid. The method is suitable for wide area surveys requiring accurate positioning, such as seafloor imaging and sampling.
Oceans occupy about 70% of the Earth's surface. Because of water pressure and light attenuation, the seafloor is not easy to access and is still mysterious to humans. Many scientifically meaningful objects such as seafloor minerals, 1 special ecosystems and habitats, 2,3 and terrain features exist on the seafloor. Moreover, searching for lost artifi-F I G U R E 1 The concept of the alternating landmark navigation approach was first proposed by Kurazume and Hirose, 13 where it was referred to as a cooperative positioning system (CPS). To the best of our knowledge, this is the first application of the CPS to the field of AUV navigation.
The navigation of multiple vehicles in land and aerial environments has been extensively investigated, and many navigational methods have been proposed and demonstrated using actual vehicles. [14][15][16][17] In marine environments, however, there is less research than in land or aerial environments. In one report, the research group of Woods Hole Oceanographic Institute (WHOI) in the USA has conducted an investigation of the Arctic Ocean using two AUVs called "JAGUAR" and "PUMA". 18 In another approach, two moving AUVs realize cooperative positioning from range-only measurements. 19 A research group from Massachusetts Institute of Technology (MIT) proposed a navigation method that uses multiple autonomous surface vehicles (ASVs), 20 and have studied cooperation between ASVs and AUVs. The methods regarding supporting ASVs for navigation of AUVs have been proposed. [21][22][23] This paper is organized as follows. The method is explained in Section 2. Section 3 describes the system to realize the method. Section 4 presents and discusses the experimental results. This section also evaluates the performance of the method by postprocessing simulation using experimental data. The performance of the proposed method is compared with conventional navigation methods through simulation in Section 5. Section 6 discusses the method based on sea experiments and simulation. Conclusions and ideas for future work are presented in Section 7. The work of our previous study 24 is extended in this paper. This paper is different from the previous study in the followings: • The performance of the method is statistically evaluated through a series of postprocessing simulations using experimental data.
• The performance of the method is analyzed against multiple dives, and the robustness of the method is also evaluated.
• For showing one example of the applications of the method, a photomosaic of the seafloor obtained by two AUVs is shown.
• The performance of the method is compared with conventional methods through simulations of long distance navigation.
• Requirements to improve the estimation accuracy of the method are examined.

Alternating landmark navigation
Alternating Landmark Navigation (ALN) is a navigation method where two AUVs alternate between the moving and landmark roles (defined as the "main AUVs") and the other AUVs constantly estimate their own positions based on the landmark AUV (defined as the "sub AUVs"). All the AUVs can expand their observational coverage with high positioning accuracy based on the landmark AUV. To generalize the ALN, four AUV case is considered. Figure 1 illustrates the concept of the ALN for four AUVs: A, B, C, and D. Let us assume that A and B are the main AUVs and C and D are the sub AUVs. Initially, A is in the moving role, and B is in the landmark role. Then, the procedure is as follows: 1. The moving AUVs A, C, and D perform observation tasks relative to AUV B, which remains stationary on the seafloor. The moving AUVs estimate their states based on B through a probabilistic approach (a particle filter is adopted, which will be described in

After communication between A and B has been completed, A
becomes the new landmark, and B, C, and D start moving based on A.
This paper deals with the navigation of main AUVs.

Characteristics of the ALN
The ALN has the following advantages: • Support from the surface is not necessary.
• Observation coverage is not limited by the positioning range because AUVs exchange the landmark role before leaving the range. On the other hand, there are also some problems: • Position error will occur in the landmark AUV as the AUVs exchange the landmark role. This is caused by measurement errors from the velocity sensor, the angular velocity sensor and the acoustic positioning sensor. In particular, accuracy of the acoustic positioning sensor is easily influenced by environments. Thus the next landmark AUV cannot completely correct position error with respect to the previous landmark AUV when they exchange the landmark. As the AUVs perform landmark exchange, position errors can increase.
• At least one AUV must be a landmark and remain stationary on the seafloor.
The ALN is expected to be one of the leading new seafloor survey technologies. It will become possible to obtain environmental information, such as seafloor photomosaics, chemical concentration maps, and geographical feature maps, from a wide area of the seafloor using only AUVs.

State estimation
State estimation is the most basic technique involved in realizing the method 25 and is performed by moving AUVs. Here, the state estimation technique for main AUVs is shown.

State
An AUV's state consists of its three-dimensional position (x, y, z), attitude (roll , pitch , and yaw ), and altitude a. The depth z and altitude a can be precisely measured by a pressure sensor and an acoustic range In the main group, the moving AUV estimates the parameters of the landmark AUV as well as its own. The states in the main group at time where the suffixes M and L denote "moving" and "landmark," respectively.

Procedure
A stochastic approach (such as a particle filter and an extended Kalman filter: EKF) is introduced. 26 Here, the particle filter, in which the probability density of the states is expressed by a set of particles, is adopted.
As the number of particles increases, more complicated distributions can easily be expressed. In the ALN, as the landmark AUV also has state uncertainties, states include two AUVs' positions and headings F I G U R E 1 2 Location of the experimental station in "OKI SEATEC" (Google) F I G U R E 1 3 Experimental station in "OKI SEATEC" in the main group. As the states consist of more parameters than in a single AUV case, they can change with complex correlation between each parameter. As the particle filter expresses the states by a set of particles, complex state distributions can be expressed accurately. Several particle filter-based navigation algorithms for vehicular navigation have been proposed, some of which have been implemented in AUVs. 9,11,12,[27][28][29] The particle filter updates the states through two phases: the prediction phase and the observation phase. In the prediction phase, the moving AUV estimates the states from its navigation sensors. The ground velocity sensor and heading rate gyro provide the ground velocitŷt and the angular velocitŷt, respectively. The hat symbol indicates sensor measurements. In the observation phase, the states are updated from relative acoustical positioning measurements between the moving and landmark AUVs. The positioning measurements are the relative distancer t and the relative directionŝM L t ,̂L M t . Note that̂M L t is the direction from the moving AUV to the landmark AUV, whereaŝL M t is the reverse direction. The moving AUV transmits an interrogating signal to the landmark AUV. Then, the landmark AUV receives this signal and calculates the direction to the moving AUV (̂L M t ). After that, the landmark AUV transmits the reply signal with the direction information (̂L M t ). Then, the moving AUV receives this reply signal and calculates the ranger t and the direction to the landmark AUV (̂M L t ). Finally, the moving AUV estimates the states based on range and two direction measurements. 30 Figure 2 shows the concept of state estimation. Figure 3 shows the timeline of the state • The interval of measurements has delay.
• The interval of measurements for the observation phase is longer than that for the prediction phase.

Formulation
The state of the main AUVs S t at any given time t can be represented as follows: where i t is the ith particle and n is the number of particles.

Prediction phase
The state from t to t + Δt is estimated from the ground velocitŷt and the angular velocitŷt, as discussed above, in the prediction phase. Sampling frequency is assumed to be Δt. Thus, the state of the moving AUV is updated as where is the rotation matrix expressed as Mi where t and t are standard deviations of the ground velocity and angular velocity, respectively. N( , 2 ) is a Gaussian sampling with mean and variance 2 . The probability density function of the Gaussian distribution f(x) is expressed as follows: Since the landmark AUV is stationary on the seafloor, its ground velocity and angular velocity are assumed as 0. The concept of the prediction phase is shown in Figure 4.

Observation phase
Observation is implemented in the second phase. If the measurements of relative direction and distance between the two AUVs are successful, they are used by the moving AUV to update the particles. The likelihood of each particle is given by where L ML and L LM are the likelihoods estimated from measurements collected by the moving and landmark AUVs, respectively. w i t denotes the weight of the ith particle. When no positioning measurements are obtained, the weight is assigned as 1, and the likelihood value remains unchanged. The observation data are the relative distancer t and the where the terms are defined as in Figure 5. The likelihood L ML ( i t ) is then calculated as follows: where r and M are the standard deviations of the distance and direction measured by the moving AUV. Gaussian errors are assumed in the measurements. The parameters k r and k M prevent extreme fallout of the likelihood when outliers enter the measurements. The terms k 2 r ∕2 and (k M ) 2 ∕2 in the exponential functions smooth the output at the boundaries. 9 Similarly, L LM ( i t ) is calculated from the relative direction̂L M t measured by the landmark AUV, where the terms are also defined as in Figure 6. (15) where L is the standard deviation of the direction measurement by the landmark AUV. According to the likelihood obtained by Eq. (10), each particle is resampled and made to form S t+ΔT .

Particle reconstruction
Although the particle filter ensures robustness to sensor noises or lack of measurements, it offers no protection against positioning errors, which may cause incorrect convergence of the particles. This problem is significant for the ALN because it degrades the accuracy of the state of the landmark AUV during the landmark role exchange. Such local-F I G U R E 2 0 Enlarged figure of Figure 19. The upper panel shows the heading angle from the magnetic sensor. The center and lower panels show the heading angle and angular velocity from TD's FOG. As the magnetic sensor measures magnetic direction and the FOG measures angular change from turning on the power, both zero points are different ization failure, known as "robot kidnapping," can be resolved by adding random particles based on the probability of sensor measurements. 26 In our approach, the average likelihood of the state L(S t ) is monitored and localization failure is corrected by adding new particles (particle reconstruction). 31 The average likelihood is defined as Localization failure is indicated by a marked drop in the average likelihood. In the absence of errors, the likelihood is defined as In the absence of valid positioning measurements, both likelihoods [Eqs. (18) and (19)] are set to 1. The average likelihood also decreases when outliers enter the measurements. To distinguish localization failure from outliers, the likelihood transit is monitored. Continual decreased likelihood is attributed to local- where ΔT is the time interval between positioning measurements, and is an arbitrary multiplication threshold that decides whether particle reconstruction will be implemented.
a is an arbitrary trial number that determines the time of likelihood monitoring.
Particles are selected and replaced by new particles in order of ascending likelihood. The number of new particles is determined by ⌊x⌋ denotes the largest integer not exceeding x (the floor function). The logarithmic function prevents extreme fallout of the likelihood caused by the exponential function. To prevent exchange of the entire particle set, the number of replacements is limited to 100r%. At least a measurements are required between one particle reconstruction and the next.
A new ith particle is determined from the ith particle of the landmark AUV and positioning measurements. First, the ith particle's posi-  24) and (25). In particle reconstruction, only the state of the moving AUV is revised. The landmark state is unchanged. To prevent from adding particles based on accidental outliers, particle reconstruction is conducted only when offsets and Δ , respectively, wherēM t and̄M t indicate the average position and heading angle of particles. The concept of particle reconstruction is shown in Figure 7. The trial number of monitoring a 3 The ratio of particle replacement r 50%

State communication 2.4.1 Outline
As estimated states are complete summaries of the past, the main AUVs need to share the states when they exchange the landmark role.
However, as the states are expressed by particles, complete state sharing is precluded by the typically low data rates of acoustical communications in underwater environments. To overcome this problem, the previously moving AUV A compresses its estimated states before transmitting this information to the next moving AUV B, 25 as detailed in the following procedure:

2.
To reduce the communication data size, A compresses its estimated states by "particle clustering" using a clustering method and a model selection method.

3.
A transmits the compressed information regarding its estimated states to B.

Procedure
The particle clustering approach is illustrated in Figure 8. The original particles are first divided into groups by k-means clustering To determine the optimal approximate model, processes A-C in

K-means clustering
The particles of the AUVs are subdivided by k-means clustering, which partitions a set of particles into k clusters. Each particle is assigned to the cluster with the nearest mean.

Normalization of the particles
To calculate Euclidean distance between the particle and the cluster center, the particles are normalized. The ith normalized particle i t (i = 1, … , n) is expressed by Eq. (26), where the bar denotes the average of the particles and indicates their standard deviation.

Initialization for clustering
Initially, the centers of the k clusters are undefined. Initial cluster centers are defined by the k-means++ method, 35 an initialization algorithm that prevents local optimal clustering when initial centers are randomly selected. Initialization by the k-means++ method proceeds as follows: F I G U R E 2 6 Estimation errors of the DR 1. The first center 1 t is randomly selected from the particles. 2. D( i t ), the distance between i t and the nearest center (i.e., already selected center), is calculated for each normalized particle i t (i = 1, … , n).

3.
The new center j t is stochastically selected according to a weighted probability distribution, from which particle i t is chosen with prob-

4.
Steps 2 and 3 are iterated until k centers have been selected.

Clustering
Based on the initial centers j t (j = 1, ⋯ , k), the cluster number n i c to which the ith particle belongs is determined by Once each particle has been assigned to one cluster, the new clus-

Approximation
Once the particles are clustered, the k averages j t (j = 1, … , k) and variances j t (j = 1, … , k) of the clusters are obtained. To approximate a set of original particles, a mixed Gaussian distributions is compiled from the cluster statistics.
where j is the ratio of the number of particles in the jth cluster to the total number of particles. N( j t , j t ) is the jth Gaussian distribution derived from the statistics of the jth cluster ( j t , j t ).

Selection of an optimal model
The extent to which the approximated model fits the original particles is evaluated by the AIC. 34 The AIC measures the relative quality of a statistical model and is expressed as follows: .
is the likelihood by substituting the ith particle i t into a multivariate normal distribution with average vector j t and variance matrix j t , which are derived from the statistical values of the jth cluster. To reduce the required communication size, the covariance is not considered here. Alternatively, the detail of the original particles are expressed by incrementing the cluster size. As each particle of the AUV is composed of six parameters, the degree m is six.
The AIC returns L( ) and F(k), expressing the goodness of fit and the penalty function, respectively. The penalty discourages overfitting as the number of free parameters is increased in the approximation. The smaller the AIC value, the better the statistical model. Based on the AIC, the steps in Figure 8 are repeated to construct an optimal approx-imated model. Assumed that the latest AIC value is AIC n and the current optimal model's AIC value is AIC o , the latest model is recorded as the new optimal model if AIC n < AIC o .

Positioning and communication device
A positioning and communication device was developed to realize the method. The system is called an Acoustic Localization and Communication (ALOC) shown in Figure 9. 30

AUVs
The method is implemented on the AUV "Tri-Dog 1" (TD) and AUV "Tri-TON" (TT). Both AUVs are hovering-type AUVs with thrusters that can independently control surge, sway, heave, and yaw motions. 36

SEA EXPERIMENT
This section describes the sea experiments for verifying the performance of the ALN using two AUVs (TD and TT).

Objectives
• To realize a wide area survey using two AUVs with the ALN in a sea environment, • To evaluate the performance of the ALN in a sea environment, and • To compare the ALN with a conventional navigation method using sea experimental data.

Experimental site
The series of experiments were conducted in August, 2014 at "OKI SEATEC" in Uchiura Bay in Japan (Fig. 12) and was supported by the staff of "OKI SEATEC." Figure 13 shows the appearance of the experimental station in "OKI SEATEC." The terrain of the experimental site is almost flat.

Conditions
The experiments were conducted under the following conditions. The setup of the experiments is illustrated in Figure 14.
• TD is the first moving AUV and TT is the first landmark AUV.
• The moving AUV takes photographs of the seafloor.
• The moving AUV estimates the states using measurements from the DVL, the FOG, and the ALOC. • Particle reconstruction was not used.
The positions obtained by the SSBL were just used for off-line performance evaluation.

Parameters
The sensor errors and the parameters of the particle filter were set as shown in Table 3. Sensor errors were determined through tank tests or sea experiments. 12 The number of particles was determined

Procedure
First, the initial landmark AUV, TT, was deployed. Next, the initial moving AUV, TD, was deployed. After the two AUVs had dived, they surveyed the seafloor, alternately taking on the landmark role. The AUV in the moving role surfaced first after completing the mission. Figure 32

Outline of the results
Four dives were conducted. Dives 1 and 2 were for short distance navigation. Dives 3 and 4 were for long distance and wide area navigation.
The outline of each dive is explained below. Here, we focus on the results of Dive 4.    Figure 17 shows the horizontal ground velocities of both AUVs during the mission. From this figure, we observe that while one AUV was moving, the other remained stationary (ground velocity was around 0).

Sensor measurements
The surge velocities (Vx) of TD and TT when they are in the moving role were around 0.15 m/s, which is the reference value. It is clear that the two AUVs alternately moved. Figure 18 shows the altitude measurements of both AUVs. We observe that while one AUV was moving at the reference altitude, the other remained on the seafloor. Offset values when they are landed indicate the height of the landing gear.     Table 4 shows the averages and standard deviations of the displacements of the corresponding features. As displacements are around 1 pixel for each landmark time, it is obvious that TT kept stable during the time when it was landed.

Analysis of landing stability based on seafloor pictures
Next, TD's case is examined. Figure 22 Table 4, it is also obvious that TD remained stable when it was at the first and second landing positions.
From both the results of sensor measurements and seafloor pictures, it was verified that both AUVs kept stable on the seafloor except for the time when TD was at the third landing position.

Performance analysis: Estimation accuracy-
To support discussion of the performance of the ALN, postprocess-

Conditions
The simulations were carried out under the following conditions: • The number of particles increased from 300 (TD) and 500 (TT) to 5000 to enhance the accuracy of the state estimation.
• The parameters of the particle filter were set to the same values as those shown in Table 3. The parameter setting of particle reconstruction is shown in Table 5. The determination of the parameters is shown in Ref. 31.  In real-time navigation, estimation errors increased greatly during TD-2, TT-2, and TD-3 (Fig. 16). The following three items are considered as a cause.
• The number of particles Since the number of particles was smaller than postprocessing simulation for computational cost, the state distribution cannot be expressed accurately and localization failure was likely to occur.
• The recovery method from localization failure During TD-2, estimation uncertainty increased due to lack of positioning measurements. As the recovery method from localization failure (particle reconstruction) was not used in real-time navigation, incorrect convergence during TT-2 caused great errors.
• Heading change of TD

Results (Dive 1-3)
To evaluate the robustness of the ALN, postprocessing state estimation was also carried out against Dive 1-3.

Application example of the ALN
The AUVs obtained seafloor pictures in the experiments. Figure 47 shows a photomosaic of the seafloor in Dive 4, which was obtained

Conditions
In Section 4, the performance of the ALN was compared with the DR.
Comparison with the other typical navigation methods was performed in this section. A series of simulations of long distance navigation were performed. The following cases were compared. The states were estimated by the particle filter (Case 1-4). The number of particles was set to 5000. The parameters of the particle filter were set to the same values as those shown in Table 3. The navigation conditions are almost the same as in Case 1.
It is assumed that AUVs have a high-grade positioning sensor for relative positioning (Teledyne Benthos). The performance of this sensor is shown in Table 6. AUVs used this sensor for positioning instead of the ALOC. The AUV performed only the prediction phase. This is same as in Case 2 in Section 4.4
The AUV estimated the states based on the measurements from the DVL as well as the triple-axis FOG. As the triple-axis FOG can measure true north, the heading error is assumed to be 0. The AUV performed only the prediction phase.   However, these conventional methods have several drawbacks such as time-consuming calibrations and system costs. As the ALN does not require these support systems, it provides a promising method in AUV navigation.

DISCUSSION
Throughout the experiments and simulations, it was verified that the ALN provides a stable and accurate survey of the seafloor. From the experiments, postprocessing simulations and long distance simulations, the following items are important for the ALN to improve positioning accuracy in real-time navigation.
• To improve AUV's stability during the landmark period.
In the ALN, the landmark AUV is kept on the seafloor by its own weight. There is possibility that the landmark AUV is moved by disturbances, such as currents. As the moving AUV estimates the states and cannot notice the state change of the landmark AUV in real time, this change can cause great errors. Thus, a method where the landmark AUV keeps its stability is necessary.

F I G U R E 4 7 Photomosaic of the seafloor obtained by two AUVs
• To implement high-grade positioning sensors.
Although it requires sensor cost, estimation errors through landmark exchange can be reduced. It can also reduce trial numbers of the landmark exchange.
• To recover from state estimation failure (particle reconstruction).
The recovery method will reduce the risk of increasing errors through the landmark exchange.
• To ensure a sufficient quantity of particles.
This will reduce the risk of estimation failure.
• To converge state uncertainties sufficiently before the landmark exchange.
From Figures 28 and 32-34, it was found that the particles were converged incorrectly, as the AUVs exchange the landmark role without By considering these items, the performance of the ALN will conduct sufficient performance in real-time navigation.

CONCLUSIONS AND FUTURE VISIONS
This paper reported the performance verification of the ALN for wide area surveys of the seafloor using multiple AUVs. For self-localization, AUVs are typically supported by LBL or SSBL of the support system. Through the simulation against all dives, it was statistically verified that the ALN has robust performance. In addition, it was also shown that the performance of the ALN is comparable to high-grade conventional navigation methods such as LBL or SSBL through simulation for long distance navigation.
As a result, it was verified that the ALN has the performance to conduct wide seafloor surveys with high positioning accuracy, enabling applications such as accurate seafloor photomosaicking, without any support. The ALN can be applied to several types of surveys such as bathymetry mapping, monitoring of seafloor life, resource surveys, searching for lost objects, and so on. The ALN will be a new observation technology of the seafloor and will contribute to enhance our understanding of the seafloor.