A new autopilot system for unmanned underwater vehicle (UUV) using multi-single-beam sonars is proposed for environmental exploration. The proposed autopilot system is known as simultaneous detection and patrolling (SDAP), which addresses two fundamental challenges: autonomous guidance and control. Autonomous guidance, autonomous path planning, and target tracking are based on the desired reference path which is reconstructed from the sonar data collected from the environmental contour with the predefined safety distance. The reference path is first estimated by using a support vector clustering inertia method and then refined by Bézier curves in order to satisfy the inertia property of the UUV. Differential geometry feedback linearization method is used to guide the vehicle entering into the predefined path while finite predictive stable inversion control algorithm is employed for autonomous target approaching. The experimental results from sea trials have demonstrated that the proposed system can provide satisfactory performance implying its great potential for future underwater exploration tasks.
Underwater exploration often encounters environment that is difficult or even impossible for humans to access due to their physical constraints such as deep depth, narrow spaces, and severe working conditions. Unmanned underwater vehicle has a number of advantages for exploring underwater environments, such as autonomous control ability and self-sufficient energy supply. Autopilot of UUV often relies on the information or characteristics (e.g., geometrical information) of the surrounding environment, reflected by data collected from sensors such as sonars.
When in operation, sonar sends out an acoustic beam and the returned (usually the fastest) beam from the environment is collected to determine the distance and location of the environment. This means that it can detect the point on the contour that has the shortest distance from the sonar. Therefore, sonar data can be used to plan the desired path of the UUV and control it by changing thruster forces and rudder angles of the UUV to approach the target. An important issue for designing UUV control systems is the strength of the signal observed from sonar. It is weak primarily due to the random effect caused by complicated marine disturbance; other interferences between received beams can be due to delay and scattering effect.
In this paper a new autopilot system, known as simultaneous detection and patrolling (SDAP), is proposed to address this challenge. Autonomous guidance and control are implemented synchronously where the reconstructed environment contour is used as the guidance path for UUV navigation. For the environment contour reconstruction, the major focus of research is on simultaneous localization and mapping (SLAM) [
In this paper autopilot of UUV for both closed and open environments is considered, as shown in Figure
Illustration of the proposed SDAP system for different environments.
The main novelties of this paper are as follows. To address the weak sonar data, a wavelet transform is applied to preprocess the original data so as to eliminate possible outliers in the original sonar data. To reduce the information loss in the preprocessing, the wavelet coefficient values of the current time are estimated using those coefficients estimated in the past times and the original sonar data. All the estimated wavelet coefficients are then regarded as the data resource for the contour reconstruction processes. A support vector clustering (SVC) inertia algorithm is proposed to cluster the data into different classes so as to determine the property of the original sonar data and obtain the boundaries of the classes (also known as contour). The resulting contour after this step is composed of successively connected lines. To satisfy the inertia property of the UUV path, the initial contour is smoothed using different order Bézier curves which are automatically determined by the local properties of the structural environments. With the information of the smoothed contour as the reference path and a predefined safety distance, an improved inversion algorithm, finite predictive stable inversion is proposed to control vehicle navigation.
The remainder of this paper is organized as follows: in Section
In this paper five single-beam sonars are configured on the vehicle in order to automatically detect the underwater environment: three sonars in the front to detect local environment characteristics and two on the left and the right side for contour reconstruction. The three front sonars are deployed in a way where the middle one is located on the axis of the vehicle surge direction and the other two are installed on the left and right of the middle one with an angle of 7.5 degree, respectively.
Data collected from sonars often include useful data describing obstacles and noise from random outliers. To address the “false alarm” problem in vehicle navigation, those outliers have to be detected and eliminated as much as possible. Outliers can be divided into noise patches and objects (e.g., fish swarm) that have less or no threats to the vehicle. Therefore, three different types of objects are defined as follows.
With the above definitions, data describing TO is considered to be useful while LTO and noise are regarded as outliers in this paper. Let
Metrics to categorize obstacles.
|
|
|
Class |
---|---|---|---|
1 | 1 | No | TO |
1 | 1 | Yes | GLTO |
1 | 0 | No contour | Noise or SLTO |
Outliers mixed in the dataset can be described as singularities by estimating local Lipchitz exponent using wavelet transforms. Defined either at a certain time instant or in an interval, Lipschitz exponent can be calculated by numerical methods. A wavelet transform modulus maximum (WTMM) is introduced to preprocess the sonar data.
Let
Mathematically the local regularity indicated by Lipschitz exponent is the precondition for data reconstruction using wavelet transform. Owing to the relationship between the WTMM and Lipschitz exponent, the pattern of change in WTMM at different scales is of great importance for the preprocessing of weak data. At a certain scale, if the maximum modulus exists at some time point, search along the scale decrease direction within the cone of influence will find a singular point or a peak point close to the zero scale, which can be determined by the Lipschitz exponent.
In order to remedy the eliminated sonar data and to guarantee the continuity of the reconstructed contour, the wavelet coefficient estimation method proposed by Liu and Mao [
Confidence limit is introduced to assess the degree of match between the wavelet coefficients and the model calculated using the data. Hypothesis test is used to estimate this confidence limit.
Assume that
The tracking evaluation function is introduced to estimate the confidence limit,
If
Determination of class types.
Ratio | Class type |
---|---|
≥1 | Outliers |
<1 | Valid data |
The preprocess sonar data by using the wavelet transform can locally amplify abnormal signals or outliers. This observation helps detect and eliminate potential outliers in order to reconstruct the contour of environmental structure. Support vector clustering (SVC) inertial algorithm was used to achieve the initial contour reconstruction.
The main idea of SVC is to project sonar data
In high dimension space, the distance from
After the clustering, the sonar data are separated into three classes according to the position with respect to the class bound, shown in Table
Criterion of clustering.
Class | Condition | Conclusion |
---|---|---|
Nonbounded support vector |
|
Class contour |
Bounded support vector |
|
Outliers |
Data class |
|
Class data |
Adjacency matrix
Inertia algorithm is a common action delay method proposed to avoid unnecessary actions of the UUV in order to escape from potentially threatening obstacles [
Flow chart of outlier inertia detection for preprocessed data.
Let
The conditions for classifying the sonar data into the alternative set can be described as follows. There is not any known class.
At the beginning of path planning, there is not enough sonar data to be clustered and to clearly indicate any obstacles. The data If any
where
Assume that
Outlier set is symbol by
For arbitrary data
Visible space is an artificial sphere space centered at
To determine the property of any
It is observed that the objects for reclustering
Sonar data
In environmental structure detection, data gradually accumulates. Through preprocessing using wavelet transform and clustering by SVC inertia algorithm, an initial contour can be reconstructed with data class bound as reference. The initial contour consists of several successively connected lines.
Based on the assumption that the data collected from the 5 sonars are accurate, three different local environmental characteristics can be determined, and they are described as follows.
Figure
Diagram illustrating line path.
If the left (resp., right) side sonar data is valid and the right (resp., left) one shows maximum effective distance, then the vehicle is on a line path and on the right (resp., left) side of the contour. Remark: energy carried with an UUV is often limited. When there is no obstacle on one side of the vehicle, the sonar on that side can be turned off in order to conserve energy and extend the working time for the mission.
If the distance between the environment contours on both sides of the path is not wide enough for the vehicle to turn safely, the vehicle is in a narrow path. Figure
Diagram illustrating narrow turn path.
The triangle inequality theorem states that any one side of a triangle is always shorter than the sum of the other two sides. For the triangle with
Let
The determination of regular turning path is similar to the narrow turning path. If the left side sonar data is effective, the vehicle in regular turning path can be separated into two situations according to the data from the 3 sonars at the front; see Figure
Diagram illustrating normal turn paths.
The initial contour reconstructed by using the SVC inertia algorithm comprises lines that are successively connected. Due to the inertia property of the underwater vehicle, this cannot be used as the reference path for tracking. In this paper, Bézier curve is introduced to smooth the initial contour in order to extract a reference path that can be used for navigation.
Given a set of control points
Based on Section
Based on the definition of
For the first and last segments,
Given all the above conditions, the total number of the control points required to be known is 5 for the first and last segment, respectively. This implies that 4th-order Bézier curves are needed for both of them.
To guarantee
Orders of Bézier curve.
Local environment character | Order of Bézier curve |
---|---|
Turning | 2nd-order |
Start and final segments | 4th-order |
Middle segments | 5th-order |
Two types of feedback linearization methods are used for path tracking control: differential geometry feedback linearization and stable inversion, which can be used for exactly automatic target approaching in known region and contour reconstruction in unknown region, two stages of the navigating process. This will be detailed in this section.
The path tracking control model for a UUV can be described with state vectors as follows:
The UUV is diving underwater with arbitrary states (including heading and position) at any point and has to be able to navigate towards a preset target near the structural environment. This is known as
Rolling path with different orientations to find initial points on reference path.
Let model output be
It has been proved that any nonlinear path can be reconstructed by circular arcs and lines [ Circle Path. Assume that
where
According to the position between the desired path and the current position of the vehicle, radius of a rolling path can be derived as follows: when the initial position of the UUV is outside of the circular path (see Figure when the initial position of the UUV is inside of the circular path (see Figure Line Path. With line path
where
Rolling path generation for three different situations. (a) UUV is outside circle path. (b) UUV is outside circle path. (c) UUV is outside line path.
UUV tracking system satisfies
Figure
Assume (i) the mass, added mass, and damping coefficients are diagonal matrixes; (ii) Assumption
The lines and circular arcs can be combined to form any nonlinear path; therefore, the proof is established from the following two aspects. Desired path is a circle path.
Obtaining a direct relationship between the output
Define state function
Choose a new input
The input vector can be shown as
Desired path is line path.
The proving process is similar to the above:
Let
The control output can be shown as
For
A finite predictive path is regarded as known variables in the time window
Given the nonlinear tracking model (
Let
With Picard iteration method, the bounded solution for both parts of the inner dynamic can be derived as
For any Initial solution is shown with With
It is clear that the integration operation for the stable and unstable inner dynamics are from current time instant
Inner dynamics character
A positive constant
If Assumptions
If Lipchitz constants
The proof is not included here due to space limit. The reader is referred to the original paper for details [
Evaluation criteria are set out for assessing the contour accuracy and predictive controlperformance towards detection mission using the UUV under weak observable conditions, respectively.
Errors between the reconstructed contour and the environment model are computed in order to evaluate the accuracy of the contour reconstruction (only the contours estimated using the SVC inertia algorithm are evaluated here). Considering the characteristics of the environment, “accumulate error” and “overall error” are proposed. Figure
Illustration of the accumulate error and overall error.
(1)
As shown in Figure
(2)
To estimate the performance of autonomous tracking control, the error is defined as
(1)
(2)
The performance of the proposed model is verified with the data collected from a sea trial operated at Xiaoping Island in Dalian, China, in August 2009. We choose sonar data collected from two different environments, respectively, a port and two islands. The single-beam sonars were assembled on one side of a fishing boat to simulate UUV sonars. To guarantee the number of sonar data satisfying the clustering requirement, 3 single beam sonars were fixed in the boat side; see Figure
Deployment of the sonars.
Sonar data are collected during the boat navigating along islands horizontally in real time. To verify the effectiveness of the proposed control algorithm in disturbance situation, synthetic disturbance noise is added:
Sonar data collection in sea trial.
In the first experiment, the boat navigates between two small islands in order to move close to them (see Figure
Sea trial in islands environment.
Islands contour construction and patrolling.
On the basis of initial contour (see solid green line in Figures
Patrolling errors at
The mean (standard deviation) value along
Error autocorrelation coefficients of error serials.
With the same deployment and trial methods as above, sonar data was collected in a port as Figure
Sea trial in port environment.
Port contour construction and tracking.
Figure
Path error serials at
Error autocorrelation coefficients of error serials.
A new autopilot system, known as SDAP, is proposed for the exploration of underwater environments using UUV equipped with multiple single-beam sonars. The main issue studied is the control problem in detection process which is separated into two stages according to different requirements of the mission, accurate tracking and autonomous tracking. A rolling path generation method is present to guide the vehicle to follow a preset path accurately. For autonomous tracking stage, wavelet transform is introduced to preprocess weak observable data and the wavelet coefficients obtained are used to reconstruct the contour of the environment using the SVC inertia algorithm. To satisfy the inertia property of the UUV which requires a smooth reference path, different order Bézier curves are included to fit the initial contours for the desired reference path by considering a fixed safety distance. Finite predictive stable inversion method is applied to control the vehicle in order to follow the predictive path in real time. Data collected from a sea trial is used to validate the proposed technique, and the results have demonstrated that the algorithms are able to control vehicle navigating along the desired paths that are either preset or predicted automatically. It has laid a solid foundation for using UUV to perform SDAP mission.
During environment detection, the accuracy of environment information obtained is vital to guide UUV steering safely. With the insight, the navigation error will affect the environment outline constructed. In this paper, it is assumed that the navigation error is not considered in the UUV steering. In the future study, it is necessary to include navigation error into the SDAP issue for completeness. Otherwise, the further verification should be implemented through inserting the algorithms into UUV and executing mission in the real environment underwater.
This work is partially supported by the Natural Science Foundation of China (51179038), the Program of New Century Excellent Talents in University (NCET-10-0053), and Fundamental Research Funds for the Central Universities (HEUCF041323).