This paper addresses the problem of accurate path following control for an underactuated unmanned underwater vehicle (UUV) in the horizontal plane. For an underactuated UUV, the lineofsight (LOS) guidance method is adopted to map 2D reference trajectory into a desired orientation, and through the tracking of heading to achieve path following, where the sideslip is introduced to modify the desired orientation. In this paper, we propose a method called dynamic surface and active disturbance rejection control (DSADRC) to solve the path following control problem. This controller can effectively avoid the phenomenon of explosion of terms in the conventional backstepping method, reduce the dependence on the UUV controller mathematical model, and enhance the antijamming ability. Simulation is carried out to verify the effectiveness of the proposed control method for an underactuated UUV. The results show that, even for this controller with disturbance, the crosstrack error of UUV is gradually converged to zero and has some certain robustness.
The high accuracy path following mission is a typical behavior of UUVs, and it is an important method for UUVs to complete other tasks (such as topography examination and long distance navigation) [
At present, the research on UUV’s tracking control mainly focuses on the following three aspects: waypoint tracking [
Usually, the accurate mathematical model of an UUV is difficult to obtain. Even with a precise mathematical model, it is also so complex that it needs to do some simplification when doing control system design, which eventually leads to model error. Based on the DSADRC technique, this paper designs a horizontal path following controller for an underactuated UUV, which effectively avoids the “explosion of terms” phenomenon when using backstepping method and also reduces the high requirements of the dynamic surface control technology to the accurate mathematical model. It does realtime estimation to the internal and external disturbance in the loop and eventually compensates the estimation into the control system, which improves the control accuracy and has high stability.
This paper selects Minesniper MkII as a simulation object, which is shown in Figure
Minesniper MkII.
Here, we assume that the position vector of the UUV is
According to [
UUV relevant parameters.















Considering the underactuated UUV in this paper, we select the LOS guidance as adopted in [
For the horizontal path following, it can divide the expecting path into a series of points:
Lineofsightguidance.
Through the geometric relation, we can obtain
For the selection of
There are currents in the case of interference; if we get the desired heading angle as desired input for the UUV control system with the above method, eventually the heading tracking is achieved, but there will be a stable track error. In this paper, in order to eliminate it, we introduce a sideslip angle
When
The horizontal movement of the UUV can be divided into two subaspects as follows [
The dynamic surface control (DSC) technique has efficiently avoided the “explosion of terms” phenomenon which is caused by repeatedly instructing on the virtual controlling, but it needs the precise model of the controlled object. The active disturbance rejection control (ADRC) technique does not depend on the precise model of the controlled object, but the feedback efficiency is not high enough, and its control signal may easily have high frequency oscillation. With the help of DSC and ADRC, this paper designs a longitudinal velocity controller and a heading controller, respectively, by using the DSADRC method.
In order to use the ADRC technique more conveniently, it firstly converts the UUV mathematical model to a standard form according to the ADRC, and then the controllers are designed, respectively.
From the model of (
In the above model,
Assume
Hereinto,
Taking
In the same way, from (
Here
Supposing that
Hereinto,
Taking
The ADRC controller is made up of four parts [
Arrange the transition process of expected signal using the trackingdifferentiator (TD). And calculate the signal
Estimate the system total disturbance through the ESO in real time.
Calculate the part of control input
Compensate the estimation using ESO to
The schematic of the controller is shown in Figure
Design of the DSADRC controller.
For the stability analysis of ESO, please refer to [
Define the first dynamic surface as
Define the second dynamic surface as
In order to stabilize the system, we choose a variable
The stabilization analysis of the DSC algorithm is discussed as follows. Defining
Through the above analysis, we can know that the DSC algorithm can guarantee all the states of the closedloop system final convergence. And with appropriate coefficients
Through the above four steps, we can finally obtain the controller as follows:
Similar to the derivation of heading controller, the longitudinal velocity controller can be deduced based on DSADRC as follows:
In (
A numerical example is given to illustrate the proposed path following control algorithm. In the simulation, our objective is to control the UUV to follow the path with speed at
The responses of path following.
The crosstrack error.
The output of force.
The output of moment.
The responses of path following.
The crosstrack error.
The output of force.
The output of moment.
In the northeast coordinates, we set the current velocity as
Figures
Under the above constant current condition, we add a disturbance with which amplitude is 0.2 N·m and period is
In the presence of other disturbances, it is interesting to note that the UUV’s crosstrack error of the proposed method in this paper is still gradually converged to zero according to Figures
Through the above two groups of simulation contrast, it can be seen that the effects of the DSC and the DSADRC are similar under the constant current, but when there are other external disturbances, the effect of the DSADRC is much better than the simple DSC, which show strong antidisturbance characteristic to the external unknown disturbances.
This paper has presented a novel path following control method to UUV; it uses the lineofsight guidance method to solve the realtime expectations of UUV’s heading and has revised the method heading under the condition of current interference with introducing sideslip at the same time; it eliminates the stable crosstrack error which is caused by the normal lineofsight guidance method with current interference. Combining the advantages of the DSC technique and the ADRC technology, we, respectively, designed the UUV heading controller and the longitudinal velocity controller. This control method avoids the conventional dynamic surface control systems, relies on accurate mathematical models and improved antijamming capability. At the same time, the control method for a class of strict feedback forms is applicable, which makes the design of the controller be in common use and be more conducive to the engineering practice. The simulation results also show that the control method has an excellent performance.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research work is supported by the National Natural Science Foundation of China (Grant No. 51309067/E091002), the Fundamental Research Funds for the Center Universities (HEUCFX041402), and the National Defense Key Laboratory of Autonomous Underwater Vehicle Technology (9140C270208140C27004).