CN109116857A - A kind of underactuated surface vessel path trace nonlinear control method - Google Patents

Abstract

The present invention provides a non-linear control method for underactuated ship path tracking, the method at least includes: Step 1: Obtain virtual ship position information (x _d , y _d ) and azimuth angle ψ _d information of the target path at the current moment ; Step 2: calculate the relative position error _ze of the real ship and the virtual ship; Step 3: calculate the target position command derivative of the virtual ship, the real ship course command signal ψ _r and its first derivative sum Second derivative; Step 4: Calculate the main engine thrust command signal τ _u and the yaw control torque command signal τ _r , determine whether the target tracking error is 0, if "Yes", end the tracking, if "No", update the state and enter Step 2 . By applying the embodiment of the present invention, the approximate smooth heading angle command signal and derivative at the turn of the non-smooth curve path are obtained by the pre-filtering method, and the buffeting of the heading and yaw control torque at the turn of the target path is effectively reduced.

Description

A nonlinear control method for path tracking of underactuated ships

technical field

The invention relates to the technical field of ship path tracking, in particular to a nonlinear control method for underactuated ship path tracking.

Background technique

In the past two decades, the path tracking control of underactuated ships has attracted extensive attention in the field of ship motion control. The currently commonly used tracking control methods are mainly virtual ship guidance methods based on the Line of Sight (LOS) guidance algorithm, as shown in Figure 1. Show. Assuming that the target path is the track of the virtual ship, the goal of path tracking is achieved by controlling the real ship to accurately track the virtual ship. This guidance method has better effect for straight-line path tracking. For curve tracking, the target path needs to be assumed to be a smooth curve. For a non-smooth curve path, the problem of heading and control force refusal to chatter will occur at the turning point.

The linear control method based on the deterministic model has a good effect on the control of the deterministic disturbance system, but for the underactuated ship path tracking control system disturbed by the unknown marine environment, it also needs to face the nonlinear and uncertain problems of the ship motion model. Some scholars have studied the tracking control of underactuated ships with uncertain model parameters, and adopted the nonlinear ship motion model of the following formula:

Among them: (x, y, ψ) is the actual ship position and heading angle, (u, v, r) is the actual ship's surge, sway and yaw motion state, (m ₁₁ , m ₂₂ , m ₃₃ ) is the three The moment of inertia of each motion direction, (τ _u ,τ _r ) is the main thrust and yaw control torque, (τ _wu ,τ _wv ,τ _wr ) is the ocean disturbance force and moment in the three motion directions.

The nonlinear control methods based on this type of model all need to assume that the parameters of the nonlinear hydrodynamic part of the model are unknown constants with known dimensions, and assume that the nonlinear part is a known smooth function, and realize the under-flow by estimating the unknown model parameters. Accurate tracking control of the driven vessel. However, when the ship is disturbed by severe sea conditions, the nonlinear hydrodynamic part has the characteristics of uncertainty and unmodeled dynamics, and the parameters do not have the characteristics of unknown constants. At this time, the control method based on this type of model cannot guarantee the path tracking control. Robustness of the system.

SUMMARY OF THE INVENTION

In view of the above-mentioned shortcomings of the prior art, the purpose of the present invention is to provide a non-linear control method for the path tracking of an underactuated ship, which obtains an approximately smooth heading angle command signal and a derivative at the turn of the non-smooth curve path through a pre-filtering method, Effectively reduce the steering and yaw control torque buffeting at the turn of the target path.

In order to achieve the above object and other related objects, the present invention provides a nonlinear control method for path tracking of an underactuated ship, the method comprising at least:

Step 1: According to the command time series signal of the target path generated by the virtual ship, obtain the virtual ship position information (x _d , y _d ) and azimuth angle ψ _d information of the target path at the current moment;

Step 2: Calculate the relative position error _ze of the real ship and the virtual ship, and the LOS heading angle of the real ship according to the measured current position information (x, y) of the real ship and the heading angle ψ signal Operation command signal

Step 3: Calculate the target position command derivative of the virtual ship and the actual ship heading command according to the virtual ship position information, the heading angle information, the relative position error and the LOS heading angle operation command signal. the signal ψ _r and its first and second derivatives;

Step 4: Design the control law according to the adaptive backstepping control strategy, calculate the main engine thrust command signal τ _u and the yaw control torque command signal τ _r , and drive the real ship to track the virtual ship by controlling the main engine and steering;

Step 5: Update the position measurement information of the actual ship, and judge whether the target tracking error is 0, if "Yes", end the tracking, if "No", update the status and go to step (2).

In an implementation manner of the present invention, the LOS heading angle operation command signal of the real ship in the step (2) The specific calculation formula is:

Among them, x _d represents the x-axis component of the virtual ship, y _d represents the y-axis component of the virtual ship, x represents the current position of the real ship on the x-axis component, y represents the current position of the real ship on the y-axis component, z _e Indicates the relative position error of the real ship and the virtual ship.

In an implementation manner of the present invention, the actual ship heading command signal ψ _r and its first derivative in step (3) and the second derivative The calculation formula is specifically expressed as:

Among them, ξ and ω are the damping and frequency of the filter, ψ _r is the filtered real ship heading command signal, when When constant,

In an implementation mode of the present invention, the specific expression of the calculation formula of the main engine thrust command signal τ _u and the yaw control torque command signal τ _r in step (4) is:

Among them, θ is the motion state of the real ship, m ₁₁ and m ₃₃ are the parameters of the moment of inertia of the ship, α _u and α _r are the virtual control signals of thrust and yaw, _{ue and r e are} the virtual errors of thrust and yaw, k ₁ , k ₂ , δ ₁ , and δ ₂ are all set parameters, and is the overall estimate of the nonlinear hydrodynamic part of the underactuated ship model, and is the estimation of the upper bound of marine environmental disturbance, _{ze represents the relative position error between the real ship and the virtual ship, and ψ e is} the heading tracking error of the real ship.

As mentioned above, the non-linear control method of the underactuated ship path tracking of the present invention obtains the approximately smooth heading angle command signal and derivative at the turn of the non-smooth curve path through the pre-filtering method, and effectively reduces the heading and bow at the turn of the target path. At the same time, the overall estimation of the nonlinear hydrodynamic part in the ship motion model is performed without knowing the prior information of the nonlinear hydrodynamic part, which can improve the robustness of path tracking control under severe sea conditions.

Description of drawings

1 is a schematic flow diagram of the prior art;

Fig. 2 is the flow chart of the nonlinear control method of underactuated ship path tracking based on pre-filtering;

3 is a schematic structural diagram of a path tracking control method in the present invention;

Fig. 4 is the schematic diagram of the ship path tracking control result in the embodiment;

5 is a schematic diagram of the tracking error of the ship path tracking control in the embodiment;

FIG. 6 is a schematic diagram showing the calculation results of the main thrust and the yaw control force rejection of the ship in the embodiment.

Detailed ways

The embodiments of the present invention are described below through specific specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

See Figure 2-6. It should be noted that the drawings provided in this embodiment are only to illustrate the basic concept of the present invention in a schematic way, so the drawings only show the components related to the present invention rather than the number, shape and the number of components in actual implementation. For dimension drawing, the type, quantity and proportion of each component can be changed at will in actual implementation, and the component layout may also be more complicated.

As shown in the flow chart of the control system in FIG. 2 and the schematic structural diagram of the control method in FIG. 3 , the specific implementation of the nonlinear control method for underactuated ship path tracking disclosed in the present invention is as follows:

Step 1: Plan the reference path, generate the time series signal of the reference path according to the virtual ship motion track, obtain the current time tracking target position (x _d , y _d ) and azimuth angle ψ _d information, and enter the tracking control state.

It should be noted that the target path is the track of the virtual ship, and the purpose of path tracking needs to be achieved by controlling the real ship to accurately track the virtual ship in the actual sailing process. It can be understood that during the navigation of the ship, a coordinate axis can be formed according to the current longitude and latitude information of the ship and the target path of the ship. It changes with the passage of time during the voyage, so it is a set of signals that change with time, becoming a time-series signal. Specifically, the signal can include the position of the ship at each moment (x _d , y _d ) and the direction angle ψ _d .

Therefore, this process is a ship tracking control state. Specifically, the position and direction angle of the ship at each recording time can be drawn on a curve, and the navigation curve of the ship can be obtained, which is convenient for tracking, and other methods can also be used for ship tracking control. state.

Step 2: Obtain the relative position error ze between the real ship and the virtual ship according to the measured current position (x, y) and target position (x _d , y _d ) of the real _ship , and according to the relative position error between the real ship and the virtual ship z _e , calculate the LOS heading angle command signal of the real ship The specific expression is as formula (2):

Among them, the relative position error When z _e > 0, it means that the real ship has not tracked the target position; z _e =0 means that the real ship has tracked the target point of the reference path, and the heading angle of the real ship is consistent with that of the virtual ship.

According to the calculation results of step (1) and step (2), calculate the actual ship heading command ψ _r and its first derivative and the second derivative Prepare for control laws.

The planned reference path is a non-smooth continuous curve path, and the derivative of the virtual ship target position command can be directly obtained by the analytical method The actual ship heading command signal ψ _r and its derivative are the LOS heading angle operation command The smooth signal obtained by the pre-filter, the pre-filter is represented by Equation (3):

The analytic method used for the derivative of the target position command of the virtual ship can use advanced mathematical methods to directly find the derivative of the function, and the specific derivative should be obtained according to the specific function, because the target path is different for each ship. Therefore, it is an individual difference, which is not specifically limited in this embodiment of the present invention.

Among them: the damping of the ξ wave filter, ω is the frequency of the filter, the specific value can be set according to the actual working conditions; ψ _r is the filtered real ship heading command, when When constant, there are

As shown in Fig. 2, according to the adaptive backstepping control strategy design control law, the main engine propulsion control force rejection command signal τ _u and the yaw control torque command signal τ _r are calculated, and the real ship is driven to track the virtual ship by controlling the main engine and the steering device. , and finally realize the path tracking control.

The main thrust control torque signal and the yaw control force rejection signal are calculated and obtained by the control laws expressed by formula (4) and formula (5):

Among them, θ=(u, v, r) is the motion state of the real ship, α _u and α _r are the virtual control signals of thrust and yaw, _ue = α _u -u and r _e = α _r -r are the thrust sum The virtual error of the bow, (k ₁ , k ₂ , δ ₁ , δ ₂ ) is the normal value parameter set according to the actual working condition, and are the overall estimates of the nonlinear hydrodynamic parts of the nonlinear motion model of the underactuated ship in the direction of the surge and yaw motion, respectively, and is the estimation of the upper bound of the unknown marine environmental disturbances suffered by the sway and yaw motion directions; since the sway motion attitude v is assumed to be passively bounded, the design of the control law does not need to take it into account.

As in formula (6),

In order to be different from the ship motion model in the prior art, the nonlinear motion model of the ship under the control law at this time replaces the nonlinear hydrodynamic parts of the three motion degrees of freedom with an unknown nonlinear function as a whole, forming formula (6) expression.

in,

Among them, (x, y, ψ) is the actual ship position and heading angle, (u, v, r) is the actual ship's surge, sway and yaw motion states, (m ₁₁ , m ₂₂ , m ₃₃ ) are three The moment of inertia of each motion direction, θ=(u,v,r) ^T is the motion attitude vector, f _u (θ), f _v (θ) and _fr (θ) are the nonlinear hydrodynamic functions of the three motion directions , (τ _u ,τ _r ) are the main thrust and yaw control moments, and (τ _wu ,τ _wv ,τ _wr ) are the ocean disturbance forces and moments in the three motion directions.

The virtual control signals α _u and α _r in the control law are calculated by formula (7) and formula (8), respectively:

Among them, (k _ze , k _ψe ) are the normal value parameters set according to the actual working conditions, ψ _e =ψ _r -ψ is the course tracking error of the actual ship, is the position tracking error.

Update the position measurement information of the actual ship to determine whether the target tracking error is 0, if "Yes", end the tracking, if "No", update the status and enter step (2).

Example: Take a monohull with a length of 3.8 meters as the controlled object, and use MATLAB to carry out computer numerical simulation. The nonlinear ship motion model is used as shown in formula (6), and the specific parameters in the model are as follows.

m ₁₁ =120×10 ³ m ₂₂ =177.9×10 ³ m ₃₃ =636×10 ⁵

d _u1 = 215×10 ² d _v1 = 147×10 ³ d _r1 = 802×10 ⁴

d _u2 =0.2d _u1 d _v2 =0.2d _v1 d _u2 =0.2d _v1

d _u3 =0.1d _u3 d _v3 =0.1d _v3 d _r3 =0.1d _r3

In this embodiment, the designed non-smooth target path is determined by four fixed position points, namely (0,0), (175,0), (450,100) and (650,80), and each point is connected by a straight line , the ship sails in a straight horizontal direction after passing the fourth point. The initial state of the ship's motion attitude at t=0 is [x ₀ , y ₀ , ψ ₀ , u ₀ , v ₀ , r ₀ ]=[-80,-20,0,0,0,0], the marine environment is disturbed Considering the complex disturbance factors of wind, waves and currents, the disturbance model is used for simulation. In order to ensure the stable operation of the path tracking closed-loop control system, the nonlinear hydrodynamic global estimation of the degrees of freedom of the surge and yaw and perturbed upper bound estimates Adopt the adaptive algorithm in the literature (Jihong Li, Panmook Lee, Bonghuan Jun, Yongkon Lim. Point-to-point navigation of underactuated ships. Automatica, 2008, 44(12): 3201-3205.).

Figures 3-6 show the nonlinear control results of underactuated ship path tracking based on pre-filtering under the above simulation conditions. Figure 3 shows the comparison curve of the track tracking of the real ship. It can be seen that the track of the real ship is effectively tracked and controlled, and smooth steering can be achieved at the inflection point. Figure 4 shows the time variation curve of the tracking error, including the position tracking error and the heading deviation. It can be seen that the heading deviation and the position tracking deviation can both converge in a small neighborhood range, and there is no large fluctuation and chattering phenomenon at the inflection point. . Fig. 5 shows the time variation curves of the main engine propulsion control force and steering control force calculated by the control laws of formula (4) and formula (5). The torque curve is relatively smooth without large fluctuations and buffeting. It can be seen that the non-smooth curve path tracking control of the underactuated ship realized by the invention meets the actual needs of ship motion control engineering, can effectively ensure the path tracking control accuracy, and can effectively reduce the heading at the inflection point and the control force against buffeting. phenomenon, which improves the robustness of path tracking control in complex sea conditions.

The above-mentioned embodiments merely illustrate the principles and effects of the present invention, but are not intended to limit the present invention. Anyone skilled in the art can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical idea disclosed in the present invention should still be covered by the claims of the present invention.

Claims (4)

1. an underactuated ship path tracking nonlinear control method, is characterized in that, described method comprises the following steps: Step 1: According to the command time series signal of the target path generated by the virtual ship, obtain the virtual ship position information (x _d , y _d ) and azimuth angle ψ _d information of the target path at the current moment; Step 2: Calculate the relative position error _ze of the real ship and the virtual ship, and the LOS heading angle of the real ship according to the measured current position information (x, y) of the real ship and the heading angle ψ signal Operation command signal Step 3: Calculate the target position command derivative of the virtual ship and the actual ship heading command according to the virtual ship position information, the heading angle information, the relative position error and the LOS heading angle operation command signal. the signal ψ _r and its first and second derivatives; Step 4: Design the control law according to the adaptive backstepping control strategy, calculate the main engine thrust command signal τ _u and the yaw control torque command signal τ _r , and drive the real ship to track the virtual ship by controlling the main engine and steering; Step 5: Update the position measurement information of the actual ship, and judge whether the target tracking error is 0, if "Yes", end the tracking, if "No", update the status and go to step (2). 2. a kind of underactuated ship path tracking nonlinear control method according to claim 1 is characterized in that: the LOS heading angle operation command signal of the described real ship in step (2) The specific calculation formula is: Among them, x _d represents the x-axis component of the virtual ship, y _d represents the y-axis component of the virtual ship, x represents the current position of the real ship on the x-axis component, y represents the current position of the real ship on the y-axis component, z _e Indicates the relative position error of the real ship and the virtual ship. 3. a kind of underdriven ship path tracking nonlinear control method according to claim 1, is characterized in that: the real ship course command signal ψ _r and its first derivative in step (3) and the second derivative The calculation formula is specifically expressed as: Among them, ξ and ω are the damping and frequency of the filter, ψ _r is the filtered real ship heading command signal, when When constant, 4. a kind of underdriven ship path tracking nonlinear control method according to claim 1, is characterized in that: the calculation formula of main engine thrust command signal τ _u in step (4) and yaw control torque command signal τ _r Specifically expressed as: Among them, θ is the motion state of the real ship, m ₁₁ and m ₃₃ are the parameters of the moment of inertia of the ship, α _u is the virtual control signal of the thrust, α _r is the virtual control signal of the yaw, and u _e and r _e are the virtual control signals of the thrust and the yaw. Error, k ₁ , k ₂ , δ ₁ , δ ₂ are all set parameters, and is the overall estimate of the nonlinear hydrodynamic part of the underactuated ship model, and is the estimation of the upper bound of marine environmental disturbance, _{ze represents the relative position error between the real ship and the virtual ship, and ψ e is} the heading tracking error of the real ship.