A path tracking constraint control method for unmanned ship based on trigonometric function mapping

Abstract

The present invention discloses a path tracking constraint control method for an unmanned ship based on trigonometric function mapping. The present invention relates to the field of path tracking technology, and in particular to a path tracking constraint control method for an unmanned ship based on trigonometric function mapping, comprising the following steps: step (1): establishing a three-degree-of-freedom mathematical model of the unmanned ship's motion; step (2): constructing a nonlinear mapping function; step (3): performing a nonlinear mapping transformation on the state of the original system to obtain an unconstrained system; step (4): designing a bow direct constraint controller based on trigonometric function mapping; step (5): designing a longitudinal direct constraint controller based on trigonometric function mapping; step (6): simulation verification. The present invention aims to solve the constraint problem caused by the restricted environment of the unmanned ship during its driving process, and by constructing a trigonometric function mapping function to process state constraints, the original constrained system is mapped into a new unconstrained system, and a controller is designed based on the new system.

Description

Technical field:

[0001] The present invention relates to the technical field of path tracking, and in particular to a path tracking constraint control method for an unmanned ship based on trigonometric function mapping. Background technology:

[0002] An unmanned ship is an unmanned surface vessel that is mainly used to perform dangerous tasks that are not suitable for manned ships. So far, only military powers such as the United States and Israel have made great progress in the research of unmanned ships, and applied them to actual combat during the Second Gulf War. Although there is still uncertainty in the development of unmanned ships, with the acceleration of social development and the surge in population, people are eager to explore, utilize and protect the marine environment, so unmanned ships are widely used in harsh and dangerous environments.

[0003] Unmanned ships are small in size and have limited thrust. They are typical under-actuated systems. In complex marine environments, they are easily affected by wind, waves, and currents, resulting in excessive yaw distance and unstable heading. Therefore, in terms of unmanned ship motion control, it is necessary to deal with the constraints imposed on the ship during navigation to ensure that the unmanned ship is not restricted by the environment during navigation and to improve operability and feasibility. The present invention proposes an unmanned ship path tracking constraint control method based on trigonometric function mapping, in the hope of obtaining better operability under environmental constraints. Summary of the invention:

[0004] The invention discloses an unmanned ship path tracking constraint control method based on trigonometric function type mapping under state constraints.

[0005] The object of the present invention is achieved in that:

[0006] A path tracking constraint control method for an unmanned ship based on trigonometric function mapping comprises the following steps:

[0007] Step (1): Establish a three-degree-of-freedom mathematical model for the unmanned ship:

[0008] According to the movement of the unmanned ship on the water surface, the three-degree-of-freedom mathematical model of the unmanned ship is established in the fixed coordinate system and the hull coordinate system, including the three-degree-of-freedom kinematic model and the three-degree-of-freedom dynamic model.

[0009] Step (2): Construct a nonlinear mapping function:

[0010] A trigonometric mapping function based on the state of nonlinear system is proposed to describe the conditions satisfied by the function, map the constrained state and obtain the new unconstrained state after mapping.

[0011] Step (3): Perform a trigonometric nonlinear mapping transformation on the state of the existing system to obtain an unconstrained system:

[0012] Based on the mathematical model established in step (1), the trigonometric function mapping function constructed in step (2) is used to perform nonlinear mapping on the bow swing subsystem and the longitudinal swing subsystem, respectively, so as to convert the original constrained system into a new unconstrained system;

[0013] Step (4): Design a heading direct constraint controller based on trigonometric function mapping:

[0014] Based on the mapped second-order heading subsystem obtained in step (3), a first-order filtering error is introduced, and a dynamic surface design method is adopted to design a heading direct constraint controller based on trigonometric function mapping;

[0015] Step (5): Design a direct constraint controller for sloshing based on trigonometric function mapping:

[0016] Based on the mapped first-order oscillatory subsystem obtained in step (3), a backstepping recursive method is used to design a oscillatory direct constraint controller based on trigonometric function mapping.

[0017] Step (6): Simulation verification:

[0018] The bow direct constraint controller and surge direct constraint controller designed in steps (1) to (5) were simulated on a certain type of unmanned ship.

[0019] The present invention has the following beneficial effects:

[0020] The unmanned ship path tracking constraint control method based on trigonometric function mapping described in the present invention targets the constraints on the longitudinal speed, bow angle and bow pitch angular velocity caused by the environment during the driving of the unmanned ship, and transforms the original state into an unconstrained state through a trigonometric function mapping function, thereby eliminating the feasibility conditions of the virtual controller parameter dependence that is necessary for the unmanned ship to ensure the constraint conditions during operation, thereby improving the maneuverability of the unmanned ship. Description of the drawings:

[0021] Figure 1 A flowchart of the steps of the present invention;

[0022] Figure 2 is the trigonometric function type mapping function described in the present invention;

[0023] Figure 3 The following are the heading and surge tracking curves of the original system of a certain type of unmanned ship under the present invention;

[0024] Figure 4 The following are the heading and surge tracking curves of a certain type of unmanned ship under the unconstrained new system of the present invention;

[0025] Figure 5 It is a tracking error variable curve diagram of a certain type of unmanned ship under the present invention;

[0026] Figure 6 It is a control force curve diagram of a certain type of unmanned ship under the present invention; Specific implementation method:

[0027] like Figure 1 , a path tracking constraint control method for an unmanned ship based on trigonometric function mapping, comprising the following steps:

[0028] Step (1): Establish a three-degree-of-freedom mathematical model for the unmanned ship:

[0029] According to the movement of the unmanned ship on the water surface, the three-degree-of-freedom mathematical model of the unmanned ship is established in the fixed coordinate system and the hull coordinate system, including the three-degree-of-freedom kinematic model and the three-degree-of-freedom dynamic model, based on the angular velocity of the surge, sway and bow pitch.

[0030] Three-degree-of-freedom model of unmanned ship in fixed coordinate system:

[0031]

[0032] The three-degree-of-freedom model of the unmanned ship in the hull coordinate system:

[0033]

[0034] In the above formula, x, y, ψ represent the north position, east position and heading angle of the unmanned ship in the fixed coordinate system, u, v, r represent the longitudinal velocity, transverse velocity and bow angular velocity of the unmanned ship, respectively; m 11 ,m 22 ,m 33 Represents the inherent mass of the unmanned ship, m 23 ,m 32 represents the added mass of the unmanned ship; Coriolis matrix and damping matrix.

[0035] τ u ,τ r They represent surge controller and heading controller respectively.

[0036] Step (2): Construct the mapping function:

[0037] A trigonometric mapping function based on the state of the nonlinear system is proposed:

[0038] Where k>0 is the constraint value of variable .x., and -k<x<k;

[0039] The constructed trigonometric mapping function satisfies the following conditions:

[0040] 1)

[0041] 2) When x→-k, y(x)→-∞; when x→k, y(x)→+∞;

[0042] 3) When k→∞, y(x)=x;

[0043] 4)y(x) is an odd function;

[0044] Define the following mapping process:

[0045]

[0046] Taking the derivative of ζ(x) we get: Wherein k>0 is the constraint value of state x, and -k<x<k.

[0047] Step (3): Perform a triangular nonlinear mapping transformation on the state of the existing system to obtain the unconstrained bow motion mathematical model and the sway motion mathematical model as follows:

[0048]

[0049] In the above formula, ζ ψ and r is the mapped yaw angle and yaw angular velocity, ζ u is the longitudinal velocity after mapping, k 1 is the constraint boundary of the original state ψ, k 2 is the constraint boundary of the original state r, k 3 is the constraint boundary of the original state u.

[0050] Step (4): Design a heading direct constraint controller based on trigonometric function mapping:

[0051] The actual heading angle and heading angular velocity obtained by the unmanned ship during driving are used to introduce the first-order filter error equation. Based on the unconstrained system established in step (3), a heading direct constraint controller τ is designed for the second-order heading subsystem. r :

[0052] Define the heading error variable:

[0053]

[0054] In the above formula, is the expected heading angle after mapping.

[0055] In order to solve the computational explosion problem caused by a large number of derivatives in the backstepping recursive control method, the dynamic surface control method is now adopted, defining α2f The output of the following filter:

[0056]

[0057] Where: 2 >0 low-pass filter time constant, α is the filter input, α 2f is the filter output.

[0058] For closed-loop stability system analysis, the first-order filter error is defined as follows:

[0059] κ=α 2f -α;

[0060] Taking the derivative of it, we get:

[0061]

[0062] Define the velocity error variable:

[0063] r e =ζ r -α 2f ;

[0064] Then, a heading direct constraint controller based on trigonometric function mapping is designed, as shown in steps 1 and 2:

[0065] Step 1: Prove the convergence of the heading tracking error.

[0066] Take the Lyapunov function:

[0067]

[0068] Taking the derivative of it, we get:

[0069]

[0070] In order to stabilize the heading tracking error, the filter input α is designed as follows:

[0071]

[0072] From Young's inequality we can get:

[0073]

[0074] In the above formula,

[0075] The first-order filter input α and the derivative of the first-order filter error Substituting in, we get:

[0076]

[0077] Step 2: Prove the convergence of the yaw rate tracking error.

[0078] Take the Lyapunov function:

[0079]

[0080] Taking the derivative of it, we get:

[0081]

[0082] The heading direct constraint controller based on trigonometric function mapping is designed as follows:

[0083]

[0084] In the above formula, c 1 ,c 2 represents a design parameter greater than zero, ε 2 Specifies a time filter constant greater than zero.

[0085] The controller τ r Substituting in, we get:

[0086]

[0087] There exists a positive constant M such that |l 2 |<M 2 .

[0088]

[0089] In the above formula, According to Lyapunov's stability theorem, the above formula shows that ψ e and r e is uniformly asymptotically convergent.

[0090] Step (5): Design a direct constraint controller for sloshing based on trigonometric function mapping:

[0091] Based on the unconstrained system established in step (3), a direct constraint controller τ is designed for the first-order surge subsystem. u :

[0092] In the above formula, c 3 represents a positive design parameter, u e is the surge tracking error, u d is the expected sway speed.

[0093] Step (6): Simulation verification:

[0094] Based on the above steps, the heading direct constraint controller and the sloshing direct constraint controller based on trigonometric function mapping are designed. The simulation environment is set as follows: the unmanned ship is 1.2 meters long and has a mass of 17.5 kg. The initial heading angle of the unmanned ship is ψ(t 0 )=π / 4, the initial bow angular velocity is 0rad / s, and the initial surge velocity is 0m / s.

[0095] A triangular mapping function is used to process the heading constraint, and a certain type of unmanned ship is taken as a simulation object to simulate and verify the unmanned ship path tracking constraint control method based on triangular function type of the present invention.

[0096] Figure 2 The conditional characteristics of the constructed trigonometric mapping function are shown, indicating that the constructed trigonometric mapping function meets the construction conditions and converges to the constraint boundary at a faster speed.

[0097] Figure 3 The bow and surge tracking curves of a certain type of unmanned ship under the present invention are shown. By comparing the reference bow angle and reference surge speed before processing the constraints and the bow angle and surge speed before processing the constraints, the unmanned ship path tracking constraint control method based on the triangular function type of the present invention has good tracking performance and a short response time.

[0098] Figure 4 The mapped bow angle and surge velocity direct constraint tracking curve of a certain type of unmanned ship under the present invention is presented. The bow angle after constraint processing converges to the reference bow angle after constraint processing, the bow angular velocity after constraint processing converges to the output of the first-order filter, and the surge velocity after constraint processing converges to the reference surge velocity after constraint processing. The results show that the unmanned ship path tracking constraint control method based on triangular function type of the present invention has good constraint processing effect and fast convergence speed.

[0099] Figure 5 The following is a curve diagram of the tracking error variables of a certain type of unmanned ship under the present invention. The curve results show that the bow tracking error, bow angular velocity tracking error and surge velocity error have been asymptotically converging.

[0100] Figure 6 This is a control force curve of a certain type of unmanned ship under the present invention, which shows that the designed control law is relatively smooth and conforms to practical engineering applications.

[0101] The present invention constructs a trigonometric function mapping function to process state constraints and designs a trigonometric function-based unmanned ship path tracking constraint control method, which solves the problem of environmental constraints during the unmanned ship's driving process and solves the feasibility problem of the virtual controller that arises in the controller design process.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A path tracking constraint control method for an unmanned ship based on trigonometric function mapping, characterized in that: It includes the following steps: Step (1): Establish a three-degree-of-freedom mathematical model for the unmanned ship: According to the movement of the unmanned ship on the water surface, a three-degree-of-freedom mathematical model of the unmanned ship is established for its longitudinal, transverse and bow pitch in the fixed coordinate system and the hull coordinate system, including a three-degree-of-freedom kinematic model and a three-degree-of-freedom dynamic model; Step (2): Construct a nonlinear mapping function: A trigonometric mapping function based on the state of nonlinear system is proposed to describe the conditions satisfied by the function, map the constrained state and obtain the new unconstrained state after mapping. Step (3): Perform a trigonometric nonlinear mapping transformation on the state of the existing system to obtain an unconstrained system: Based on the mathematical model established in step (1), the trigonometric function mapping function constructed in step (2) is used to perform nonlinear mapping on the bow swing subsystem and the longitudinal swing subsystem, respectively, so as to convert the original constrained system into a new unconstrained system; Step (4): Design a heading direct constraint controller based on trigonometric function mapping: Based on the mapped second-order heading subsystem obtained in step (3), a first-order filtering error is introduced, and a dynamic surface design method is adopted to design a heading direct constraint controller based on trigonometric function mapping; Step (5): Design a direct constraint controller for sloshing based on trigonometric function mapping: Based on the mapped first-order oscillatory subsystem obtained in step (3), a backstepping recursive method is used to design a oscillatory direct constraint controller based on trigonometric function mapping. Step (6): Simulation verification: The heading direct constraint controller and the sway direct constraint controller based on trigonometric function mapping designed in steps (1) to (5) are simulated on an unmanned ship; In step (2), a nonlinear mapping function is constructed: A trigonometric mapping function based on the state of the nonlinear system is proposed: Where k>0 is the constraint value of variable x, and -k<x<k; The constructed trigonometric mapping function satisfies the following conditions: 1) 2) When x→-k, y(x)→-∞; when x→k, y(x)→+∞; 3) When k→∞, y(x)=x; 4)y(x) is an odd function; Define the following mapping process: Taking the derivative of ζ(x) we get: Where k>0 is the constraint value of state x, and -k<x<k; The unconstrained system established in step (3) based on the trigonometric nonlinear mapping is: In the above formula, ψ is the bow angle of the unmanned ship in the fixed coordinate system; u, v, r represent the longitudinal velocity, lateral velocity and bow angular velocity of the unmanned ship respectively; ζ u ,ζ ψ ,ζ r are the mapped surge velocity, heading angle and yaw angular velocity, k1 is the constraint boundary of the original state ψ, k2 is the constraint boundary of the original state r, k3 is the constraint boundary of the original state u, m 11 ,m 22 ,m 33 Represents the inherent mass of the unmanned ship, m 23 ,m 32 represents the added mass of the unmanned ship; represents the Coriolis matrix and the damping matrix; τ u ,τ r They represent surge controller and heading controller respectively.

2. The unmanned ship path tracking constraint control method based on trigonometric function mapping according to claim 1 is characterized in that: In step (4), the heading direct constraint controller is designed: The first-order filter input α for unmanned ship path tracking based on trigonometric function mapping is: In the above formula, c1 is a positive design parameter, ψ d is the desired heading angle, ψ e =ζ ψ -ζ ψd is the heading tracking error; Unmanned ship path tracking constrained heading direct constraint controller τ based on trigonometric function mapping r : In the above formula, c2 is a positive design parameter, ε2>0 is the low-pass filter time constant, and κ=α 2f -α is the first-order filtering error, α 2f is the output of the first-order filter, r e is the yaw angular velocity error.

3. The unmanned ship path tracking control method based on trigonometric function mapping according to claim 2 is characterized in that: In step (5), the direct constraint controller for sloshing is designed: A direct constraint controller for unmanned ship's path tracking and sloshing based on trigonometric function mapping u : In the above formula, c3 represents a positive design parameter, u d is the expected sloshing speed, u e =ζ u -ζ ud is the surge tracking error.

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