Under-actuated USV trajectory tracking control method with signal quantization based on extended state observer

Abstract

The invention provides an under-actuated USV trajectory tracking control method with signal quantization based on an extended state observer, and the method comprises the steps: constructing a kinematics model and a dynamics model of a USV, employing a uniform quantizer to quantize a control signal, and employing a linear analysis model to describe an input quantization process and external interference; designing a position guidance law and an attitude guidance law based on the constructed kinematics model of the USV; defining an integral sliding mode surface on the basis of the constructed kinetic model of the USV, designing a quantization controller, and estimating quantized state feedback information, system uncertain items and external interference by using an extended observer; based on the Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed USV double-loop trajectory tracking control system with signal quantization are proved. Aiming at the USV trajectory tracking problem under the condition that the maritime communication bandwidth is limited, a quantitative feedback controller is designed, and the USV adaptive trajectory tracking control problem with signal quantization is solved.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to an under-actuated USV trajectory tracking control method with signal quantization based on an extended state observer. Background Art

[0002] Unmanned surface vehicles (USVs) possess intelligence and autonomy, enabling them to perform tasks in complex sea conditions and are widely used in marine engineering. To ensure the stability and performance of USVs during missions, it is crucial to study trajectory tracking control strategies.

[0003] Most trajectory control methods are designed based on the assumption of continuous feedback information. However, these control methods may encounter challenges when communication bandwidth is limited at sea. Therefore, it is meaningful to consider quantization issues when studying trajectory tracking control strategies for USVs.

[0004] Most quantization-related control methods only consider state quantization and input quantization. However, in maritime practice, due to the limitation of network channel bandwidth, state quantization and input quantization should be considered simultaneously. Summary of the Invention

[0005] Based on the above-mentioned technical problem of limited communication bandwidth in navigation practice, for a USV trajectory tracking control system with input quantization and state quantization, the present invention aims at the model uncertainty and complexity of trajectory tracking control of under-actuated unmanned surface vehicles (USVs) in complex marine environments, and proposes a trajectory tracking control method for under-actuated USVs with signal quantization based on an extended state observer (ESO). The present invention solves the problem of adaptive trajectory tracking control of USVs with signal quantization by designing a quantized feedback controller.

[0006] The technical means adopted in the present invention are as follows:

[0007] A trajectory tracking control method for an underactuated USV with signal quantization based on an extended state observer comprises:

[0008] S1. Construct the kinematic and dynamic models of the USV, use a uniform quantizer to quantize the control signal, and use a linear analysis model to describe the input quantization process and external interference;

[0009] S2. Design position guidance law and attitude guidance law based on the constructed USV kinematic model;

[0010] S3. Based on the constructed USV dynamic model, the integral sliding surface is defined and a quantitative controller is designed. The extended observer is used to estimate the quantized state feedback information, system uncertainties, and external disturbances.

[0011] S4. Based on Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed USV dual-loop trajectory tracking control system with signal quantization are proved.

[0012] Furthermore, step S1 specifically includes:

[0013] S11. Under the environmental interference of wind, waves and currents, the kinematic model and dynamic model of the USV are constructed as follows:

[0014]

[0015] Where, (p x ,p y ) and θ are the position and bow angle of the unmanned vessel, respectively; U represents the cruising speed of the USV; β represents the drift angle; u, v, r represent the forward speed, lateral speed, and bow angular velocity, respectively; τ u and τ r Both represent control input; τ uw ,τ vw ,τ rw Both represent environmental disturbances related to wind, waves and currents; f u (u,v,r) represents the nonlinear term of Coriolis, f v (u,v,r) represents the nonlinear term of the centripetal force matrix, f r (u, v, r) represents the nonlinear term of hydrodynamic damping; Where m represents the mass of USV, and Both represent additional mass, I Z represents the moment of inertia about the vertical axis;

[0016] S12. All state variables and control inputs are quantized using a uniform quantizer:

[0017]

[0018] Where χ=[p x ,p y ,θ,u,v,r,U] T ;γ>0 indicates quantization step size; K1=γ, K i+1 =K i +γ, the quantization error is bounded and satisfies

[0019] S13. Let Q(τ) = q1τ + q2, defined as follows:

[0020]

[0021] Where a>0, q1 is time-varying and unknown, Since the sign remains unchanged during the quantization process, we know that q1>0; because Then Q(τ U )-τ U and Q(τ r )-τ r is bounded, |q 2U |and|q 2r | is also bounded.

[0022] Furthermore, step S2 specifically includes:

[0023] S21. According to the kinematic model of the constructed USV, it is known that the system is under-driven. The ideal angle θ d As a controlled object to solve the under-actuated problem of USV, let Θ=(U x ,U y ) T ,but:

[0024]

[0025] Define the position of USV as p=(p x ,p y ) T , the ideal position information is p d , the control target is p→p d ;

[0026] S22. Design the linear velocity guidance law as follows:

[0027] U c =U d -k p (pp d )

[0028] Where k p >0, U d is the ideal linear velocity, and is obtained from the formula in step S21:

[0029]

[0030] S23. Due to If θ d The range of is (-π / 2,π / 2), then:

[0031]

[0032] Among them, θ d Design the required angle for the outer ring position guidance law;

[0033] S24. Design the attitude guidance law as follows:

[0034]

[0035] Furthermore, step S3 specifically includes:

[0036] S31. Based on the constructed dynamic model of USV, the dynamic equation of USV is written as:

[0037]

[0038] S32. Set the control objectives as follows:

[0039]

[0040] Among them, δ1 and δ2 are constants greater than zero;

[0041] S33. Convert the dynamic equation of the USV into a first-order nonlinear control system as follows:

[0042]

[0043] in,

[0044] S34. To facilitate the design of ESO, define Δ U =d U +F U , Δ r =d r +F r , then:

[0045]

[0046] S35. Design ESO as follows:

[0047]

[0048] Among them, the designed ESO is used to estimate U,Δ U ,r,Δ r , Δ r are the observed values ​​of the corresponding variables, is the observer parameter;

[0049] S36, set reference speed d =(Θ,r d ) T, tracking error e=(e U ,e r ) T =Ξ-Ξ d , define the integral sliding surface as follows:

[0050]

[0051] Among them, c U >0,c r >0; and taking the derivative of the defined integral sliding surface, we get:

[0052]

[0053]

[0054] Among them, l U ,η U ,l r ,η r are all constants greater than zero;

[0055] S37. Definition Then we have:

[0056]

[0057] S38. Define time-varying gain q 1U (t) and q 1r The lower bounds of (t) are q 1U (t) min ,q 1r (t) min , design the control law as follows:

[0058]

[0059] S39. Design the adaptive law as follows:

[0060]

[0061] Among them, γ1,γ2,b U ,b r ,ω U ,ω r are all constants greater than zero; then the error system of the dynamics is expressed as:

[0062]

[0063] Furthermore, step S4 specifically includes:

[0064] S41. Based on the designed ESO, design its error system as follows:

[0065]

[0066] definition Taking the derivative of the above formula, we get:

[0067]

[0068] S42. Define the error state equation of the observer as follows:

[0069]

[0070] in,

[0071] S43. Define the Lyapunov function as follows:

[0072] V1=μ T Pμ

[0073] And take the derivative of the defined Lyapunov function and get:

[0074]

[0075] in, λ min (Q) is the minimum eigenvalue of Q, when When , the convergence condition of ESO is obtained as

[0076] S44. For the designed kinematic control subsystem, define the following Lyapunov function:

[0077]

[0078] And take the derivative of the defined Lyapunov function and get:

[0079]

[0080] Define η0<2k p ,η0<k θ ,but

[0081] S45. For the dynamic subsystem, the following Lyapunov function is designed:

[0082]

[0083] And take the derivative of the defined Lyapunov function and get:

[0084]

[0085] Substituting the designed guidance law and control law into the equation, we get:

[0086]

[0087] Shaped like Then there is Taking into account Depend on get:

[0088]

[0089] because Then we have:

[0090]

[0091] Where D = D U +D r , c=min{2l U ,2l r ,γ1ω U ,γ2ω r};

[0092] S46. For the entire closed-loop control system, design the following Lyapunov function:

[0093] V=V1+V0+V2

[0094] And the designed Lyapunov function is derived to obtain:

[0095]

[0096] The entire system is eventually uniformly bounded, and the system error can converge to a smaller residual range.

[0097] Compared with the prior art, the present invention has the following advantages:

[0098] 1. The present invention provides an underactuated USV trajectory tracking control method with signal quantization based on an extended state observer. A linear analytical model is introduced to describe the input quantization process. When designing the control law, there is no need to consider the prior information of the quantization parameters, thereby improving the adaptability and versatility of the control system and simplifying the control law design process.

[0099] 2. The present invention provides an under-actuated USV trajectory tracking control method with signal quantization based on an extended state observer. By designing a quantitative feedback controller, it solves the problem of USV adaptive trajectory tracking control with signal quantization, which is more in line with the control law of actuators in navigation practice.

[0100] 3. The present invention provides an under-actuated USV trajectory tracking control method with signal quantization based on an extended state observer. This method takes into account the impact of quantized state variables on the control system and estimates and compensates for the uncertainty introduced by quantization by utilizing the extended state observer, thereby improving the overall robustness and reliability of the control system.

[0101] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0103] Figure 1 Flow chart of the method of the present invention.

[0104] Figure 2 This is a diagram of the ship trajectory tracking results provided by an embodiment of the present invention.

[0105] Figure 3 This is a ship trajectory tracking error diagram provided by an embodiment of the present invention.

[0106] Figure 4 A diagram showing the change in forward speed and heading angle of a ship provided by an embodiment of the present invention

[0107] Figure 5 A comparison diagram of control input before and after quantization provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0108] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0109] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products or apparatuses.

[0110] like Figure 1 As shown, the present invention provides an under-actuated USV trajectory tracking control method with signal quantization based on an extended state observer, comprising:

[0111] S1. Construct the kinematic and dynamic models of the USV, use a uniform quantizer to quantize the control signal, and use a linear analysis model to describe the input quantization process and external interference;

[0112] S2. Based on the constructed USV kinematic model, design the position guidance law and attitude guidance law to solve the under-actuation problem of the USV;

[0113] S3. Based on the constructed USV dynamic model, the integral sliding surface is defined and a quantitative controller is designed. The extended observer is used to estimate the quantized state feedback information, system uncertainties, and external disturbances.

[0114] S4. Based on the Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed USV dual-loop trajectory tracking control system with signal quantization are proved, and the effectiveness of the control strategy is verified through simulation experiments.

[0115] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0116] S11. Under the environmental interference of wind, waves and currents, the kinematic model and dynamic model of the USV are constructed as follows:

[0117]

[0118] Where, (p x ,p y ) and θ are the position and bow angle of the unmanned vessel, respectively; U represents the cruising speed of the USV; β represents the drift angle; u, v, r represent the forward speed, lateral speed, and bow angular velocity, respectively; τ u and τ r Both represent control input; τ uw ,τ vw ,τ rw Both represent environmental disturbances related to wind, waves and currents; f u (u,v,r) represents the nonlinear term of Coriolis, f v (u,v,r) represents the nonlinear term of the centripetal force matrix, f r (u, v, r) represents the nonlinear term of hydrodynamic damping; Where m represents the mass of USV, and Both represent additional mass, I Zrepresents the moment of inertia about the vertical axis;

[0119] S12. All state variables and control inputs are quantized using a uniform quantizer:

[0120]

[0121] Where χ=[p x ,p y ,θ,u,v,r,U] T ;γ>0 indicates quantization step size; K1=γ, K i+1 =K i +γ, the quantization error is bounded and satisfies

[0122] S13. Let Q(τ) = q1τ + q2, defined as follows:

[0123]

[0124] Where a>0, q1 is time-varying and unknown, Since the sign remains unchanged during the quantization process, we know that q1>0; because Then Q(τ U )-τ U and Q(τ r )-τ r is bounded, |q 2U |and|q 2r | is also bounded.

[0125] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0126] S21. According to the kinematic model of the constructed USV, it is known that the system is under-driven. Designing U alone cannot track the x and y directions. Therefore, the ideal angle θ is set to d As a controlled object to solve the under-actuated problem of USV, let Θ=(U x ,U y ) T ,but:

[0127]

[0128] Define the position of USV as p=(p x ,p y ) T , the ideal position information is p d , the control target is p→p d ;

[0129] S22. Design the linear velocity guidance law as follows:

[0130] U c =U d -k p (pp d )

[0131] Where k p >0, U d is the ideal linear velocity, and is obtained from the formula in step S21:

[0132]

[0133] S23. Due to If θ d The range of is (-π / 2,π / 2), then:

[0134]

[0135] Among them, θ d Design the required angle for the outer ring position guidance law;

[0136] S24. Design the attitude guidance law as follows:

[0137]

[0138] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0139] S31. Based on the constructed dynamic model of USV, the dynamic equation of USV is written as:

[0140]

[0141] S32. Set the control objectives as follows:

[0142]

[0143] Among them, δ1 and δ2 are both small constants greater than zero;

[0144] S33. Convert the dynamic equation of the USV into a first-order nonlinear control system as follows:

[0145]

[0146] in,

[0147] S34. To facilitate the design of ESO, define Δ U =d U +F U , Δ r =d r +Fr , then:

[0148]

[0149] S35. Design ESO as follows:

[0150]

[0151] Among them, the designed ESO is used to estimate U,Δ U ,r,Δ r , Δ r are the observed values ​​of the corresponding variables, is the observer parameter;

[0152] S36, set reference speed d =(Θ,r d ) T , tracking error e=(e U ,e r ) T =Ξ-Ξ d , define the integral sliding surface as follows:

[0153]

[0154] Among them, c U >0,c r >0; and taking the derivative of the defined integral sliding surface, we get:

[0155]

[0156]

[0157] Among them, l U ,η U ,l r ,η r are all constants greater than zero;

[0158] S37. Definition Then we have:

[0159]

[0160] S38. Define time-varying gain q 1U (t) and q 1r The lower bounds of (t) are q 1U (t) min ,q 1r (t) min , design the control law as follows:

[0161]

[0162] S39. Design the adaptive law as follows:

[0163]

[0164] Among them, γ1,γ2,b U ,b r ,ω U ,ω r are all constants greater than zero; then the error system of the dynamics is expressed as:

[0165]

[0166] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0167] S41. Based on the designed ESO, design its error system as follows:

[0168]

[0169] definition Taking the derivative of the above formula, we get:

[0170]

[0171] S42. Define the error state equation of the observer as follows:

[0172]

[0173] in,

[0174] S43. Define the Lyapunov function as follows:

[0175] V1=μ T Pμ

[0176] And take the derivative of the defined Lyapunov function and get:

[0177]

[0178] in, λ min (Q) is the minimum eigenvalue of Q, when When , the convergence condition of ESO is obtained as

[0179] S44. For the designed kinematic control subsystem, define the following Lyapunov function:

[0180]

[0181] And take the derivative of the defined Lyapunov function and get:

[0182]

[0183] Define η0<2k p ,η0<k θ ,but

[0184] S45. For the dynamic subsystem, the following Lyapunov function is designed:

[0185]

[0186] And take the derivative of the defined Lyapunov function and get:

[0187]

[0188] Substituting the designed guidance law and control law into the equation, we get:

[0189]

[0190] Shaped like Then there is Taking into account Depend on get:

[0191]

[0192] because Then we have:

[0193]

[0194] Where D = D U +D r , c=min{2l U ,2l r ,γ1ω U ,γ2ω r};

[0195] S46. For the entire closed-loop control system, design the following Lyapunov function:

[0196] V=V1+V0+V2

[0197] And the designed Lyapunov function is derived to obtain:

[0198]

[0199] The entire system is eventually uniformly bounded, and the system error can converge to a smaller residual range.

[0200] Example

[0201] In order to verify the effectiveness of the solution of the present invention, this embodiment uses MATLAB to perform track tracking control simulation.

[0202] Figure 2-5 The initial state of the controlled object is I = (-85, 0, 0, 0, 0), and the expected trajectory is p d =[t-40,t+40] T The trajectory tracking results, ship tracking error, ship speed and heading changes, and control input before and after quantification. Figure 2 The ship trajectory tracking results are given. Figure 3 The tracking error of the ship is given. Figure 4 Given the changes in the ship's forward speed and heading angle, Figure 5 (a) and Figure 5 (b) shows the control input before and after quantization. Simulation results show that the quantization process reduces the controller's execution frequency and control amplitude, effectively alleviating the signal transmission burden on the network communication platform and making it more suitable for marine engineering practice. Simulation results confirm that incorporating the signal quantization mechanism in the control system ensures control system stability without significantly sacrificing tracking control quality.

[0203] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A trajectory tracking control method for an underactuated USV with signal quantization based on an extended state observer, comprising: S1. Construct the kinematic and dynamic models of the USV, use a uniform quantizer to quantize the control signal, and use a linear analysis model to describe the input quantization process and external interference; S2. Design position and attitude guidance laws based on the constructed USV kinematic model. S3. Based on the constructed USV dynamic model, the integral sliding surface is defined and a quantitative controller is designed. The extended observer is used to estimate the quantized state feedback information, system uncertainties, and external disturbances. S4. Based on Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed USV dual-loop trajectory tracking control system with signal quantization are proved.

2. The underactuated USV trajectory tracking control method with signal quantization based on an extended state observer according to claim 1, step S1 specifically comprising: S11. Under the environmental interference of wind, waves and currents, the kinematic model and dynamic model of the USV are constructed as follows: Where, (p x ,p y ) and θ are the position and bow angle of the unmanned vessel, respectively; U represents the cruising speed of the USV; β represents the drift angle; u, v, r represent the forward speed, lateral speed, and bow angular velocity, respectively; τ u and τ r Both represent control input; τ uw ,τ vw ,τ rw Both represent environmental disturbances related to wind, waves and currents; f u (u,v,r) represents the nonlinear term of Coriolis, f v (u,v,r) represents the nonlinear term of the centripetal force matrix, f r (u, v, r) represents the nonlinear term of hydrodynamic damping; Where m represents the mass of USV, and Both represent additional mass, I Z represents the moment of inertia about the vertical axis; S12. All state variables and control inputs are quantized using a uniform quantizer: Where χ=[p x ,p y ,θ,u,v,r,U] T ;γ>0 indicates quantization step size; K1=γ, K i+1 =K i +γ, the quantization error is bounded and satisfies S13. Let Q(τ) = q1τ + q2, defined as follows: Where a>0, q1 is time-varying and unknown, Since the sign remains unchanged during the quantization process, we know that q1>0; because Then Q(τ U )-τ U and Q(τ r )-τ r is bounded, |q 2U |and|q 2r | is also bounded.

3. The underactuated USV trajectory tracking control method with signal quantization based on an extended state observer according to claim 1, step S2 specifically comprising: S21. According to the kinematic model of the constructed USV, it is known that the system is under-driven. The ideal angle θ d As a controlled object to solve the under-actuated problem of USV, let Θ=(U x ,U y ) T ,but: Define the position of USV as p=(p x ,p y ) T , the ideal position information is p d , the control target is p→p d ; S22. Design the linear velocity guidance law as follows: IN c =U d -k p (pp d ) Where k p >0, U d is the ideal linear velocity, and is obtained from the formula in step S21: S23. Due to If θ d The range of is (-π / 2,π / 2), then: Among them, θ d Design the required angle for the outer ring position guidance law; S24. Design the attitude guidance law as follows:

4. The underactuated USV trajectory tracking control method with signal quantization based on an extended state observer according to claim 1, step S3 specifically comprising: S31. Based on the constructed dynamic model of USV, the dynamic equation of USV is written as: S32. Set the control objectives as follows: Among them, δ1 and δ2 are constants greater than zero; S33. Convert the dynamic equation of the USV into a first-order nonlinear control system as follows: in, S34. To facilitate the design of ESO, define Δ U =d U +F U , Δ r =d r +F r , then: S35. Design ESO as follows: Among them, the designed ESO is used to estimate U,Δ U ,r,Δ r , Δ r are the observed values ​​of the corresponding variables, is the observer parameter; S36, set reference speed d =(Θ,r d ) T , tracking error e=(e U ,e r ) T =Ξ-Ξ d , define the integral sliding surface as follows: Among them, c U >0,c r >0; and taking the derivative of the defined integral sliding surface, we get: Among them, l U ,η U ,l r ,η r are all constants greater than zero; S37. Definition Then we have: S38. Define time-varying gain q 1U (t) and q 1r The lower bounds of (t) are q 1U (t) min ,q 1r (t) min , design the control law as follows: S39. Design the adaptive law as follows: Among them, γ1,γ2,b U ,b r ,ω U ,ω r are all constants greater than zero; then the error system of the dynamics is expressed as:

5. The underactuated USV trajectory tracking control method with signal quantization based on an extended state observer according to claim 1, step S4 specifically comprising: S41. Based on the designed ESO, design its error system as follows: definition Taking the derivative of the above formula, we get: S42. Define the error state equation of the observer as follows: in, S43. Define the Lyapunov function as follows: V1=μ T PM And take the derivative of the defined Lyapunov function and get: in, λ min (Q) is the minimum eigenvalue of Q, when When , the convergence condition of ESO is obtained as S44. For the designed kinematic control subsystem, define the following Lyapunov function: And take the derivative of the defined Lyapunov function and get: Define η0<2k p ,η0<k θ ,but S45. For the dynamic subsystem, the following Lyapunov function is designed: And take the derivative of the defined Lyapunov function and get: Substituting the designed guidance law and control law into the equation, we get: Shaped like Then there is Taking into account Depend on get: because Then we have: where D = D U + D r , c = min{2l U , 2l r , γ1ω U , γ2ω r}; S46. For the entire closed-loop control system, design the following Lyapunov function: V=V1+V0+V2 And the designed Lyapunov function is derived to obtain: The entire system is eventually uniformly bounded, and the system error can converge to a smaller residual range.

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