Underactuated unmanned ship multi-constraint trajectory tracking control method based on disturbance observer

Abstract

The invention provides an underactuated unmanned ship multi-constraint trajectory tracking control method based on a disturbance observer, and the method comprises the steps: building a trajectory tracking control mathematical model of an unmanned ship, and converting the model into an underactuated unmanned ship trajectory tracking control mathematical model in view of the human underactuated characteristics of the unmanned ship under the actual sea condition; a composite quantizer is adopted to quantize control input, and a linear analysis model is used to describe an input quantization process; solving an input constraint problem by using a saturation function; designing a disturbance observer, a longitudinal propulsive force control law and a bow turning torque control law, and obtaining an adaptive law of trajectory tracking of the under-actuated unmanned ship; an event triggering mechanism based on a time-varying threshold value is introduced, and a control law of the under-actuated unmanned ship system is updated; on the basis of the Lyapunov stability theory, it is proved that all signals in the whole closed-loop control system are finally bounded on the basis of the stability of the anti-interference and multi-constraint under-actuated unmanned ship trajectory tracking control system when priori information of parameters does not need to be quantized.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer. Background Art

[0002] As autonomous mobile platforms on water, unmanned vessels (UAVs) typically exhibit dynamic characteristics that suggest underactuated systems. This means that the dimensionality of their control inputs is smaller than the dimensionality of the system's state. In most cases, the position of the UAV is controlled by surge forces and yaw moments. Designing robust and accurate trajectory tracking algorithms for underactuated control systems is crucial, especially in complex environments with external disturbances, input / output constraints, and actuator constraints.

[0003] To date, numerous methods have been applied to trajectory tracking control for unmanned vessels, including neural network control, sliding mode control, and robust control. However, a key challenge facing underactuated unmanned vessels is effectively handling the effects of external disturbances. External disturbances such as currents, wind speeds, and waves can significantly deviate from the vessel's trajectory. This requires a control system that not only accurately tracks the trajectory but also exhibits strong robustness to withstand these disturbances.

[0004] Furthermore, when an unmanned vessel needs to complete commands issued by the control system, given that sensor output signals are often continuous, the unmanned vessel controller can only process discrete data. Unmanned vessel controllers are typically embedded in resource-constrained hardware platforms with limited computing power, memory, processing speed, and storage space. Furthermore, when operating remotely or transmitting data, unmanned vessels may be limited by communication bandwidth. Limited communication bandwidth reduces transmission rates, leading to increased latency in control commands and sensor data, and potentially causing data loss and corruption. Therefore, considering input quantization techniques in the design of unmanned vessel controllers can improve the system's real-time responsiveness and ensure control system stability. However, while many studies on trajectory tracking control for underactuated unmanned vessels have considered input quantization techniques, they fail to further alleviate the pressure on limited maritime communication resources and reduce the execution frequency of actuators, and fail to consider event triggering mechanisms in the controller design. Therefore, overcoming these difficulties and designing innovative controllers to achieve optimal trajectory tracking control for underactuated unmanned vessels remains a hot topic in the current development of unmanned vessels. Summary of the Invention

[0005] In response to the technical problems raised above, a multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer is provided, which is applied to an underactuated unmanned vessel system with multiple constraints.

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

[0007] A multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer comprises:

[0008] S1. Establish a mathematical model for trajectory tracking control of unmanned vessels. Considering the under-actuated characteristics of unmanned vessels under actual sea conditions, the model is converted into a mathematical model for trajectory tracking control of under-actuated unmanned vessels.

[0009] S2. Use a composite quantizer to quantize the control input in the control system, use a linear analytical model to describe the input quantization process, and use a saturation function to solve the input constraint problem to prevent the divergence or structural failure of the control system;

[0010] S3. Design a disturbance observer, longitudinal propulsion control law, and bow torque control law to obtain an adaptive law for the trajectory tracking of the underactuated unmanned vessel. In addition, introduce an event trigger mechanism based on a time-varying threshold to update the control law of the underactuated unmanned vessel system and complete the anti-interference synchronization design.

[0011] S4. Based on Lyapunov stability theory, the stability of the designed underactuated unmanned vessel trajectory tracking control system based on anti-interference and multi-constraints is proved when no prior information of quantitative parameters is required, and all signals in the entire closed-loop control system are ultimately bounded.

[0012] Furthermore, step S1 is specifically as follows:

[0013] S11. The mathematical model of the unmanned ship's motion is established as follows:

[0014]

[0015] Where η represents the position vector in the fixed carrier coordinate system, η=[x,y,ψ] T ; ν represents the velocity vector in the fixed carrier coordinate system, ν = [u, v, r] T ; d represents external disturbance, d=[d1,d2,d3] T ; τ represents the control input vector, τ=[τ u ,τ v ,τ r ] T ; J(ψ) represents the rotation matrix, M represents the moment of inertia matrix, C(ν) represents the centripetal force, D(ν) represents the damping matrix,

[0016] S12. Considering the underactuated characteristics of unmanned vessels under actual sea conditions, the conversion model is a kinematic mathematical model of underactuated unmanned vessels, as follows:

[0017]

[0018] in, is the lateral position of the unmanned ship, is the longitudinal position of the unmanned ship, is the heading angle of the unmanned ship, u, v, and r are the forward speed, lateral speed, and yaw speed of the unmanned ship respectively; the mathematical model of the underactuated unmanned ship dynamics is described as follows:

[0019]

[0020] Among them, τ u represents the longitudinal propulsion force; τ r represents the bow moment; d1, d2, d3 represent external disturbances caused by wind, current, waves, etc.; f u (·) represents the nonlinear function of centripetal force, Υ 11 (u) represents the hydrodynamic damping term, Υ 11 (u)=-(X u +X |u|u |u|);f v (·) represents the nonlinear function of the Coriolis force, Υ 22 (v,r) and Υ 23 (v, r) both represent the fluid dynamic damping term, Υ 22 (v,r)=-(Y v +Y |v|v |v|+Y |r|v |r|), Υ 23 (v,r)=-(Y r +Y |v|r |v|+Y |r|r |r|);f r (·) represents the nonlinear function of the hydrodynamic damping effect, Υ 32 (v,r) and Υ 33 (v, r) both represent the fluid dynamic damping term, Υ 32 (v,r)=-(N v +N |v|v |v|+N |r|v |r|), Υ 33 (v,r)=-(N r +N |v|r |v|+N |r|r |r|); where m ii represents the inertia of the ship, including the hydrodynamic added mass; X u , Y v , Y r , N v , N r , X|u|u , Y |v|v , Y |r|v , Y |v|r , Y |r|r , N |v|v ,N |r|v ,N |v|r and N |r|r Both represent hydrodynamic derivatives;

[0021] S13. The swaying motion of the unmanned ship satisfies the passive bounded condition. Considering that the underactuated unmanned ship has two controllable inputs τ u and τ r , according to step S12, the conversion formula is obtained:

[0022]

[0023] Among them, Q(τ u ) and Q(τ r ) represents the u and τ r The results after quantification.

[0024] Furthermore, step S2 is specifically as follows:

[0025] S21. Use a composite quantizer to quantize the control input in the system. The specific quantization process is described as follows:

[0026]

[0027] Where q1(·) represents the logarithmic quantizer; f i (·) is defined as the rounding function less than or equal to (·); τ i,s >0 is the switching threshold between logarithmic quantization and uniform quantization; σ i is the quantization density of the uniform quantizer;

[0028] For the unmanned ship model, considering the quantized control input, let Q(τ u )=q 1u (t)τ u +q 2u (t), Q(τ r )=q 1r (t)τ r +q 2r (t), take:

[0029]

[0030] Among them, q 1u (t) and q 1r (t) are unknown, since q 1u and q 1rThe sign of will not change during the quantization process, and we can get q from the above formula. 1u (t)>0,q 1r (t)>0; when |τ u (t)|<a,|τ r (t)|<a, Q(τ u (t)), Q(τ r (t)) is bounded, so q 2u (t),q 2r (t) is bounded,

[0031] S22. To solve the problem of input constraints, a method based on the hyperbolic tangent function is used to directly design bounded control inputs. The saturation function sat(τ) is used instead of the sign function sgn(τ) in the controller design:

[0032]

[0033] Among them, τ max is the maximum value of τ, τ = sat(τ);

[0034] S23. Define the ideal trajectory as follows:

[0035]

[0036] Among them, x d and y d It represents the ideal trajectory of the unmanned ship in the inertial coordinate system, and the trajectory parameter U d (t) represents a continuously differentiable vector;

[0037] S24. Set the control goal to design a controller that satisfies the actual position U of the unmanned ship and tracks the desired trajectory U. d (t), and ensure that no violation and z e The limitations are described as follows:

[0038]

[0039] Among them, U=[x,y] T is the actual position of the unmanned ship in the inertial coordinate system, l0 is a small constant and satisfies l0>0.

[0040] Furthermore, step S3 is specifically as follows:

[0041] S31. To compensate for external disturbances, a disturbance observer is designed as follows:

[0042]

[0043] in, It is d i (t) estimate, ρ i (t) represents the auxiliary state variable, ε i Is a positive number; define the external disturbance estimation error as The estimation error is specifically expressed as:

[0044]

[0045] S32. Define the position error as follows:

[0046]

[0047] Among them, z e represents the position error, sgn(·) represents the sign function, and sgn(0)=1;

[0048] S33. Design the longitudinal propulsion controller of the underactuated unmanned ship and define the Lyapunov function as follows:

[0049]

[0050] Where log(·) represents the natural logarithm of (·), k a =k d -B0; limit z e Satisfaction|z e |<k a , we get V u1 is positive; according to step S32, we get

[0051] S34. Deriving the Lyapunov function defined in step S33 yields:

[0052]

[0053] S35, let α u =u e +u, define the stability function α u ,as follows:

[0054]

[0055] Among them, k ze >0, and k ze is a constant, so we have:

[0056]

[0057] S36, due to u e Without constraints, define the following Lyapunov function:

[0058]

[0059] S37. Derivative the Lyapunov function defined in step S36 to obtain:

[0060]

[0061] make get:

[0062]

[0063] S38. Design the system control law and adaptive law as follows:

[0064]

[0065] in, is μ u Estimate of θ u are constants, γ1 and σ u is a positive number,

[0066] S39. Design the bow torque controller of the underactuated unmanned ship and define the Lyapunov function as follows:

[0067]

[0068] S310, deriving the Lyapunov function defined in step S39, to obtain:

[0069]

[0070] S311, let α r =r e +r, define the stability function α r , α r Bringing it into step S310, we get:

[0071]

[0072] S312, due to r e Without constraints, define the following Lyapunov function:

[0073]

[0074] S313, deriving the Lyapunov function defined in step S312, to obtain:

[0075]

[0076] make get:

[0077]

[0078] S314. Design the system control law and adaptive law as follows:

[0079]

[0080] in, is μ r Estimate of θ r are constants, γ2 and σ r is a positive number,

[0081] S315. While considering input quantization, an event triggering strategy based on a time-varying threshold is adopted, which is defined as follows:

[0082]

[0083] Among them, ρ u >0,ρ r >0, e u (t) = τ u (t)-ω u (t), e r (t) = τ r (t)-ω r (t);

[0084] S316: From step S315, we know that there is a continuous time-varying coefficient φ 2u (t) and φ 2r (t), satisfying and |φ 2u (t)|≤1; and |φ 2r (t)|≤1, such that:

[0085]

[0086] Among them, φ 1u (t) = φ 2u (t)sgn(τ u (t)),φ 1r (t) = φ 2r (t)sgn(τ r (t)); due to |φ 2u (t)|≤1,|φ 2r (t)|≤1 and|sgn(τ u (t))|≤1,|sgn(τ r (t))|≤1; then |φ 1u(t)|=|φ 2u (t)sgn(τ u (t))|≤1,|φ 1r (t)|=|φ 2r (t)sgn(τ r (t))|≤1, so we get:

[0087]

[0088] S317. Based on the event-driven strategy of the time-varying threshold, the control law of the underactuated unmanned vessel system is updated as follows:

[0089]

[0090] Furthermore, step S4 is specifically as follows:

[0091] S41. Define the Lyapunov function as:

[0092]

[0093] S42. According to step S41, derive V to obtain:

[0094]

[0095] S43. Substitute the control law and adaptive law into the equation to obtain:

[0096]

[0097] S44. Due to Then there is make Then we have:

[0098]

[0099] S45, according to Then we get:

[0100]

[0101] Combining step S43 and step S45, we obtain:

[0102]

[0103] S46. Due to: Thus we get:

[0104]

[0105] S47. According to the output restricted lemma: for k b >0, if the formula satisfies Then we have: Thus we can get:

[0106]

[0107] S48. According to steps S46 and S47, the following is obtained:

[0108]

[0109] S49. Considering the control law updated by the event triggering mechanism based on the time-varying threshold, we obtain:

[0110]

[0111] S410, due to There is u e ω u ≤0, r e ω r ≤0, we get:

[0112]

[0113] Since |φ2ρ|≤ρ, and 1-δ≤|1+φ1δ|, we have:

[0114]

[0115] S411. According to steps S49 and S410, the following is obtained:

[0116]

[0117] S412, due to q 1u >0,q 1r >0, according to the lemma: for any unknown real variable e, there exists a constant n that satisfies the following inequality Then we get:

[0118]

[0119] in, and It is q 1u ,q 1u The upper bound of , so we get:

[0120]

[0121] Among them, C>0, D>0, and satisfy:

[0122]

[0123] in,

[0124] S413. According to step S412, obtain Therefore, according to Lyapunov stability theory, all signals in the entire closed-loop system are ultimately bounded, and the tracking error of the system can converge to a smaller residual set.

[0125] Compared with the prior art, the present invention has the following advantages:

[0126] 1. The present invention provides a multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer. Compared with existing underactuated unmanned vessel trajectory tracking control methods, the present invention combines multiple constraints, input quantization, and event triggering mechanisms to better adapt to marine engineering practices. By estimating disturbances and compensating for them with the observer, the method ensures that the trajectory tracking error of the underactuated unmanned vessel is controlled within a smaller range, thereby improving the performance and accuracy of the control system.

[0127] 2. The present invention provides a multi-constraint trajectory tracking control method for an under-actuated unmanned vessel based on an interference observer. This method takes into account the multiple constraints of the unmanned vessel for the first time, including the input constraints, output constraints and execution constraints of the under-actuated unmanned vessel. This not only improves the stability and safety of the unmanned vessel, but also helps to achieve more efficient management and flexible mission planning, and maximizes the success rate of the unmanned vessel mission execution.

[0128] 3. The present invention uses a composite quantizer to linearly describe the quantization process. It does not require prior knowledge of the quantization parameters and does not regard the quantized variables as disturbances of the unquantized variables. In order to further save communication resources and reduce the execution frequency of the actuator, the present invention also updates the design of the controller and adopts a time-varying threshold event triggering mechanism.

[0129] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] 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.

[0131] Figure 1 Flow chart of the method of the present invention.

[0132] Figure 2 This is a flow chart of the control method of the present invention.

[0133] Figure 3 This is a diagram of the unmanned ship trajectory tracking results provided by an embodiment of the present invention.

[0134] Figure 4 This is a diagram of the unmanned ship trajectory tracking error provided by an embodiment of the invention.

[0135] Figure 5 A comparison diagram of the control input curves provided by an embodiment of the present invention.

[0136] Figure 6 This is a diagram of the event-triggered sampling time interval provided by an embodiment of the present invention.

[0137] Figure 7 This is an external interference estimation diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0138] 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.

[0139] 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.

[0140] like Figure 1 As shown, the present invention provides a multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer, comprising:

[0141] S1. Establish a mathematical model for trajectory tracking control of unmanned vessels. Considering the under-actuated characteristics of unmanned vessels under actual sea conditions, the model is converted into a mathematical model for trajectory tracking control of under-actuated unmanned vessels.

[0142] S2. Use a composite quantizer to quantize the control input in the control system, use a linear analytical model to describe the input quantization process, and use a saturation function to solve the input constraint problem to prevent the divergence or structural failure of the control system;

[0143] S3. Design a disturbance observer, longitudinal propulsion control law, and bow torque control law to obtain an adaptive law for the trajectory tracking of the underactuated unmanned vessel. In addition, introduce an event trigger mechanism based on a time-varying threshold to update the control law of the underactuated unmanned vessel system and complete the anti-interference synchronization design.

[0144] S4. Based on Lyapunov stability theory, the stability of the designed underactuated unmanned vessel trajectory tracking control system based on anti-interference and multi-constraints is proved when no prior information of quantitative parameters is required, and all signals in the entire closed-loop control system are ultimately bounded.

[0145] In specific implementation, as a preferred embodiment of the present invention, step S1 is specifically as follows:

[0146] S11. The mathematical model of the unmanned ship's motion is established as follows:

[0147]

[0148] Where η represents the position vector in the fixed carrier coordinate system, η=[x,y,ψ] T ; ν represents the velocity vector in the fixed carrier coordinate system, ν = [u, v, r] T ; d represents external disturbance, d=[d1,d2,d3] T ; τ represents the control input vector, τ=[τ u ,τ v ,τ r ] T ; J(ψ) represents the rotation matrix, M represents the moment of inertia matrix, C(ν) represents the centripetal force, D(ν) represents the damping matrix,

[0149] S12. Under actual sea conditions, the execution force of unmanned vessels is usually limited by the physical characteristics of the propeller and environmental influences, resulting in the dimension of its control input being less than the dimension of the system state. Therefore, the dynamic characteristics of unmanned vessels are usually manifested as underactuated systems, and in most cases, the position of the unmanned vessel is controlled by the longitudinal propulsion force and the bow torque. Therefore, given the underactuated characteristics of unmanned vessels under actual sea conditions, the conversion model is the mathematical kinematic model of the underactuated unmanned vessel, as follows:

[0150]

[0151] in, is the lateral position of the unmanned ship, is the longitudinal position of the unmanned ship, is the heading angle of the unmanned ship, u, v, and r are the forward speed, lateral speed, and yaw speed of the unmanned ship respectively; the mathematical model of the underactuated unmanned ship dynamics is described as follows:

[0152]

[0153] Among them, τ urepresents the longitudinal propulsion force; τ r represents the bow moment; d1, d2, d3 represent external disturbances caused by wind, current, waves, etc.; f u (·) represents the nonlinear function of centripetal force, Υ 11 (u) represents the hydrodynamic damping term, Υ 11 (u)=-(X u +X |u|u |u|);f v (·) represents the nonlinear function of the Coriolis force, Υ 22 (v,r) and Υ 23 (v, r) both represent the fluid dynamic damping term, Υ 22 (v,r)=-(Y v +Y |v|v |v|+Y |r|v |r|), Υ 23 (v,r)=-(Y r +Y |v|r |v|+Y |r|r |r|);f r (·) represents the nonlinear function of the hydrodynamic damping effect, Υ 32 (v,r) and Υ 33 (v, r) both represent the fluid dynamic damping term, Υ 32 (v,r)=-(N v +N |v|v |v|+N |r|v |r|), Υ 33 (v,r)=-(N r +N |v|r |v|+N |r|r |r|); where m ii represents the inertia of the ship, including the hydrodynamic added mass; X u , Y v , Y r , N v , N r , X |u|u , Y |v|v , Y |r|v , Y |v|r , Y |r|r , N |v|v ,N |r|v ,N |v|r and N |r|r Both represent hydrodynamic derivatives;

[0154] S13. The swaying motion of the unmanned ship satisfies the passive bounded condition. Considering that the underactuated unmanned ship has two controllable inputs τ u and τr , according to step S12, the conversion formula is obtained:

[0155]

[0156] Among them, Q(τ u ) and Q(τ r ) represents the u and τ r The results after quantification.

[0157] In specific implementation, as a preferred embodiment of the present invention, step S2 is specifically as follows:

[0158] S21. Use a composite quantizer to quantize the control input in the system. The specific quantization process is described as follows:

[0159]

[0160] Where q1(·) represents the logarithmic quantizer; f i (·) is defined as the rounding function less than or equal to (·); τ i,s >0 is the switching threshold between logarithmic quantization and uniform quantization; σ i is the quantization density of the uniform quantizer;

[0161] For the unmanned ship model, considering the quantized control input, let Q(τ u )=q 1u (t)τ u +q 2u (t), Q(τ r )=q 1r (t)τ r +q 2r (t), take:

[0162]

[0163] Among them, q 1u (t) and q 1r (t) are unknown, since q 1u and q 1r The sign of will not change during the quantization process, and we can get q from the above formula. 1u (t)>0,q 1r (t)>0; when |τ u (t)|<a,|τ r (t)|<a, Q(τ u (t)), Q(τ r (t)) is bounded, so q 2u (t),q 2r (t) is bounded,

[0164] S22. In the field of motion control, input constraints can affect the stability and performance of the control system to some extent, and can even render the entire control system unstable. To address the input constraint problem, a method for directly designing bounded control inputs based on the hyperbolic tangent function is used. The saturation function sat(τ) is used instead of the sign function sgn(τ) in the controller design:

[0165]

[0166] Among them, τ max is the maximum value of τ, τ = sat(τ);

[0167] S23, the flow chart of the control method of the present invention is as follows Figure 2 As shown. The ideal trajectory is defined as follows:

[0168]

[0169] Among them, x d and y d It represents the ideal trajectory of the unmanned ship in the inertial coordinate system, and the trajectory parameter U d (t) represents a continuously differentiable vector;

[0170] S24. Set the control goal to design a controller that satisfies the actual position U of the unmanned ship and tracks the desired trajectory U. d (t), and ensure that no violation and z e The limitations are described as follows:

[0171]

[0172] Among them, U=[x,y] T is the actual position of the unmanned ship in the inertial coordinate system, l0 is a small constant and satisfies l0>0.

[0173] In specific implementation, as a preferred embodiment of the present invention, step S3 is specifically as follows:

[0174] S31. To compensate for external disturbances, a disturbance observer is designed as follows:

[0175]

[0176] in, It is d i (t) estimate, ρ i (t) represents the auxiliary state variable, ε i Is a positive number; define the external disturbance estimation error as The estimation error is specifically expressed as:

[0177]

[0178] S32. Define the position error as follows:

[0179]

[0180] Among them, z e represents the position error, sgn(·) represents the sign function, and sgn(0)=1;

[0181] S33. Design the longitudinal propulsion controller of the underactuated unmanned ship and define the Lyapunov function as follows:

[0182]

[0183] Where log(·) represents the natural logarithm of (·), k a =k d -B0; limit z e Satisfaction|z e |<k a , we get V u1 is positive; according to step S32, we get

[0184] S34. Deriving the Lyapunov function defined in step S33 yields:

[0185]

[0186] S35, let α u =u e +u, define the stability function α u ,as follows:

[0187]

[0188] Among them, k ze >0, and k ze is a constant, so we have:

[0189]

[0190] S36, due to u e Without constraints, define the following Lyapunov function:

[0191]

[0192] S37. Derivative the Lyapunov function defined in step S36 to obtain:

[0193]

[0194] make get:

[0195]

[0196] S38. Design the system control law and adaptive law as follows:

[0197]

[0198] in, is μ u Estimate of θ u are constants, γ1 and σ u is a positive number,

[0199] S39. Design the bow torque controller of the underactuated unmanned ship and define the Lyapunov function as follows:

[0200]

[0201] S310, deriving the Lyapunov function defined in step S39, to obtain:

[0202]

[0203] S311, let α r =r e +r, define the stability function α r , α r Bringing it into step S310, we get:

[0204]

[0205] S312, due to r e Without constraints, define the following Lyapunov function:

[0206]

[0207] S313, deriving the Lyapunov function defined in step S312, to obtain:

[0208]

[0209] make get:

[0210]

[0211] S314. Design the system control law and adaptive law as follows:

[0212]

[0213] in, is μ r Estimate of θ r are constants, γ2 and σ r is a positive number,

[0214] S315. While considering input quantization, in order to further save communication resources and effectively reduce the execution frequency of the actuator, the present invention adopts an event triggering strategy based on a time-varying threshold, which is defined as follows:

[0215]

[0216] Among them, ρ u >0,ρ r >0, e u (t) = τ u (t)-ω u (t), e r (t) = τ r (t)-ω r (t);

[0217] S316: From step S315, we know that there is a continuous time-varying coefficient φ 2u (t) and φ 2r (t), satisfying and |φ 2u (t)|≤1; and |φ 2r (t)|≤1, such that:

[0218]

[0219] Among them, φ 1u (t) = φ 2u (t)sgn(τ u (t)),φ 1r (t) = φ 2r (t)sgn(τ r (t)); due to |φ 2u (t)|≤1,|φ 2r (t)|≤1 and|sgn(τ u (t))|≤1,|sgn(τ r (t))|≤1; then |φ 1u (t)|=|φ 2u (t)sgn(τ u (t))|≤1,|φ 1r (t)|=|φ2r (t)sgn(τ r (t))|≤1, so we get:

[0220]

[0221] S317. Based on the event-driven strategy of the time-varying threshold, the control law of the underactuated unmanned vessel system is updated as follows:

[0222]

[0223] In specific implementation, as a preferred embodiment of the present invention, step S4 is specifically as follows:

[0224] S41. Define the Lyapunov function as:

[0225]

[0226] S42. According to step S41, derive V to obtain:

[0227]

[0228] S43. Substitute the control law and adaptive law into the equation to obtain:

[0229]

[0230] S44. Due to Then there is make Then we have:

[0231]

[0232] S45, according to Then we get:

[0233]

[0234] Combining step S43 and step S45, we obtain:

[0235]

[0236] S46. Due to: Thus we get:

[0237]

[0238] S47. According to the output restricted lemma: for k b >0, if the formula satisfies Then we have: Thus we can get:

[0239]

[0240] S48. According to steps S46 and S47, the following is obtained:

[0241]

[0242] S49. Considering the control law updated by the event triggering mechanism based on the time-varying threshold, we obtain:

[0243]

[0244] S410, due to There is u e ω u ≤0, r e ω r ≤0, we get:

[0245]

[0246] Since |φ2ρ|≤ρ, and 1-δ≤|1+φ1δ|, we have:

[0247]

[0248] S411. According to steps S49 and S410, the following is obtained:

[0249]

[0250] S412, due to q 1u >0,q 1r >0, according to the lemma: for any unknown real variable e, there exists a constant n that satisfies the following inequality Then we get:

[0251]

[0252] in, and It's q 1u ,q 1u The upper bound of , so we get:

[0253]

[0254] Among them, C>0, D>0, and satisfy:

[0255]

[0256] in,

[0257] S413. According to step S412, obtain Therefore, according to Lyapunov stability theory, all signals in the entire closed-loop system are ultimately bounded, and the tracking error of the system can converge to a smaller residual set.

[0258] Example

[0259] In order to verify the effectiveness of the solution of the present invention, this embodiment uses MATLAB to conduct computer simulation research. The simulation object is the "Lanxin" unmanned ship of Dalian Maritime University. The parameters of the unmanned ship are shown in Table 1.

[0260] Table 1 Parameters of unmanned boat

[0261]

[0262] Set the ideal course of the unmanned ship to U d =[sin(t)+4t,cos(t)] T , the initial state of the actual controlled object is [0,1], and the controller designed in step S3 is used to control the unmanned ship. The design parameters are as follows: k ze =0.05, k ue =150, k re =0.6,γ1=1,γ2=2,θ u =0.03,θ r =0.02,σ u =σ i =0.1.

[0263] The experimental results are as follows Figure 3-Figure 7 As shown in the figure, the trajectory tracking results of the unmanned ship are as follows Figure 3 As shown. Using the control method designed by the present invention, the unmanned ship can quickly track the ideal trajectory from the initial position. The tracking error of the unmanned ship gradually converges to zero, as shown in Figure 4 shown. Figure 5 It represents the changing curve of the unmanned ship power control law. Specifically, Figure 5 The blue curve in describes the control input without considering quantization, while Figure 5 The pink curve in Figure 1 depicts the control input after input quantization. The simulation results show that after input quantization and event triggering, the controller execution frequency is significantly reduced, thereby reducing the communication load. Figure 6 Shows the time interval between two consecutive sampling moments. Figure 7 As shown in Figure 2, the minimum interval between events is 0.01 seconds, and the maximum is 0.42 seconds and 8.1 seconds respectively. In addition, events do not always occur, and some moments are not triggered, which shows that Zeno behavior does not exist. By observing Figure 7From the disturbance compensation diagram in , we can infer that the disturbance estimation accuracy is high and the estimation error of the disturbance observer is small. Figures 3 to 7 It can be seen that the controller designed in this invention has strong robustness and adaptability, which is helpful for the trajectory tracking control of unmanned ships in multi-task scenarios and complex environments.

[0264] 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 multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer, characterized in that: include: S1. Establish a mathematical model for trajectory tracking control of unmanned vessels. Considering the under-actuated characteristics of unmanned vessels under actual sea conditions, the model is converted into a mathematical model for trajectory tracking control of under-actuated unmanned vessels. S2. Use a composite quantizer to quantize the control input in the control system, use a linear analytical model to describe the input quantization process, and use a saturation function to solve the input constraint problem to prevent the divergence or structural failure of the control system; S3. Design the disturbance observer, longitudinal propulsion control law, and bow torque control law to obtain the adaptive law for trajectory tracking of the underactuated unmanned vessel. An event trigger mechanism based on time-varying thresholds is introduced to update the control law of the underactuated unmanned vessel system and complete the anti-interference synchronization design; S4. Based on Lyapunov stability theory, the stability of the designed underactuated unmanned vessel trajectory tracking control system based on anti-interference and multi-constraints is proved when no prior information of quantitative parameters is required, and all signals in the entire closed-loop control system are ultimately bounded.

2. The multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer according to claim 1 is characterized in that: Step S1 is as follows: S11. The mathematical model of the unmanned boat's motion is as follows: Where η represents the position vector in the fixed carrier coordinate system, η=[x,y,ψ] T ; ν represents the velocity vector in the fixed carrier coordinate system, ν = [u, v, r] T ; d represents external disturbance, d=[d1,d2,d3] T ; τ represents the control input vector, τ=[τ u ,τ v ,τ r ] T ; J(ψ) represents the rotation matrix, M represents the moment of inertia matrix, C(ν) represents the centripetal force, D(ν) represents the damping matrix, S12. Considering the underactuated characteristics of unmanned vessels under actual sea conditions, the conversion model is a kinematic mathematical model of underactuated unmanned vessels, as follows: in, is the lateral position of the unmanned ship, is the longitudinal position of the unmanned ship, is the heading angle of the unmanned ship, u, v, and r are the forward speed, lateral speed, and yaw speed of the unmanned ship respectively; the mathematical model of the underactuated unmanned ship dynamics is described as follows: Among them, τ u represents the longitudinal propulsion force; τ r represents the bow moment; d1, d2, d3 represent external disturbances caused by wind, current, waves, etc.; f u (·) represents the nonlinear function of centripetal force, represents the hydrodynamic damping term, f v (·) represents the nonlinear function of the Coriolis force, and Both represent the fluid dynamic damping term, Υ 22 (v,r)=-(Y v +Y |v|v |v|+Y |r|v |r|), Υ 23 (v,r)=-(Y r +Y |v|r |v|+Y |r|r |r|);f r (·) represents the nonlinear function of the hydrodynamic damping effect, and Both represent the fluid dynamic damping term, Among them, m ii represents the inertia of the ship, including the hydrodynamic added mass; X u , Y v , Y r , N v , N r , X |u|u , Y |v|v , Y |r|v , Y |v|r , Y |r|r , N |v|v ,N |r|v ,N |v|r and N |r|r Both represent hydrodynamic derivatives; S13. The swaying motion of the unmanned ship satisfies the passive bounded condition. Considering that the underactuated unmanned ship has two controllable inputs τ u and τ r , according to step S12, the conversion formula is obtained: Among them, Q(τ u ) and Q(τ r ) represents the u and τ r The results after quantification.

3. The multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer according to claim 1, characterized in that: Step S2 is as follows: S21. Use a composite quantizer to quantize the control input in the system. The specific quantization process is described as follows: Where q1(·) represents the logarithmic quantizer; f i (·) is defined as the rounding function less than or equal to (·); τ i,s >0 is the switching threshold between logarithmic quantization and uniform quantization; σ i is the quantization density of the uniform quantizer; For the unmanned ship model, considering the quantized control input, let Q(τ u )=q 1u (t)τ u +q 2u (t), Q(τ r )=q 1r (t)τ r +q 2r (t), take: Among them, q 1u (t) and q 1r (t) are unknown, since q 1u and q 1r The sign of will not change during the quantization process, and we can get q from the above formula. 1u (t)>0,q 1r (t)>0; when |τ u (t)|<a,|τ r (t)|<a, Q(τ u (t)), Q(τ r (t)) is bounded, so q 2u (t),q 2r (t) is bounded, S22. To solve the problem of input constraints, a method based on the hyperbolic tangent function is used to directly design bounded control inputs. The saturation function sat(τ) is used instead of the sign function sgn(τ) in the controller design: Among them, τ max is the maximum value of τ, τ = sat(τ); S23. Define the ideal trajectory as follows: Among them, x d and y d It represents the ideal trajectory of the unmanned ship in the inertial coordinate system, and the trajectory parameter U d (t) represents a continuously differentiable vector; S24. Set the control goal to design a controller that satisfies the actual position U of the unmanned ship and tracks the desired trajectory U. d (t), and ensure that no violation and z e The limitations are described as follows: Among them, U=[x,y] T is the actual position of the unmanned ship in the inertial coordinate system, l0 is a small constant and satisfies l0>0.

4. The multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer according to claim 1, characterized in that: Step S3 is as follows: S31. To compensate for external disturbances, a disturbance observer is designed as follows: in, It is d i (t) estimate, ρ i (t) represents the auxiliary state variable, ε i Is a positive number; define the external disturbance estimation error as The estimation error is specifically expressed as: S32. Define the position error as follows: Among them, z e represents the position error, sgn(·) represents the sign function, and sgn(0)=1; S33. Design the longitudinal propulsion controller of the underactuated unmanned ship and define the Lyapunov function as follows: Where log(·) represents the natural logarithm of (·), k a =k d -B0; limit z e Satisfaction|z e |<k a , we get V u1 is positive; according to step S32, we get S34. Deriving the Lyapunov function defined in step S33 yields: S35, let α u =u e +u, define the stability function α u ,as follows: Among them, k ze >0, and k ze is a constant, so we have: S36, due to u e Without constraints, define the following Lyapunov function: S37. Derivative the Lyapunov function defined in step S36 to obtain: make get: S38. Design the system control law and adaptive law as follows: in, is μ u Estimate of θ u are constants, γ1 and σ u is a positive number, S39. Design the bow torque controller of the underactuated unmanned ship and define the Lyapunov function as follows: S310, deriving the Lyapunov function defined in step S39, to obtain: S311, let α r =r e +r, define the stability function α r , α r Bringing it into step S310, we get: S312, due to r e Without constraints, define the following Lyapunov function: S313, deriving the Lyapunov function defined in step S312, to obtain: make get: S314. Design the system control law and adaptive law as follows: in, is μ r Estimate of θ r are constants, γ2 and σ r is a positive number, S315. While considering input quantization, an event triggering strategy based on a time-varying threshold is adopted, which is defined as follows: Among them, p u >0,ρ r >0, e u (t)=τ u (t)-ω u (t),e r (t)=τ r (t)-ω r (t); S316: From step S315, we know that there is a continuous time-varying coefficient φ 2u (t) and φ 2r (t), satisfying and |φ 2u (t)|≤1; and |φ 2r (t)|≤1, such that: where, φ 1u (t) = φ 2u (t) sgn(τ u (t)), φ 1r (t) = φ 2r (t) sgn(τ r (t)); Since |φ 2u (t)| ≤ 1, |φ 2r (t)| ≤ 1 and |sgn(τ u (t))| ≤ 1, |sgn(τ r (t))| ≤ 1; then |φ 1u (t)| = |φ 2u (t) sgn(τ u (t))| ≤ 1, |φ 1r (t)| = |φ 2r (t) sgn(τ r (t))| ≤ 1, thus obtaining: S317. Based on the event-driven strategy of the time-varying threshold, the control law of the underactuated unmanned vessel system is updated as follows:

5. The multi-constraint trajectory tracking control method for an underactuated unmanned vessel based on a disturbance observer according to claim 1, characterized in that: Step S4 is as follows: S41. Define the Lyapunov function as: S42. According to step S41, derive V to obtain: S43. Substitute the control law and adaptive law into the equation to obtain: S44. Due to Then there is make Then we have: S45, according to Then we get: Combining step S43 and step S45, we obtain: S46. Due to: Thus we get: S47. According to the output restricted lemma: for k b >0, if the formula satisfies Then we have: Thus we can get: S48. According to steps S46 and S47, the following is obtained: S49. Considering the control law updated by the event triggering mechanism based on the time-varying threshold, we obtain: S410, due to There is u e ω u ≤0, r e ω r ≤0, we get: Since |φ2ρ|≤ρ, and 1-δ≤|1+φ1δ|, we have: S411. According to steps S49 and S410, the following is obtained: S412, due to q 1u >0,q 1r >0, according to the lemma: for any unknown real variable e, there exists a constant n that satisfies the following inequality Then we get: in, and It is q 1u ,q 1u The upper bound of , so we get: Among them, C>0, D>0, and satisfy: in, S413. According to step S412, obtain Therefore, according to Lyapunov stability theory, all signals in the entire closed-loop system are ultimately bounded, and the tracking error of the system can converge to a smaller residual set.

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