Under-actuated unmanned ship trajectory tracking control method based on preset time error constraint

Abstract

The invention discloses an under-actuated unmanned ship trajectory tracking control method based on preset time error constraint. The method comprises the following steps: acquiring a three-degree-of-freedom kinematics and dynamics model of an actual underactuated unmanned ship; determining a position tracking error and an azimuth angle tracking error between the underactuated unmanned ship and the reference trajectory; designing a preset time virtual control law; setting a longitudinal speed error and a yawing angular speed error of the underactuated unmanned ship; and designing a time-varying gain auxiliary dynamic system, and designing a preset time controller by using an adaptive self-organizing neural network. According to the invention, through the asymmetric preset performance function constraint error, the self-organizing neural network dynamic approximation disturbance and the model uncertainty, the preset time filter suppression differential explosion and the auxiliary dynamic system compensation input saturation, the high-precision trajectory tracking in the preset time is realized; the method has the advantages of controllable convergence time, unconstrained initial error and high calculation efficiency, and is suitable for autonomous navigation of the underactuated unmanned ship in a complex marine environment.

Description

Technical Field

[0001] The present invention relates to the technical field of trajectory tracking control of underactuated unmanned surface vehicles, and specifically relates to a trajectory tracking control method for underactuated unmanned surface vehicles based on a preset time error constraint. Background Art

[0002] In ocean exploration and development, underactuated unmanned surface vehicles are widely used due to advantages such as simple structure and low cost. However, they achieve three-degree-of-freedom motion only through limited control inputs (such as propellers and rudders), resulting in a highly coupled model, and trajectory tracking control faces the following challenges:

[0003] (1) Input saturation limitation: When the control signal reaches the limit of the actuator, the tracking error increases, affecting stability.

[0004] (2) External disturbances and model uncertainties: Environmental disturbances such as water currents, wind and waves, and nonlinear dynamic characteristics lead to a decrease in control accuracy.

[0005] (3) Initial error constraint and convergence time dependence problems: Existing preset performance control methods need to strictly limit the initial error, and finite-time / fixed-time convergence has problems such as initial state dependence or parameter sensitivity.

[0006] (4) Differential explosion: The derivative of the virtual control law is prone to cause a sharp increase in computational complexity.

[0007] In summary, in the prior art, although the neural network-based controller can approximate the nonlinear system, it does not combine the preset time theory and the dynamic structure adjustment mechanism, and lacks an effective compensation method for input saturation and asymmetric error constraints. Summary of the Invention

[0008] Aiming at the above deficiencies in the prior art, the trajectory tracking control method for underactuated unmanned surface vehicles based on a preset time error constraint provided by the present invention can solve the problems of input saturation, external disturbances, model uncertainties, differential explosion, and uncontrollable convergence time, and at the same time eliminate the strict constraint on the initial error and achieve asymmetric preset performance tracking.

[0009] In order to achieve the above invention object, the technical solution adopted by the present invention is:

[0010] A trajectory tracking control method for underactuated unmanned surface vehicles based on a preset time error constraint, comprising the following steps:

[0011] S1. Establish a three-degree-of-freedom kinematic and dynamic model of the underactuated unmanned surface vehicle, and decouple it through coordinate transformation to obtain the actual three-degree-of-freedom kinematic and dynamic model of the underactuated unmanned surface vehicle;

[0012] S2. Based on the three-degree-of-freedom kinematic and dynamic models of the underactuated unmanned surface vehicle (USV) in reality, determine the position tracking error and the yaw angle tracking error between the underactuated USV and the reference trajectory;

[0013] S3. Based on the position tracking error and the yaw angle tracking error between the underactuated USV and the reference trajectory, design an asymmetric preset performance function, construct a barrier Lyapunov function through error mapping, so as to design a preset-time virtual control law;

[0014] S4. Based on the preset-time virtual control law, construct a preset-time filter, obtain the filtered output, and set the longitudinal velocity error and the yaw angular velocity error of the underactuated USV according to the filtered output;

[0015] S5. Based on the longitudinal velocity error and the yaw angular velocity error of the underactuated USV, design a time-varying gain auxiliary dynamic system, and based on the time-varying gain auxiliary dynamic system and the three-degree-of-freedom kinematic and dynamic models of the underactuated USV in reality, design a preset-time controller by using an adaptive self-organizing neural network, so as to conduct trajectory tracking control on the underactuated USV.

[0016] Further, in step S1, the three-degree-of-freedom kinematic and dynamic models of the underactuated USV after coordinate transformation are expressed as:

[0017]

[0018] Where: (x 1 , y 1 ) are the actual position coordinates of the underactuated USV, is the yaw angle of the underactuated USV, u is the longitudinal velocity of the underactuated USV, v 1 is the actual sway velocity of the underactuated USV, r is the yaw angular velocity of the underactuated USV, f u , f v and f r are all unknown dynamic terms of the underactuated USV, d u is the external environmental disturbance corresponding to the longitudinal velocity, d v is the external environmental disturbance corresponding to the sway velocity, d r is the external environmental disturbance corresponding to the yaw angular velocity, τ u1 = Υ u τ fu , τ r1 = Υ r τ fr , τ fu and τ fr are the actual control inputs corresponding to the longitudinal velocity and the yaw angular velocity respectively, Υ u = 1 / m 11 , Υ r = m22 / (m 22 m 33 -m 32 m 23 ),m 11 =m - X du ,m 22 =m - Y dv ,m 23 =mx g -Y dr ,m 32 =mx g -Y dr ,m 33 =I z -N dr , where m is the mass of the underactuated unmanned surface vehicle, x g is the longitudinal position of the center of gravity of the underactuated unmanned surface vehicle, X du is the acceleration coefficient of the longitudinal component force in the x-axis direction of motion, Y dv and Y dr are the acceleration coefficients of the lateral component force in the y-axis direction of motion and the acceleration coefficient of rotation about the z-axis direction respectively, I z is the moment of inertia of the underactuated unmanned surface vehicle about the z-axis, N dr is the acceleration coefficient of the yaw moment about the z-axis direction of rotation.

[0019] Furthermore, step S2 includes the following steps:

[0020] S21. Based on the three-degree-of-freedom kinematic and dynamic model of the actual underactuated unmanned surface vehicle, calculate the tracking error between the underactuated unmanned surface vehicle and the reference trajectory, expressed as:

[0021]

[0022] where: (x d , y d ) is the ideal position coordinate of the underactuated unmanned surface vehicle, (x 1 , y 1 ) is the actual position coordinate of the underactuated unmanned surface vehicle;

[0023] S22. According to the tracking error between the underactuated unmanned surface vehicle and the reference trajectory, determine the position tracking error between the underactuated unmanned surface vehicle and the reference trajectory, expressed as:

[0024] Y e =E - ι,

[0025]

[0026] where: Y eLet \(e_p\) be the position tracking error between the underactuated unmanned surface vehicle (USV) and the reference trajectory, \(E\) be the line-of-sight error between the underactuated USV and the reference trajectory, and \(\iota\) be a designed positive threshold parameter;

[0027] S23. Determine the azimuth tracking error between the underactuated USV and the reference trajectory according to the tracking error between the underactuated USV and the reference trajectory, which is expressed as:

[0028]

[0029] where: \(e_{\psi}\) is the azimuth tracking error between the underactuated USV and the reference trajectory, \(\psi\) is the yaw angle of the underactuated USV.

[0030] Furthermore, step S3 includes the following steps:

[0031] S31. Determine the performance constraint conditions of the controller based on the position tracking error and the azimuth tracking error between the underactuated USV and the reference trajectory, which is expressed as:

[0032]

[0033] where: \(\varPsi\) dj and \(\varPsi\) uj , \(j = 1, 2\) is a new type of ln-type performance function, \(t\) is time, \(Y\) e is the position tracking error between the underactuated USV and the reference trajectory, \(e_{\psi}\) is the azimuth tracking error between the underactuated USV and the reference trajectory;

[0034] S32. Design an asymmetric preset performance function based on the performance constraint conditions of the controller, which is expressed as:

[0035]

[0036] where: and \(\gamma\) j are two positive constants, \(\xi\in(0, 1]\) is a tuning function, specifically a smooth and monotonically decreasing function, is a constant, \(T\) c > 0 is a preset convergence time;

[0037] S33. Based on the asymmetric preset performance function, the position tracking error and the azimuth tracking error between the underactuated USV and the reference trajectory, construct a barrier Lyapunov function through error mapping to design a preset-time virtual control law, which is expressed as:

[0038]

[0039] where: \(\alpha\) uis the virtual control rate in the longitudinal velocity direction, α r is the virtual control rate in the yaw angular velocity direction, is the constructed obstacle Lyapunov function, η k is the transformation function, (x d , y d ) are the ideal position coordinates of the underactuated unmanned surface vehicle, is the ideal yaw angle of the underactuated unmanned surface vehicle, v 1 is the actual sway velocity of the underactuated unmanned surface vehicle, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, ξ ∈ (0, 1] is the tuning function, specifically a smooth and monotonically decreasing function, c 1 > 2, c 2 > 2, κ 1 and κ 2 are both positive constants, μ k and are two computable and realizable variables in the controller design, is a new type of time-varying scaling transformation function, E is the line-of-sight error between the underactuated unmanned surface vehicle and the reference trajectory.

[0040] Furthermore, in step S4, a preset-time filter is constructed based on the preset-time virtual control law, expressed as:

[0041]

[0042] where: α fu and α fr are the filtering outputs of the preset-time filters in the longitudinal velocity direction and the yaw angular velocity direction respectively, m 1 , n 1 , m 2 , n 2 are all positive constants, and m 1 ≥ 2, m 2 ≥ 2, is a new type of time-varying scaling transformation function, α u is the virtual control rate in the longitudinal velocity direction, α r is the virtual control rate in the yaw angular velocity direction, ξ ∈ (0, 1] is the tuning function, specifically a smooth and monotonically decreasing function, μ k and are two computable and realizable variables in the controller design, is the constructed new obstacle function, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory.

[0043] Furthermore, in step S4, the longitudinal velocity error and yaw angular velocity error of the underactuated unmanned surface vehicle are set according to the filter output, expressed as:

[0044]

[0045] where: z 1 is the longitudinal velocity error of the underactuated unmanned surface vehicle, z 2 is the yaw angular velocity error of the underactuated unmanned surface vehicle, u is the longitudinal velocity of the underactuated unmanned surface vehicle, r is the yaw angular velocity of the underactuated unmanned surface vehicle, α fu , α fr are the filter outputs of the preset time filter.

[0046] Furthermore, in step S5, a time-varying gain auxiliary dynamic system is designed based on the longitudinal velocity error and yaw angular velocity error of the underactuated unmanned surface vehicle, including the following steps:

[0047] A1. Establish a model for the input saturation problem of the underactuated unmanned surface vehicle, expressed as:

[0048]

[0049] where: τ fi is the control input after saturation processing, sat(·) is the value after input saturation processing, τ i is the original control input designed, τ im represents the torque, whose boundaries are known and specified, sign(·) is the sign function;

[0050] A2. Based on the input saturation problem model of the underactuated unmanned surface vehicle and the longitudinal velocity error and yaw angular velocity error of the underactuated unmanned surface vehicle, design a time-varying gain auxiliary dynamic system, expressed as:

[0051]

[0052] where: θ i is the state of the time-varying gain auxiliary dynamic system, K θ , K i and C i ≥2 are all positive constants, and σ > 0 is a very small positive constant, z 1 is the longitudinal velocity error of the underactuated unmanned surface vehicle, z 2 is the yaw angular velocity error of the underactuated unmanned surface vehicle, Δτ i = τ fi - τ i , τ fi is the control input after saturation processing, τ i is the original control input designed, £(t) is a new type of time-varying scaling transformation function.

[0053] Further, in step S5, based on the time-varying gain-assisted dynamic system and the three-degree-of-freedom kinematic and dynamic models of the actual underactuated unmanned surface vehicle, a preset-time controller is designed using an adaptive self-organizing neural network, including the following steps:

[0054] B1. Design an initial preset-time controller based on the time-varying gain-assisted dynamic system and the three-degree-of-freedom kinematic and dynamic models of the actual underactuated unmanned surface vehicle;

[0055] B2. Use the adaptive self-organizing neural network to predict the comprehensive uncertainty term composed of model uncertainty and external environmental disturbances, expressed as:

[0056]

[0057] where: F u and F r are the comprehensive uncertainty terms composed of model uncertainty and external environmental disturbances in the longitudinal velocity direction and the yaw angular velocity direction, respectively. W u and W r are the ideal weights of the adaptive self-organizing neural network, Z u and Z r are the basis functions of the adaptive self-organizing neural network, X u = [u, α u T and X r = [r, α r T are the inputs of the neural network, and the approximation errors ε u ∈ R and ε r ∈ R satisfy

[0058] B3. Improve the initial preset-time controller using the comprehensive uncertainty term composed of model uncertainty and external environmental disturbances to design the preset-time controller, expressed as:

[0059]

[0060] where: i = u, r, τ i is the designed original control input, Ρ u = 1 / Υ u , Ρ r = 1 / Υ r , θ i is the state of the time-varying gain-assisted dynamic system, α fu and α fr are the filtered outputs of the preset-time filter, K θ is a positive constant, κ 3 , κ​​4 , c 3 ≥ 2 and c 4 ≥ 2 are both positive constants, z 1 is the longitudinal velocity error of the underactuated unmanned surface vehicle, z 2 is the yaw angular velocity error of the underactuated unmanned surface vehicle, ξ ∈ (0, 1] is the tuning function, specifically a smooth and monotonically decreasing function, μ k and are two computable and realizable variables in the controller design, is the constructed barrier Lyapunov function, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory.

[0061] Furthermore, in step B2, the adaptation law of the adaptive self-organizing neural network is designed as:

[0062]

[0063] where: are all positive constants.

[0064] The beneficial effects of the present invention are as follows:

[0065] (1) In this paper, the influence brought by input saturation is compensated by constructing a preset-time auxiliary dynamic system with time-varying gain;

[0066] (2) The present invention designs a preset-time self-organizing neural network to approximate the comprehensive uncertain terms composed of external environmental disturbances and model uncertainties. According to the different neuron activation effects, the self-organizing neural network can increase or decrease the number of neurons when approximating the function, thereby saving resources while obtaining the best results and improving the control performance of the system;

[0067] (3) The present invention proposes a novel asymmetric preset performance control method, which can not only achieve asymmetric constraints on the tracking error, but also eliminate the constraints on the initial tracking error, thereby improving the practical application degree of the preset performance control. And the present invention adopts the preset-time control theory to make the system state reach stability or specified performance within a predetermined time, and can meet the requirements of real-time control in a complex dynamic environment without relying on the initial conditions;

[0068] (4) The present invention introduces a preset-time filter to calculate the derivative of the virtual control law, which reduces the computational burden compared with the traditional first-order filter and avoids the problem of differential explosion. Description of the Drawings

[0069] Figure 1Schematic diagram of the trajectory tracking control method for an underactuated unmanned surface vehicle based on a preset time error constraint;

[0070] Figure 2 Schematic diagram of the self-organizing neural network algorithm;

[0071] Figure 3 Schematic diagram of the control flow of the present invention;

[0072] Figure 4 Schematic diagram of the trajectory tracking of an underactuated unmanned surface vehicle (USV);

[0073] Figure 5 Schematic diagram of the position tracking error;

[0074] Figure 6 Schematic diagram of the angle tracking error;

[0075] Figure 7 Schematic diagram of the number of neurons in the adaptive self-organizing neural network of the longitudinal speed of an underactuated unmanned surface vehicle;

[0076] Figure 8 Schematic diagram of the number of neurons in the adaptive self-organizing neural network of the yaw angular velocity of an underactuated unmanned surface vehicle;

[0077] Figure 9 Schematic diagram of the control input of the longitudinal speed of an underactuated unmanned surface vehicle;

[0078] Figure 10 Schematic diagram of the control input of the yaw angular velocity of an underactuated unmanned surface vehicle. Detailed implementation manners

[0079] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0080] As Figure 1 shown, the trajectory tracking control method for an underactuated unmanned surface vehicle based on a preset time error constraint includes steps S1 - S5, which are specifically as follows:

[0081] The trajectory tracking control method for an underactuated unmanned surface vehicle based on a preset time error constraint includes the following steps:

[0082] S1. Establish a three-degree-of-freedom kinematic and dynamic model of the underactuated unmanned surface vehicle, and decouple it through coordinate transformation to obtain the actual three-degree-of-freedom kinematic and dynamic model of the underactuated unmanned surface vehicle.

[0083] In an alternative embodiment of the present invention, the three-degree-of-freedom kinematic and dynamic models of the underactuated unmanned surface vehicle after coordinate transformation are expressed as:

[0084]

[0085] Where: (x 1 , y 1 ) are the actual position coordinates of the underactuated unmanned surface vehicle, is the yaw angle of the underactuated unmanned surface vehicle, u is the longitudinal speed of the underactuated unmanned surface vehicle, v 1 is the actual sway speed of the underactuated unmanned surface vehicle, r is the yaw angular velocity of the underactuated unmanned surface vehicle, f u , f v and f r are all unknown dynamic terms of the underactuated unmanned surface vehicle, d u is the external environmental disturbance corresponding to the longitudinal speed, d v is the external environmental disturbance corresponding to the sway speed, d r is the external environmental disturbance corresponding to the yaw angular velocity, τ u1 = Υ u τ fu , τ r1 = Υ r τ fr , τ fu and τ fr are the actual control inputs corresponding to the longitudinal speed and the yaw angular velocity respectively, Υ u = 1 / m 11 , Υ r = m 22 / (m 22 m 33 - m 32 m 23 ), m 11 = m - X du , m 22 = m - Y dv , m 23 = mx g - Y dr , m 32 = mx g - Y dr , m 33 = I z - N dr , m is the mass of the underactuated unmanned surface vehicle, x g is the longitudinal position of the center of gravity of the underactuated unmanned surface vehicle, X du is the acceleration coefficient of the longitudinal component force in the x-axis direction of motion, Y dv and Y drThey are the acceleration coefficients of the lateral component force in the y-axis direction and the acceleration coefficients of rotation in the z-axis direction, respectively. I z is the moment of inertia of the underactuated unmanned surface vehicle about the z-axis, N dr is the acceleration coefficient of the yaw moment in the z-axis direction.

[0086] The present invention establishes a three-degree-of-freedom kinematic and dynamic model of an underactuated unmanned surface vehicle, expressed as:

[0087]

[0088] Where: is the position vector of the underactuated unmanned surface vehicle defined in the earth-fixed frame; (x, y) and are the position coordinates and yaw angle of the underactuated unmanned surface vehicle, respectively; ν = [u, v, r] T is the velocity vector of the underactuated unmanned surface vehicle, and u, v, and r are the longitudinal velocity, sway velocity, and yaw angular velocity of the underactuated unmanned surface vehicle, respectively; Γ f = [τ fu , 0, τ fr T is the actual control input of the underactuated unmanned surface vehicle, Γ = [τ u , 0, τ r T is the control command calculated by the control system, Δτ = [Δτ u , 0, Δτ r T is the difference between Γ f and Γ, G = [G u , G v , G r T is the unknown external disturbance vector, G u is the unknown external environmental disturbance corresponding to the longitudinal velocity, G v is the unknown external environmental disturbance corresponding to the sway velocity, G r is the unknown external environmental disturbance corresponding to the yaw angular velocity, is the rotation matrix between the earth coordinate system and the hull coordinate system, is the mass inertia matrix, is the hydrodynamic damping coefficient matrix,

[0089] X u is the velocity coefficient of the longitudinal component force in the x-axis direction, is the second-order velocity coefficient of the longitudinal component force in the x-axis direction, is the third-order velocity coefficient of the longitudinal component force in the x-axis direction, Y v ​​​​is the velocity coefficient of the lateral component force with respect to the motion along the y-axis, is the second-order velocity coefficient of the lateral component force with respect to the motion along the y-axis, Y rv is the coupling coefficient of the lateral component force with respect to the rotation about the z-axis and the motion along the y-axis, Y r is the velocity coefficient of the lateral component force with respect to the rotation about the z-axis, Y vr is the coupling coefficient of the lateral component force with respect to the motion along the y-axis and the rotation about the z-axis, is the second-order velocity coefficient of the lateral component force with respect to the rotation about the z-axis, N v is the velocity coefficient of the yaw moment with respect to the motion along the y-axis, is the second-order velocity coefficient of the yaw moment with respect to the motion along the y-axis, N rv is the coupling coefficient of the yaw moment with respect to the rotation about the z-axis and the motion along the y-axis, N r is the coupling coefficient of the yaw moment with respect to the motion along the y-axis and the rotation about the z-axis, N vr is the coupling coefficient of the yaw moment with respect to the motion along the y-axis and the rotation about the z-axis, is the second-order velocity coefficient of the yaw moment with respect to the rotation about the z-axis;

[0090] represents the Coriolis centripetal matrix. Due to the strong coupling problem caused by the asymmetry of the mass inertia matrix M and the hydrodynamic damping matrix D(ν), it brings great complexity to system analysis and controller design. Therefore, to solve this problem, the present invention introduces the following coordinate transformation:

[0091]

[0092] where: l = m 23 / m 22 .

[0093] The present invention decouples the three-degree-of-freedom kinematic and dynamic models of the underactuated unmanned surface vehicle through the above coordinate transformation to obtain the actual three-degree-of-freedom kinematic and dynamic models of the underactuated unmanned surface vehicle.

[0094] In the actual three-degree-of-freedom kinematic and dynamic models of the underactuated unmanned surface vehicle,

[0095] f u = [-d 11 u + m 22 (v 1 - lr)r + m 23 r 2 / m 11 ,

[0096] f v = [-m 11 ur - d22 (v 1 -lr)-d 23 r] / m 22 ,

[0097]

[0098] d u =Υ u G u ,

[0099] d v =Υ v G v ,

[0100] Υ v =1 / m 22

[0101] S2. Based on the three - degree - of - freedom kinematic and dynamic models of the actual under - actuated unmanned surface vehicle, determine the position tracking error and the azimuth tracking error between the under - actuated unmanned surface vehicle and the reference trajectory.

[0102] In an alternative embodiment of the present invention, step S2 includes the following steps:

[0103] S21. Based on the three - degree - of - freedom kinematic and dynamic models of the actual under - actuated unmanned surface vehicle, calculate the tracking error between the under - actuated unmanned surface vehicle and the reference trajectory, expressed as:

[0104]

[0105] where: (x d ,y d ) is the ideal position coordinate of the under - actuated unmanned surface vehicle, and (x 1 ,y 1 ) is the actual position coordinate of the under - actuated unmanned surface vehicle.

[0106] S22. According to the tracking error between the under - actuated unmanned surface vehicle and the reference trajectory, determine the position tracking error between the under - actuated unmanned surface vehicle and the reference trajectory, expressed as:

[0107] Y e =E - ι,

[0108]

[0109] where: Y e is the position tracking error between the under - actuated unmanned surface vehicle and the reference trajectory, E is the line - of - sight error between the under - actuated unmanned surface vehicle and the reference trajectory, and ι is the designed positive threshold parameter.

[0110] S23. Determine the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory based on the tracking error between the underactuated unmanned surface vehicle and the reference trajectory, expressed as:

[0111]

[0112] Where: is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, is the yaw angle of the underactuated unmanned surface vehicle.

[0113] S3. Design an asymmetric preset performance function based on the position tracking error and the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, and construct a barrier Lyapunov function through error mapping to design a preset-time virtual control law.

[0114] In an alternative embodiment of the present invention, step S3 includes the following steps:

[0115] S31. Determine the performance constraint conditions of the controller based on the position tracking error and the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, expressed as:

[0116]

[0117] Where: Ψ dj and Ψ uj , j = 1, 2 is a new type of ln-type performance function, t is time, Y e is the position tracking error between the underactuated unmanned surface vehicle and the reference trajectory, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory.

[0118] S32. Design an asymmetric preset performance function based on the performance constraint conditions of the controller, expressed as:

[0119]

[0120] Where: and γ j are two positive constants, ξ ∈ (0, 1] is a tuning function, specifically a smooth and monotonically decreasing function, is a constant, T c > 0 is the preset convergence time.

[0121] S33. Based on the asymmetric preset performance function, the position tracking error and the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, construct a barrier Lyapunov function through error mapping to design a preset-time virtual control law, expressed as:

[0122]

[0123] where: α u is the virtual control rate in the longitudinal velocity direction, and α r is the virtual control rate in the yaw angular velocity direction, is the constructed barrier Lyapunov function, η k is the transformation function, and (x d , y d ) are the ideal position coordinates of the underactuated unmanned surface vehicle, is the ideal yaw angle of the underactuated unmanned surface vehicle, v 1 is the actual sway velocity of the underactuated unmanned surface vehicle, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, ξ ∈ (0, 1] is the tuning function, specifically a smooth monotonically decreasing function, c 1 > 2, c 2 > 2, κ 1 and κ 2 are both positive constants, μ k and are two computable and realizable variables in the controller design, is a new type of time-varying scaling transformation function, and E is the line-of-sight error between the underactuated unmanned surface vehicle and the reference trajectory.

[0124] Based on the asymmetric preset performance function, the position tracking error and the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory, the present invention constructs a barrier Lyapunov function through error mapping, specifically:

[0125] C1. Construct the transformation function, expressed as:

[0126]

[0127] where:

[0128] C2. Perform barrier error transformation on the transformation function to obtain the intermediate variable of the barrier Lyapunov function, expressed as:

[0129]

[0130] where: χ k is the intermediate variable of the barrier Lyapunov function. If the boundedness of is ensured, then χ k will strictly converge to the set

[0131] C3. Construct the barrier Lyapunov function according to the intermediate variable of the barrier Lyapunov function, expressed as:

[0132]

[0133] Wherein:

[0134] S4. Construct a preset-time filter based on a preset-time virtual control law, obtain the filtered output, and set the longitudinal velocity error and yaw angular velocity error of the underactuated unmanned surface vehicle according to the filtered output.

[0135] In an alternative embodiment of the present invention, the present invention constructs a preset-time filter based on a preset-time virtual control law, which is expressed as:

[0136]

[0137] Wherein: α fu and α fr are respectively the filtered outputs of the preset-time filters in the longitudinal velocity direction and the yaw angular velocity direction, m 1 , n 1 , m 2 , n 2 are all positive constants, and m 1 ≥2, m 2 ≥2, is a new type of time-varying scaling transformation function, α u is the virtual control law in the longitudinal velocity direction, α r is the virtual control law in the yaw angular velocity direction, ξ∈(0, 1] is a tuning function, specifically a smooth and monotonically decreasing function, μ k and are two computable and realizable variables in the controller design, is the newly constructed barrier function, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory.

[0138] The present invention sets the longitudinal velocity error and yaw angular velocity error of the underactuated unmanned surface vehicle according to the filtered output, which is expressed as:

[0139]

[0140] Wherein: z 1 is the longitudinal velocity error of the underactuated unmanned surface vehicle, z 2 is the yaw angular velocity error of the underactuated unmanned surface vehicle, u is the longitudinal velocity of the underactuated unmanned surface vehicle, r is the yaw angular velocity of the underactuated unmanned surface vehicle, α fu , α fr are the filtered outputs of the preset-time filter.

[0141] S5. Design a time-varying gain auxiliary dynamic system based on the longitudinal velocity error and yaw angular velocity error of the underactuated unmanned surface vehicle (USV), and design a preset-time controller using an adaptive self-organizing neural network based on the time-varying gain auxiliary dynamic system and the three-degree-of-freedom kinematic and dynamic models of the actual underactuated USV to perform trajectory tracking control on the underactuated USV.

[0142] In an alternative embodiment of the present invention, the present invention designs a time-varying gain auxiliary dynamic system based on the longitudinal velocity error and yaw angular velocity error of the underactuated USV, including the following steps:

[0143] A1. Establish a model for the input saturation problem of the underactuated USV, expressed as:

[0144]

[0145] where: τ fi is the control input after saturation processing, sat(·) is the value after input saturation processing, τ i is the original control input designed, τ im represents the torque, whose boundary is known and specified, and sign(·) is the sign function.

[0146] The calculation method of the sign function is as follows:

[0147]

[0148] A2. Design a time-varying gain auxiliary dynamic system based on the input saturation problem model of the underactuated USV and the longitudinal velocity error and yaw angular velocity error of the underactuated USV, expressed as:

[0149]

[0150] where: θ i is the state of the time-varying gain auxiliary dynamic system, K θ , K i and C i ≥2 are all positive constants, and σ > 0 is a very small positive constant, z 1 is the longitudinal velocity error of the underactuated USV, z 2 is the yaw angular velocity error of the underactuated USV, Δτ i = τ fi -τ i , τ fi is the control input after saturation processing, τ i is the original control input designed, is a new type of time-varying scaling transformation function.

[0151] Based on the time-varying gain-assisted dynamic system and the three-degree-of-freedom kinematic and dynamic models of an actual underactuated unmanned surface vehicle, an initial preset-time controller is designed by using an adaptive self-organizing neural network, including the following steps:

[0152] B1. Based on the time-varying gain-assisted dynamic system and the three-degree-of-freedom kinematic and dynamic models of an actual underactuated unmanned surface vehicle, design an initial preset-time controller.

[0153] Step B1 includes the following steps:

[0154] B11. Differentiate the formulas for the longitudinal velocity error and the yaw angular velocity error of the underactuated unmanned surface vehicle, and substitute the differentiation results into the three-degree-of-freedom kinematic and dynamic models of the actual underactuated unmanned surface vehicle to obtain a first intermediate relational expression, expressed as:

[0155]

[0156] B12. Construct a Lyapunov function relational expression, expressed as:

[0157]

[0158] Where: Ρ u = 1 / Υ u , Ρ r = 1 / Υ r .

[0159] B13. Differentiate the Lyapunov function relational expression to obtain the derivative expression of the Lyapunov function. Combine it with the three-degree-of-freedom kinematic and dynamic models of the actual underactuated unmanned surface vehicle, and substitute the first intermediate relational expression into the derivative expression of the Lyapunov function to obtain a transformed expression of the derivative expression of the Lyapunov function, expressed as:

[0160]

[0161] Where: F u , F r are the comprehensive uncertain terms composed of model uncertainties and external environmental disturbances in the longitudinal velocity direction and the yaw angular velocity direction respectively, F u = f u + d u , F r = f r + d r .

[0162] B14. Based on the time-varying gain-assisted dynamic system and the transformed expression of the derivative expression of the Lyapunov function, design an initial preset-time controller, expressed as:

[0163]

[0164] where: i = u, r, τ i is the original control input of the design, Ρ u = 1 / Υ u , Ρ r = 1 / Υ r , F u 、F r are the comprehensive uncertainty terms composed of model uncertainty and external environmental disturbances in the longitudinal velocity direction and the yaw angular velocity direction respectively, θ i is the state of the time-varying gain auxiliary dynamic system, α fu 、α fr are the filtering outputs of the preset time filter, K θ is a positive constant, κ 3 , κ 4 , c 3 ≥ 2 and c 4 ≥ 2 are both positive constants, z 1 is the longitudinal velocity error of the underactuated unmanned surface vehicle, z 2 is the yaw angular velocity error of the underactuated unmanned surface vehicle, ξ ∈ (0, 1] is the tuning function, specifically a smooth and monotonically decreasing function, μ k and are two computable and realizable variables in the controller design, is the constructed barrier Lyapunov function, is the azimuth tracking error between the underactuated unmanned surface vehicle and the reference trajectory.

[0165] B2. Use an adaptive self-organizing neural network to predict the comprehensive uncertainty term composed of model uncertainty and external environmental disturbances, expressed as:

[0166]

[0167] where: F u 、F r are the comprehensive uncertainty terms composed of model uncertainty and external environmental disturbances in the longitudinal velocity direction and the yaw angular velocity direction respectively, W u and W r are the ideal weights of the adaptive self-organizing neural network, Z u and Z r are the basis functions of the adaptive self-organizing neural network, X u = [u, α u T and X r = [r, α r T are the inputs of the neural network, the approximation error ε​​u ∈R and ε r ∈R satisfies

[0168] The adaptation law of the adaptive self - organizing neural network is designed as:

[0169]

[0170] Where: are all positive constants.

[0171] B3. Improve the initial preset - time controller by using the comprehensive uncertainty term composed of model uncertainty and external environmental disturbance to design the preset - time controller, expressed as:

[0172]

[0173] Where: i = u, r, τ i is the original control input designed, Ρ u = 1 / Υ u , Ρ r = 1 / Υ r , θ i is the state of the time - varying gain auxiliary dynamic system, α fu , α fr are the filtering outputs of the preset - time filter, K θ is a positive constant, κ 3 , κ 4 , c 3 ≥2 and c 4 ≥2 are both positive constants, z 1 is the longitudinal velocity error of the under - actuated unmanned surface vehicle, z 2 is the yaw angular velocity error of the under - actuated unmanned surface vehicle, ξ∈(0, 1] is the tuning function, specifically a smooth and monotonically decreasing function, μ k and are two computable and realizable variables in the controller design, is the constructed barrier Lyapunov function, is the azimuth tracking error between the under - actuated unmanned surface vehicle and the reference trajectory.

[0174] To verify the effectiveness of the method of the present invention, simulation experiments were carried out as follows:

[0175] The ideal reference trajectory of the under - actuated unmanned surface vehicle is: x d = 60sin(0.04t), y d = 60sin(0.02t); The initial position of the under - actuated unmanned surface vehicle η(0)=[-2.4, 2.2, 0] T, the initial velocity ν(0) = [0, 0, 0] T . In addition, in order to better simulate the real - environment situation, the present invention designs the external - environment disturbance as: d u = - 10 - 6cos(0.5t)cos(t)+4cos(0.5t)sin(0.5t), d v = 5sin(0.1t) and d r = 8sin(1.1t)cos(0.3t). The relevant parameters of the input saturation are: τ um = 500N, τ rm = 50N·m. The relevant parameters of the adaptive self - organizing neural network are: p u = 20, p r = 12, q u = 20, q r = 12, The adaptive self - organizing neural network is designed with 43 neurons, and the center spacing is c u = [- 126, 126], c r = [- 3.36, 3.36]; the width b u = b r = 25; the splitting threshold is: P dvu = 0.99, P dvr = 0.4; the deletion threshold is: P deu = 0.2, P der = 0.92.

[0176] The model parameters are shown in Table 1:

[0177] Table 1 Model parameters

[0178]

[0179] The control parameters are shown in Table 2:

[0180] Table 2 Control - system parameters

[0181]

[0182] For the convenience of understanding, the present invention Figure 2 shows the principle of the adaptive self - organizing neural - network algorithm, Figure 3 and shows the entire control process. Figure 4 is the trajectory - tracking effect diagram of the under - actuated unmanned surface vehicle. It can be seen that the under - actuated unmanned surface vehicle can track the ideal trajectory well, and the motion trajectory is relatively smooth. Figure 5 and Figure 6 are respectively the position - tracking error Y of the under - actuated unmanned surface vehicle e and the angle - tracking error The convergence effect diagrams under the constraints of the preset performance function show that they all converge before the predetermined time T c = 15 s, and are all within the constraint range of the preset performance function, with small error fluctuations and high precision. In addition, from the Figure 5 and Figure 6 partial enlarged views, it can be seen that the initial value of the preset performance function is unbounded, thus eliminating the constraint on the initial value of the tracking error. Figure 7 and Figure 8 show that the number of neurons in the adaptive self-organizing neural network can be adjusted in real time, effectively reducing the computational burden of the neural network, and the number of neurons in F u and F r stabilizes at 11 and 36 respectively. Figure 9 and Figure 10 show that under the compensation of the time-varying gain assisted dynamic system, the control input is constrained within the specified boundary and remains convergent, indicating that the control method provided by the present invention has high stability.

[0183] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention according to these technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A trajectory tracking control method for an underactuated unmanned vehicle based on a preset time error constraint, characterized in that: The following steps are involved: S1. Establish a three-degree-of-freedom kinematic and dynamic model of the underactuated unmanned vehicle, and decouple it through coordinate transformation to obtain the actual three-degree-of-freedom kinematic and dynamic model of the underactuated unmanned vehicle; S2. Based on the actual three-degree-of-freedom kinematics and dynamics model of the underactuated unmanned vehicle, determine the position tracking error and azimuth tracking error between the underactuated unmanned vehicle and the reference trajectory; S3. Based on the position tracking error and azimuth tracking error between the underactuated unmanned boat and the reference trajectory, an asymmetric preset performance function is designed, and an obstacle Lyapunov function is constructed through error mapping to design a preset time virtual control law; S4. constructing a preset time filter based on a preset time virtual control law, obtaining a filter output, and setting a longitudinal velocity error and a bow angular velocity error of the underactuated unmanned boat according to the filter output; S5. Based on the longitudinal velocity error and bow angular velocity error of the under-actuated unmanned boat, a time-varying gain assisted dynamic system is designed. Based on the time-varying gain assisted dynamic system and the actual three-degree-of-freedom kinematics and dynamics model of the under-actuated unmanned boat, a preset time controller is designed using an adaptive self-organizing neural network to perform trajectory tracking control on the under-actuated unmanned boat.

2. The trajectory tracking control method of an underactuated unmanned vehicle based on a preset time error constraint according to claim 1, characterized in that: In step S1, the three-degree-of-freedom kinematics and dynamics model of the underactuated unmanned vehicle after coordinate transformation is expressed as: Where: (x1, y1) is the actual position coordinate of the underactuated unmanned boat, is the yaw angle of the underactuated unmanned boat, u is the longitudinal velocity of the underactuated unmanned boat, v1 is the actual sway velocity of the underactuated unmanned boat, r is the bow angular velocity of the underactuated unmanned boat, and f u , f v and f r are the unknown dynamic terms of the underactuated unmanned vehicle, d u is the external environmental disturbance corresponding to the longitudinal velocity, d v is the external environmental disturbance corresponding to the sway velocity, d r is the external environmental disturbance corresponding to the yaw angular velocity, τ u1 =Y u τ fu , τ r1 =Y r τ fr , τ fu and τ fr are the actual control inputs corresponding to the longitudinal velocity and the yaw angular velocity, respectively. u =1 / m 11 , Υ r =m 22 / (m 22 m 33 -m 32 m 23 ), m 11 =mX du , m 22 =mY dv , m 23 =mx g -Y dr , m 32 =mx g -Y dr , m 33 =I z -N dr , m is the mass of the underactuated unmanned boat, x g is the longitudinal position of the center of gravity of the underactuated unmanned vehicle, X du is the acceleration coefficient of the longitudinal force about the x-axis direction, Y dv and Y dr are the acceleration coefficient of the lateral force about the y-axis and the acceleration coefficient of the rotation about the z-axis, I z is the inertia moment of the underactuated unmanned vehicle about the z-axis, N dr is the acceleration coefficient of the yaw moment about the z-axis.

3. The trajectory tracking control method of an underactuated unmanned vehicle based on a preset time error constraint according to claim 1, characterized in that: Step S2 includes the following steps: S21. Based on the actual three-degree-of-freedom kinematics and dynamics model of the underactuated unmanned vehicle, the tracking error between the underactuated unmanned vehicle and the reference trajectory is calculated and expressed as: Where: (x d ,y d ) is the ideal position coordinate of the underactuated unmanned vehicle, (x1, y1) is the actual position coordinate of the underactuated unmanned vehicle; S22, according to the tracking error between the underactuated unmanned boat and the reference trajectory, determine the position tracking error between the underactuated unmanned boat and the reference trajectory, expressed as: Y e =E-i, Where: Y e is the position tracking error between the underactuated unmanned vehicle and the reference trajectory, E is the line-of-sight error between the underactuated unmanned vehicle and the reference trajectory, and ι is the designed positive threshold parameter; S23, according to the tracking error between the under-actuated unmanned boat and the reference trajectory, determine the azimuth tracking error between the under-actuated unmanned boat and the reference trajectory, expressed as: in: is the azimuth tracking error between the underactuated unmanned vehicle and the reference trajectory, is the yaw angle of the underactuated unmanned vehicle.

4. The trajectory tracking control method of an underactuated unmanned vehicle based on a preset time error constraint according to claim 1, characterized in that: Step S3 includes the following steps: S31. Based on the position tracking error and azimuth tracking error between the underactuated unmanned boat and the reference trajectory, determine the performance constraint of the controller, which is expressed as: Among them: dj and uj , j = 1, 2 is a new type of ln-type performance function, t is time, Y e is the position tracking error between the underactuated unmanned vehicle and the reference trajectory, is the azimuth tracking error between the underactuated unmanned vehicle and the reference trajectory; S32. Based on the performance constraints of the controller, an asymmetric preset performance function is designed, which is expressed as: in: and are two positive constants, ξ∈(0,1] is a tuning function, specifically a smooth monotonically decreasing function, 0<ζ<1 is a constant, T c >0 is the preset convergence time; S33, based on the asymmetric preset performance function, the position tracking error and azimuth tracking error between the underactuated unmanned boat and the reference trajectory, an obstacle Lyapunov function is constructed through error mapping to design a preset time virtual control law, which is expressed as: Where: α u is the virtual control rate in the longitudinal speed direction, α r is the virtual control rate in the direction of the yaw angular velocity, is the barrier Lyapunov function constructed, η k is the transformation function, (x d ,y d ) is the ideal position coordinate of the underactuated unmanned vehicle, is the ideal yaw angle of the underactuated unmanned boat, v1 is the actual sway speed of the underactuated unmanned boat, is the azimuth tracking error between the underactuated unmanned vehicle and the reference trajectory, ξ∈(0,1] is the tuning function, specifically a smooth monotonically decreasing function, c1>2, c2>2, κ1 and κ2 are both positive constants, μ k and are two computable and realizable variables in controller design, is a new type of time-varying scaling transformation function, and E is the line-of-sight error between the underactuated unmanned vehicle and the reference trajectory.

5. The trajectory tracking control method of an underactuated unmanned vehicle based on a preset time error constraint according to claim 1, characterized in that: In step S4, a preset time filter is constructed based on the preset time virtual control law, which is expressed as: Where: α fu and α fr are the filter outputs of the preset time filters in the longitudinal velocity direction and the yaw angular velocity direction, respectively. m1, n1, m2, n2 are all positive constants, and m1≥2, m2≥2, is a new type of time-varying scaling function, α u is the virtual control rate in the longitudinal speed direction, α r is the virtual control rate in the direction of the yaw angular velocity, ξ∈(0,1] is the tuning function, specifically a smooth monotonically decreasing function, μ k and are two computable and realizable variables in controller design, is the new barrier function constructed, is the azimuth tracking error between the underactuated unmanned vehicle and the reference trajectory.

6. The trajectory tracking control method of an underactuated unmanned vehicle based on a preset time error constraint according to claim 1, characterized in that: In step S4, the longitudinal velocity error and the bow angular velocity error of the underactuated unmanned boat are set according to the filter output, which can be expressed as: Where: z1 is the longitudinal velocity error of the underactuated unmanned boat, z2 is the bow angular velocity error of the underactuated unmanned boat, u is the longitudinal velocity of the underactuated unmanned boat, r is the bow angular velocity of the underactuated unmanned boat, α fu , α fr It is the filtered output of the preset time filter.

7. The underactuated unmanned vehicle trajectory tracking control method based on preset time error constraints according to claim 1 is characterized in that: In step S5, a time-varying gain auxiliary dynamic system is designed based on the longitudinal velocity error and the bow angular velocity error of the underactuated unmanned boat, including the following steps: A1. Establish the input saturation problem model of underactuated unmanned boat, expressed as: Where: τ fi is the control input after saturation processing, sat(·) is the value after input saturation processing, τ i is the original control input of the design, τ im The table is the moment, whose bounds are known and specified, and sign(·) is the sign function; A2. Based on the input saturation problem model of the underactuated unmanned boat and the longitudinal velocity error and bow angular velocity error of the underactuated unmanned boat, a time-varying gain auxiliary dynamic system is designed, which can be expressed as: in: is the state of the time-varying gain-assisted dynamic system, K i and C i ≥2 are all positive numbers, and σ>0 is a very small positive number, z1 is the longitudinal velocity error of the underactuated unmanned boat, z2 is the bow angular velocity error of the underactuated unmanned boat, Δτ i =τ fi -τ i , τ fi is the saturated control input, τ i is the original control input of the design, It is a new type of time-varying scaling transformation function.

8. The trajectory tracking control method of an underactuated unmanned vehicle based on a preset time error constraint according to claim 1, characterized in that: In step S5, based on the time-varying gain auxiliary dynamic system and the actual three-degree-of-freedom kinematics and dynamics model of the underactuated unmanned boat, an adaptive self-organizing neural network is used to design a preset time controller, including the following steps: B1. Design the initial preset time controller based on the time-varying gain assisted dynamic system and the actual three-degree-of-freedom kinematics and dynamics model of the underactuated unmanned boat; B2. Use adaptive self-organizing neural network to predict the comprehensive uncertainty composed of model uncertainty and external environmental disturbance, expressed as: Among them: F u 、F r are the comprehensive uncertainties in the longitudinal velocity direction and the yaw angular velocity direction, which are composed of model uncertainty and external environmental disturbances. u and W r is the ideal weight of the adaptive self-organizing neural network, Z u and Z r is the basis function of the adaptive self-organizing neural network, X u =[u,α u ] T and X r =[r,α r ] T is the input of the neural network, the approximation error ε u ∈R and ε r ∈R satisfies B3. The initial preset time controller is improved by using the comprehensive uncertainty term composed of model uncertainty and external environmental disturbance to design the preset time controller, which is expressed as: Among them: i=u,r,τ i is the original control input of the design, u =1 / Υ u , P r =1 / Υ r , is the state of the time-varying gain auxiliary dynamic system, α fu , α fr is the filtered output of the preset time filter, is a positive constant, κ3, κ4, c3 ≥ 2 and c4 ≥ 2 are all positive constants, z1 is the longitudinal velocity error of the underactuated unmanned boat, z2 is the bow angular velocity error of the underactuated unmanned boat, ξ∈(0, 1] is a tuning function, specifically a smooth monotonically decreasing function, μ k and are two computable and realizable variables in controller design, is the barrier Lyapunov function constructed, is the azimuth tracking error between the underactuated unmanned vehicle and the reference trajectory.

9. The underactuated unmanned vehicle trajectory tracking control method based on preset time error constraints according to claim 8, characterized in that: In step B2, the adaptive law of the adaptive self-organizing neural network is designed as: in: p u ,p r ,q u >2,q r >2 is a normal number.

Images