A multi-USV event-triggered error-constrained control method considering input saturation

Abstract

A multi-USV event-triggered error constraint control method considering input saturation belongs to the field of unmanned boat control technology. In order to solve the problem that the existing control method cannot effectively cope with the state changes of multiple unmanned boats during navigation, and the problem of large deviations when controlling multiple unmanned boats in formation. The present invention first establishes the kinematic and dynamic equations of the USV for the model uncertainty, environmental interference and input saturation problems in the multi-USV collaborative control process, and uses a smooth hyperbolic tangent function to approximate the saturation function for the USV actuator, then constructs a saturated input estimation model and transforms the kinematic and dynamic equations, and uses a neural network to approximate the unknown nonlinear f of the USV. i , design the event trigger mechanism, and then design the multi-USV distributed event triggered error constraint controller based on the BLF method, and then realize the multi-USV event triggered error constraint control.

Description

Technical Field

[0001] The invention belongs to the technical field of unmanned boat control, and in particular relates to a multi-USV event triggering error constraint control method. Background Art

[0002] As an unmanned operating platform with high autonomy and flexibility, Unmanned Surface Vessel (USV) can perform various maritime tasks and play an important role in the marine field. Since a single USV has the disadvantages of small operating range, low work efficiency and low fault tolerance when performing tasks, the use of multiple USVs in collaborative operation can better adapt to complex marine environments and diversified marine operation tasks, and improve operational efficiency.

[0003] When multiple USVs perform tasks on the water surface, they are usually required to be able to track the specified trajectory to ensure that the multi-USV system maintains the formation and completes the task through collaborative control. In the actual navigation process, the actuators of the USV, such as the motor, are limited by physical conditions and cannot provide unlimited input force and torque. At this time, there is an input saturation problem. At the same time, the state of the USV will change during the navigation process. This change affects its own hydrodynamic parameters, which in turn leads to the uncertainty of its own model. In addition, the USV is susceptible to external interference such as wind, waves, and currents, which causes its navigation route to deviate from the normal route. It will also encounter special conditions such as obstacles in narrow waterways that affect the normal navigation of the USV, resulting in control failure. Therefore, constraining the trajectory of the USV is of great significance to the smooth completion of the task and ensuring the performance and safety of the system itself.

[0004] The error constraint control method is currently widely used in the field of multi-agents, but this method does not take into account the actual application scenarios of USVs and the resource waste problem of periodic communication. Therefore, the error constraint control method cannot be directly applied to the control of USVs, especially the control of multiple USVs. Summary of the invention

[0005] The present invention aims to solve the problem that the existing control method cannot effectively cope with the state changes of multiple unmanned boats during navigation, and the problem of large deviation when controlling multiple unmanned boats.

[0006] A multi-USV event-triggered error constraint control method considering input saturation is provided. For each USV in a multi-USV system, the kinematic and dynamic equations of the USV are established. The multi-USV system includes a leader and N followers. The follower USVs are numbered 1, 2, ..., N, and the leader USV is numbered 0. The communication mode of the multi-USV system is a directed communication topology.

[0007] The smooth hyperbolic tangent function is used to approximate the saturation function for the actuator of the USV; the saturation input estimation model of the i-th USV is constructed:

[0008] p i (τ i )=[p i (τ ik )]

[0009]

[0010] Use τ = [τ1, τ2, τ3] T represents the desired forces τ1, τ2 and torque τ3 acting on the USV, then τ i =[τ i1 ,τ i2 ,τ i3 ] represents the control force τ generated by the propulsion system of the i-th follower i1 ,τ i2 and torque τ i3 ; τ imax =[τ i1max ,τ i2max ,τ i3max ] T is the saturation control force τ i1max ,τ i2max and torque τ i3max The amplitude of

[0011] Based on p i (τ i ), the input saturation of the i-th follower USV is expressed as

[0012] sat(τ i )=p i (τ i )+q i (τ i ) (3)

[0013] In the formula, sat(τ i )=[sat(τ i1 ),sat(τ i2 ),sat(τ i3 )] T , sat(·) represents the saturation function; q i (τ i ) is the estimated model error for saturated input;

[0014] Based on the kinematic and dynamic equations of USV, the kinematic and dynamic equations of the i-th follower USV are transformed into

[0015]

[0016] In the formula, x i1 =η i , x i2 =v i , f i The model itself is nonlinear; is the inverse of the mass inertia matrix corresponding to the ith follower; J i is the transformation matrix between the inertial coordinate system and the motion coordinate system corresponding to the i-th follower; w i is the unknown external interference corresponding to the i-th follower;

[0017] Then design the input saturation auxiliary variable Among them, k i2 is a normal quantity, p i (τ i ) is the saturation input estimate of the i-th follower, τ i is the control force and torque generated by the propulsion system of the i-th follower;

[0018] The unknown nonlinearity f of the i-th USV is i Represented as f i =W i T φ i +ε i ;in, represents the weight matrix, represents the activation function, is the approximation error;

[0019] Then transform formula (4) into

[0020]

[0021] In the formula, x i1 =η i , η i is the η corresponding to the i-th follower, η=[x,y,ψ] T represents the position x, y and attitude ψ of USV in the inertial coordinate system; i2 =v i , v i is the v corresponding to the ith follower, v = [u, v, r] T Represents the velocity u, v and angular velocity r in the motion coordinate system; d i =ε i +w i represents the overall interference corresponding to the i-th follower;

[0022] Design the following disturbance observer:

[0023]

[0024] In the formula, δ i is the auxiliary system state quantity of the disturbance observer; k i is a positive constant; It is W i The estimated value of Yes i The estimated value of

[0025] Use RBF neural network to approximate f i , and determine the neural network estimation law as follows:

[0026]

[0027] In the formula, Λ i and β i For normal amount, is the speed compensation error, where is the speed error, compensation signal β i2 satisfy

[0028] Based on the designed disturbance observer and neural network estimation law, the USVs in the multi-USV system are controlled by using the multi-USV distributed event-triggered error constraint controller.

[0029] The multi-USV distributed event-triggered error constraint controller is designed based on a radial basis function neural network disturbance observer and an event trigger mechanism, as follows:

[0030]

[0031]

[0032] Among them, a ij is the element of the weighted adjacency matrix of the directed graph. For nodes i and j, when node j can receive information from node i, a ij =1, otherwise a ij =0; b i is the element of the communication topology matrix between the follower and the leader. If node i can receive the information from the leader, then b i =1, otherwise b i =0; η0(t) represents the trajectory of the leader USV; is the output value of the command filter; i is the input saturation auxiliary variable; m i is the event trigger mechanism parameter, 0<m i <1; is a constant;

[0033] α i1 is the virtual control law, which is expressed as

[0034]

[0035] in, k i1 , k i2 is a normal quantity; x j1 =η j , η j is the η corresponding to the jth follower, η=[x,y,ψ] T represents the position x, y and attitude ψ of USV in the inertial coordinate system; j2 =v j , v j is the v corresponding to the jth follower, v = [u, v′, r] T Represents the velocity u, v′ and angular velocity r in the motion coordinate system; adjustment parameters k bi (t)>0 is a time-varying continuous equation that is differentiable to the second order and is used to constrain the compensation of trajectory tracking error. have ι i is a positive constant; is the trajectory compensation error, is the trajectory error; β i1 is the trajectory error compensation signal, satisfying

[0036] Furthermore, the kinematic and dynamic equations of the USV are as follows:

[0037]

[0038]

[0039] Where η = [x, y, ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system, v = [u, v′, r] T represents the velocity u, v′ and angular velocity r in the motion coordinate system, J(η) is the transformation matrix between the inertial coordinate system and the motion coordinate system; M is the mass inertia matrix, C(v) is the Coriolis force and centripetal force matrix, D(v) is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T are the control forces τ1, τ2 and torque τ3 generated by the propulsion system, and w is the unknown external disturbance.

[0040] Furthermore, the input saturation of the i-th follower USV is represented as sat(τ ik )=p i (τ ik )+q i(τ ik ), the saturation function of the USV system needs to be determined; the saturation function of the USV system is as follows:

[0041]

[0042] Among them, τ1, τ2 represent the desired forces acting on the USV, τ3 represents the torque acting on the USV; τ 1max ,τ 2max ,τ 3max is the actuator amplitude; sat(τ)=[sat(τ1),sat(τ2),sat(τ3)] T is the saturated output matrix of the USV system; sign(·) represents the sign function.

[0043] Furthermore, the kinematic and dynamic equations of the i-th follower USV are transformed into When the model itself is nonlinear, f i =-C i (x i2 )x i2 -D i (x i2 )x i2 -g i (x i1 ), where C i is the Coriolis force and centripetal force matrix corresponding to the ith follower, D i is the hydrodynamic damping matrix corresponding to the i-th follower.

[0044] Furthermore, the output value of the command filter Determined by the following formula:

[0045]

[0046]

[0047] In the formula, α i1 and are the input value and output value of the command filter respectively, and satisfy h i (0) = 0; d i1 and d i2 are all normal numbers, satisfying d i1 >0,0<d i2 ≤1.

[0048] Furthermore, the event triggering mechanism corresponding to the multi-USV distributed event-triggered error constraint controller is as follows:

[0049]

[0050]

[0051] Δe′ i (t) = u i (t)-τ i (t) (15)

[0052] In the formula, is the current controller update time; is the next update time of the controller; Δe i ′(t) is the measurement error of the controller; the event trigger mechanism parameter m i The value of is 0<m i <1; n i =[n i1 ,n i2 ,n i3 ] T is a constant, satisfying n ij >0; inf represents the infimum.

[0053] Furthermore, the constant n i and constant n i Needs to be satisfied

[0054] Furthermore, in the process of designing the multi-USV distributed event-triggered error constraint controller, the exponential barrier Lyapunov function is selected to constrain the trajectory compensation error in the system to complete the design and proof process of the multi-USV distributed event-triggered error constraint controller.

[0055] Beneficial effects:

[0056] In view of the model uncertainty, environmental interference and input saturation problems in the collaborative control process of multiple USVs, the present invention proposes a distributed error constrained collaborative tracking control law for multiple USVs based on an event trigger mechanism, which can effectively cope with the state changes of multiple unmanned boats during navigation, and can effectively improve the control effect, reduce the deviation during the control of multiple unmanned boat formations, and also ensure that the trajectory error variables of the system can converge within a specified range, the event trigger time interval is greater than zero, and the system is stable and there is no Zeno behavior. It is proved that the control algorithm not only realizes the distributed error constrained tracking control of the multi-USV system, but also reduces the triggering frequency of the system, realizes the intermittent update of the controller, and thus reduces the consumption of the controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 Schematic diagram of the communication topology between the leader USV and the follower USV.

[0058] Figure 2 Tracking curve for the trajectory (angle) of the follower USV.

[0059] Figure 3 It is the error variable curve of the longitudinal swing direction of follower USV3.

[0060] Figure 4 It is the error variable curve of the follower USV3 in the sway direction.

[0061] Figure 5 This is the error variable curve of the bow roll angle of the follower USV3.

[0062] Figure 6 This is the control force curve of the follower USV3.

[0063] Figure 7 This is the control torque curve of the follower USV3.

[0064] Figure 8 The event triggering time of the follower USV.

[0065] Fig. 9 The event triggering interval for follower USV1.

[0066] Fig.10 The event triggering interval for follower USV2.

[0067] Fig.11 The event triggering interval for follower USV3.

[0068] Fig.12 The event triggering interval for the follower USV4.

[0069] Fig.13 The event triggering interval for follower USV5.

[0070] Fig.14 The event triggering interval for follower USV6. DETAILED DESCRIPTION

[0071] In order to use the adaptive neural network controller based on the BLF method and combine it with the event trigger mechanism to realize the distributed error constraint control of the multi-USV system, the controller u designed in the present invention can make the position and attitude η of the multi-USV system still track the expected value η in the presence of input saturation, current disturbance and model uncertainty. d And let the tracking error e = η-η d There are predetermined dynamic performance and steady-state response conditions. The following is a description of the specific implementation method. Before the specific description, the coordinate system, parameter definition, and the method and neural network used in the present invention are first described:

[0072] Inertial coordinate system (E-ξηζ): The origin E can be selected at a point on the horizontal plane. The Eξ axis and the Eη axis are placed in the horizontal plane and are perpendicular to each other. The positive direction of the Eξ axis points to the due north, and the positive direction of the Eη axis points to the due east. Eζ is perpendicular to the Eξη plane, and its positive direction points to the center of the earth.

[0073] Motion coordinate system (G-xyz): The origin G is taken at the center of gravity of the USV, and the x-axis, y-axis and z-axis are the intersection lines of the waterline, transverse section and mid-longitudinal section passing through the origin respectively. Gx points from the center of gravity to the bow along the mid-longitudinal axis, Gy points from the center of gravity to the starboard side of the USV, and Gz is perpendicular to the XOY plane and points from the center of gravity to the bottom of the ship.

[0074] Parameter definition: M is the mass inertia matrix; η=[x,y,z,φ,θ,ψ] T is the six-degree-of-freedom position and attitude value of USV in the fixed coordinate system; η d =[x d ,y d ,z d ,φ d ,θ d ,ψ d ] T is the expected value of the six-degree-of-freedom position and attitude of the USV in the fixed coordinate system; e = η-η d is the tracking error; v = [u, v, w, p, q, r] T are the velocity and angular velocity in the moving coordinate system; J(η) is the transformation matrix between the fixed coordinate system and the moving coordinate system; C(ν) is the Coriolis force and centripetal force matrix; D(ν) is the hydrodynamic damping matrix; g(η) is the force and torque vector generated by gravity and buoyancy; τ is the control force and torque generated by the propulsion system; w is the unknown external interference.

[0075] Since the mathematical model of the six degrees of freedom of USV is too complicated, the following assumptions are proposed based on the actual movement of USV and its own characteristics:

[0076] (1) USV is a rigid body with uniform mass distribution;

[0077] (2) USV is symmetric about the XOZ plane;

[0078] (3) Ignore other movements of the USV outside the horizontal plane.

[0079] Based on the above assumptions, the six degrees of freedom of the USV are converted into three degrees of freedom in the horizontal plane, namely, sway, swing and bow pitch. The motion states and symbol definitions of the USV are shown in Table 1.

[0080] Table 1 USV motion status and symbol definitions

[0081]

[0082] BLF method: BLF is a Lyapunov function with boundary constraints, which is generally logarithmic, tan or exponential. Boundary constraints can be functions of various forms, including symmetric and asymmetric, time-varying and time-invariant. The BLF method is based on the control law and adds error constraints, which is more intuitive in form.

[0083] Radial Basis Function Neural Network: Radial Basis Function Neural Network (RBFNN) is a three-layer feedforward neural network, which includes an input layer, a hidden layer, and an output layer. After the data is transmitted from the input layer, it is processed nonlinearly in the hidden layer, and finally integrated and processed and output in the output layer. The learning of this type of network is equivalent to finding the best fitting plane for training data in multidimensional space, and has good unknown parameter fitting ability. The neural network has a simple structure, concise training, fast learning convergence speed, and can approximate arbitrarily complex nonlinear functions.

[0084] This embodiment is a multi-USV event triggered error constraint control method considering input saturation, comprising the following steps:

[0085] S1. Establish the kinematic and dynamic equations of USV:

[0086]

[0087] Where η = [x, y, ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system, v = [u, v′, r] T represents the velocity u, v′ and angular velocity r in the moving coordinate system; J(η) is the transformation matrix between the inertial coordinate system and the moving coordinate system. is the mass inertia matrix, are the Coriolis and centripetal force matrices, is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T are the control forces τ1, τ2 and torque τ3 generated by the propulsion system, and w is the unknown external disturbance.

[0088] S2, USV input saturation model and dynamic model transformation:

[0089] Assume that there is a multi-USV system, including 1 leader and N followers, the follower USVs are numbered 1, 2...N, and the leader USV is numbered 0. The communication mode of the multi-USV system is directed communication topology.

[0090] In view of the input saturation problem of the USV actuator, a smooth hyperbolic tangent function is used to approximate the saturation function. The saturation function sat(τ) of the USV system is expressed as:

[0091]

[0092] Among them, τ1, τ2 represent the desired forces acting on the USV, τ3 represents the torque acting on the USV; τ 1max ,τ 2max ,τ 3max is the actuator amplitude; sat(τ)=[sat(τ1),sat(τ2),sat(τ3)] T is the saturated output matrix of the USV system; sign(·) represents the sign function.

[0093] The saturation input estimation model p of the i-th USV i (τ i ) can be expressed as

[0094] p i (τ i )=[p i (τ ik )]

[0095]

[0096] The input saturation model of the i-th follower USV can be expressed as

[0097] sat(τ i )=p i (τ i )+q i (τ i ) (3)

[0098] In the formula, sat(τ i )=[sat(τ i1 ),sat(τ i2 ),sat(τ i3 )] T , sat(·) represents the saturation function, τ i =[τ i1 ,τ i2 ,τ i3 ] represents the control force τ generated by the propulsion system of the i-th follower i1 ,τ i2 and torque τ i3 ; τ imax =[τ i1max ,τ i2max ,τ i3max ] T is the saturation control force τ i1max,τ i2max and torque τ i3max The amplitude of q i (τ i ) is the saturation input estimation model error of the i-th follower USV.

[0099] The kinematic and dynamic equations (1) for USV can be transformed into

[0100]

[0101] In the formula, x i1 =η i , x i2 =v i , f i The model itself is nonlinear, and its expression is as follows:

[0102] f i =-C i (x i2 )x i2 -D i (x i2 )x i2 -g i (x i1 ) (5)

[0103] In order to deal with the input saturation problem, an input saturation auxiliary variable χ is designed. i for:

[0104]

[0105] Among them, k i2 For normal amount, is the inverse of the mass inertia matrix corresponding to the ith follower, p i (τ i ) is the saturation input estimate of the i-th follower, τ i are the control force and torque generated by the propulsion system of the i-th follower.

[0106] S3. Selection of BLF function:

[0107] For the error constraints in the system, we select the exponential barrier Lyapunov function V bi , whose expression is

[0108]

[0109] In the formula, k bi (t)>0 is a time-varying continuous equation that is differentiable to the second order and represents the constraint range. i is the variable that needs to be constrained, which satisfies

[0110] ||γi (t)||<k bi (t) (8)

[0111] S4. Design of Radial Basis Function Neural Network Disturbance Observer:

[0112] The unknown nonlinearity f of the i-th USV i It can be expressed as

[0113] f i =W i T φ i +ε i (9)

[0114] in represents the weight matrix, represents the activation function, is the approximation error.

[0115] Therefore, equation (4) can be transformed into

[0116]

[0117] In the formula, x i1 =η i , x i2 =v i , d i =ε i +w i Indicates overall interference.

[0118] The disturbance observer is designed as follows:

[0119]

[0120] In the formula, δ i is the auxiliary system state quantity of the disturbance observer; k i is a positive constant; It is W i The estimated value of Yes i estimated value.

[0121] The RBF neural network is used to approximate the uncertain nonlinearity of the USV itself, and the neural network estimation law is as follows:

[0122]

[0123] In the formula, Λ i and β i For normal amount, is the compensation error, where the compensation signal

[0124] S5. Event trigger mechanism design:

[0125] Considering that frequent controller updates may cause resource waste, the present invention proposes an event triggering mechanism as follows:

[0126]

[0127]

[0128] In the formula, is the current controller update time; is the next update time of the controller; Δe i ′(t) is the measurement error of the controller; the event trigger mechanism parameter m i The value of is 0<m i <1; n i =[n i1 ,n i2 ,n i3 ] T is a constant, satisfying n ij >0(j=1,2,3); is a constant, satisfying

[0129] S6. Design of multi-USV distributed event-triggered error-constrained control law:

[0130] The present invention is based on radial basis function neural network disturbance observer and event trigger mechanism, and designs the controller as follows:

[0131]

[0132]

[0133] In the formula, z i1 ,z i2 are trajectory error and velocity error respectively, and the expressions are

[0134]

[0135] Among them, a ij is the weighted adjacency matrix of the directed graph A = [a ij ], for nodes i and j, when node j can receive information from node i, a ij =1, otherwise a ij =0; b i The communication topology matrix B = diag(b1,···,b N ), if node i can receive the information from the leader, then b i =1, otherwise b i=0; η0(t) represents the trajectory of the leader USV; is the output value of the command filter; i is the input saturation auxiliary variable; m i is the event trigger mechanism parameter, 0<m i <1; is a constant;

[0136] α i1 is the virtual control law, which is expressed as

[0137]

[0138] in, k i1 , k i2 For normal amount.

[0139] Theoretical derivation of the designed control law:

[0140] A1. USV dynamic model

[0141] The three-degree-of-freedom nonlinear model based on Newton's basic theorem of kinematics and the relationship between coordinate systems is expressed as follows:

[0142]

[0143] Where η = [x, y, ψ] T Represents the position and attitude of USV in the inertial coordinate system, v = [u, v, r] T represents the velocity and angular velocity in the moving coordinate system, and J(η) is the transformation matrix between the inertial coordinate system and the moving coordinate system. is the mass inertia matrix, are the Coriolis and centripetal force matrices, is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T is the control force and torque generated by the propulsion system, and w is the unknown external disturbance.

[0144] The control objective of the present invention can be expressed as: designing a controller u based on an event trigger mechanism so that the position and attitude η of the USV can still track the expected value η in the presence of system uncertainty and thruster output saturation, taking into account error constraints d , and make the tracking error e = η-η d It has predetermined dynamic performance and steady-state response.

[0145] Based on the actual engineering background, three assumptions are proposed:

[0146] Assumption 1: Position and attitude angle η and its first-order derivative Measurable.

[0147] Assumption 2: The expected position and attitude angle η d Its first- and second-order derivatives are known and bounded.

[0148] Assumption 3 Overall interference d i and its derivatives are bounded. There exists a positive constant D i , so that

[0149] A2. USV saturation input estimation model

[0150] When the system has input saturation, consider using a smooth hyperbolic tangent function to approximate the saturation function. The saturation input estimation model of the i-th USV can be expressed as:

[0151]

[0152] The input saturation model of the i-th follower USV can be expressed as

[0153] sat(τ ij )=p i (τ ij )+q i (τ ij ) (twenty two)

[0154] In the formula, sat(τ ij )=[sat(τ i1 ),sat(τ i2 ),sat(τ i3 )] T ; τ ijmax =[τ i1max ,τ i2max ,τ i3max ] T .q i (τ i ) is sat(τ ij ) and p i (τ ij )

[0155] According to the properties of the hyperbolic tangent function, we have

[0156]

[0157] In view of the "integral explosion" problem in the backstepping method, the command filter is designed as follows:

[0158]

[0159] If the input signal α1 satisfies where ο1, ο2 are positive constants, and h1(0) = α1(0), h2(0) = 0. Then for any θ>0, there exists g n >0, satisfying |h1-α1|≤θ, and and They are all bounded.

[0160] A3. Design of Neural Network Disturbance Observer

[0161] The neural network can be used to approximate the unknown nonlinearity of the USV itself, where the unknown nonlinearity f of the i-th USV is i It can be expressed as:

[0162] f i =W i T φ i +ε i f i =W i T φ i +ε i (25)

[0163] The auxiliary system state quantity δ of the disturbance observer is introduced i , the disturbance observer is designed as follows:

[0164]

[0165] In the formula, k i is a positive constant; It is W i The estimated value of Yes i estimated value.

[0166] Proof: Derivative the disturbance observer (26) yields:

[0167]

[0168] In the formula,

[0169] Select the Lyapunov function:

[0170]

[0171] Taking the derivative of formula (28), we have

[0172]

[0173] According to Young's inequality and Assumption 3, we have

[0174]

[0175] By |φ i ||≤1, we can get:

[0176]

[0177] Substituting equation (30) and equation (31) into equation (29), we can obtain:

[0178]

[0179] The proof is complete.

[0180] A4. Event-triggered error-constrained control law design

[0181] The trajectory error and velocity error of the i-th USV are defined as:

[0182]

[0183]

[0184] In the formula, a ij is the follower communication topology matrix, b i is the communication topology matrix between the follower and the leader; η0(t) represents the trajectory of the leader USV; is the output value of the command filter, χ i is the input saturation auxiliary variable.

[0185] By taking the derivative of formula (33), we get:

[0186]

[0187] In the formula, α i1 Virtual control law designed as needed.

[0188] To solve the "integral explosion" problem in the backstepping method, the following command filtering is introduced:

[0189]

[0190] In the formula, α i1 and are the input value and output value of the command filter respectively, and satisfy h i (0) = 0. i1 and d i2 are all normal numbers, satisfying d i1 >0,0<d i2 ≤1.

[0191] To eliminate Influence of trajectory error compensation signal is designed:

[0192]

[0193] Define the compensated trajectory tracking error:

[0194]

[0195] Substituting the trajectory error compensation signals (37) and (35) into the derivative of (38), we obtain

[0196]

[0197] To constrain the trajectory error of the system, the Lyapunov function is selected as follows:

[0198]

[0199] In the formula, k bi (t)>0 is a time-varying continuous equation that is differentiable to the second order and represents the constraint range. The variable that needs to be constrained is the compensation of the trajectory tracking error satisfy

[0200] Regulation Taking the derivative of (40), we get:

[0201]

[0202] definition where ι i Is a normal number.

[0203] Note that in (41), we have

[0204]

[0205] Therefore, from (41) we can get:

[0206]

[0207] According to (39), we can get:

[0208]

[0209] Design the virtual control law as

[0210]

[0211] where k i1 For normal amount.

[0212] Combining (42)-(44), we get:

[0213]

[0214] By taking the derivative of (34), we can obtain:

[0215]

[0216] In order to deal with the input saturation problem, an auxiliary system is introduced, which is designed as follows:

[0217]

[0218] where k i2 For normal amount.

[0219] Design compensation signal and compensation error:

[0220]

[0221]

[0222] Combining (46)-(49), we have

[0223]

[0224] Choosing an appropriate Lyapunov function

[0225]

[0226] By taking the derivative of (51) and combining it with (50), we can obtain:

[0227]

[0228] According to assumptions 1 to 3 and (23), we have

[0229]

[0230] Substituting (32) and (53) into (52), we can obtain

[0231]

[0232] in

[0233] The proof is complete.

[0234] To address the resource consumption problem caused by frequent controller updates, the present invention selects the following event triggering mechanism:

[0235]

[0236]

[0237] Δe′ i(t) = u i (t)-τ i (t) (57)

[0238] in, is the current controller update time; is the next update time of the controller; Δe′ i (t) is the measurement error of the controller; 0<m i <1; n i =[n i1 ,n i2 ,n i3 ] T Satisfy n ij >0(j=1,2,3); satisfy

[0239] Based on the event trigger mechanism, the controller and neural network estimation law are designed as follows:

[0240]

[0241]

[0242]

[0243] In the formula, Λ i and β i All are normal amounts.

[0244] A5. Stability analysis of event-triggered error-constrained control

[0245] For multi-USV systems

[0246]

[0247]

[0248] In the presence of model uncertainty, external disturbances, and input saturation, if the information of the leader USV can only be obtained by some followers, and assumptions 1 to 3 are established, then based on the event triggering conditions (55)-(57), under the action of the disturbance observer (26), the virtual control law (44), the anti-saturation compensator (47), the control law (58), and the neural network estimation law (60), the trajectory error of the system will converge to the specified range, and the follower USV can track the trajectory formed by the leader USV, realizing distributed error constrained collaborative tracking control.

[0249] Proof: According to the event trigger mechanism and the measurement error Δe′ i The definition of (t) can be obtained:

[0250]

[0251] Among them, λ1(t) and λ2(t) satisfy |λ1(t)|≤1, |λ2(t)|≤1 respectively.

[0252] Note that (61) we have

[0253]

[0254] For any value of ρ and a positive number ε, it satisfies

[0255] -ρtanh(ρ / ε)≤0 (63)

[0256] According to (58) and (63), there exists Since |λ1(t)|≤1,|λ2(t)|≤1, we can get

[0257]

[0258]

[0259] Combining (54) and (62), we have:

[0260]

[0261] Note that (66), according to the event triggering controller (58), we have

[0262]

[0263] Since for any ε>0 and ρ, 0<|ρ|-ρtanh(ρ / ε)≤0.2785ε, then

[0264]

[0265]

[0266] Considering (67), combined with (59), there exists

[0267]

[0268] Substituting (68)-(70) into (67), we can obtain:

[0269]

[0270] Substituting (60) and (71) into (66), we obtain

[0271]

[0272] because exist

[0273]

[0274] According to Young's inequality, we can get

[0275]

[0276] Substituting (73)-(75) into (72), we obtain

[0277]

[0278] The value ranges of parameters χ2 and κ2 are as follows:

[0279]

[0280]

[0281] Among them, k i1 >0,k i2 >1, β i -k i >0.

[0282] Formula (76) can be rewritten as

[0283]

[0284] Multiply both sides of the inequality by Integrate it in the range [0, t], and multiply the result of the integration by Finally, we get:

[0285]

[0286] According to formula (78), it can be seen that the signals of the multi-USV system converge.

[0287]

[0288] Further based on (79), there exists

[0289]

[0290] Select the following Lyapunov function:

[0291]

[0292] Taking the derivative of (81), we get

[0293]

[0294] Substituting (37) and (48) into (82), we can obtain

[0295]

[0296] After introducing command filtering (36), In (83), there is

[0297]

[0298] Combining (83) and (84), we obtain

[0299]

[0300] The parameters χ3 and κ3 satisfy the following conditions

[0301]

[0302]

[0303] Among them, K i >Δ i +b i ,

[0304] From (85), we can see that the trajectory error compensation signal β i1 is bounded, that is, β i1 →0. According to (38) and (80), when time t→∞, the trajectory tracking error satisfies ||z i1 ||<k bi , multi-USV system realizes trajectory error constraints.

[0305] When z i1 =0 N When

[0306]

[0307] Converting (86) into a column vector form, we can obtain

[0308]

[0309] For each follower USV, there is at least one leader USV with a directed path to the individual, and the matrices L and B satisfy rank(L+B)=N.

[0310] Therefore, when t→∞, Under the control law (58) and event triggering conditions (55)-(57), the follower USV can track the trajectory formed by the leader USV, the trajectory error constraint requirements of the system are met, and the multi-USV distributed error constraint collaborative tracking control is realized.

[0311] A6. Event-triggered error constraint control Zeno behavior proof

[0312] For the multi-USV system (1), under the control law (58) and event triggering conditions (55)-(57), the system does not have Zeno behavior.

[0313] Proof: For the i-th USV, when time t satisfies When the time interval is For |Δe′ i (t)|, we have

[0314]

[0315] By taking the derivative of (58), we can obtain

[0316]

[0317] From the above event-triggered error constraint control stability analysis, we can conclude that all states in the multi-USV system are bounded, so there exists a vector γ i =[γ i1 ,γ i2 ,γ i3 ] T satisfy where γ ij >0,j=1,2,3. When the event triggering condition is met, exist:

[0318]

[0319] From (56), we can see

[0320]

[0321] Combining (90) and (91), we have:

[0322]

[0323] According to (92), the event triggering time interval is greater than 0, and the designed event triggering mechanism avoids Zeno behavior. Proof completed.

[0324] Example

[0325] In order to verify the effectiveness of the control method designed by the present invention, it is applied to a multi-USV system model for simulation verification, and the effects of model uncertainty, ocean current disturbance, and input saturation are considered. The multi-USV system consists of 6 followers (numbered 1...6) and a leader (numbered 0).

[0326] The USV used in the present invention is a Cybership II model ship, and the corresponding hydrodynamic parameters of the USV model are:

[0327] m=23.8,I z =1.76,x g =0.046;

[0328] X u =-0.7225,X uu =-1.3274,X uuu =-5.8664;

[0329] Y v =-0.8612, Y vv =-36.2823, Y r =0.1079;

[0330] N v =0.1052, N vv =5.0437, N r =-1.9;

[0331] X du =-2.0;

[0332] Y dv =-10.0, Y dr =0;

[0333] N dv =0,N dr = -1.0;

[0334] Y rv =-8.05, Y vr =-0.845, Y rr =-3.45;

[0335] N rv =0.13, N vr =0.08, N rr =-0.75.

[0336] The position and speed of the leader USV are set to

[0337]

[0338] v ij (t) = J-1 η ij (t)

[0339] The initial position (angle) and speed information of the follower USV are shown in Tables 2 and 3.

[0340] Table 2 Initial position (angle) of USV

[0341]

[0342] Table 3 Initial (angular) speed of USV

[0343]

[0344] Model uncertainty

[0345] In order to facilitate simulation analysis, the present invention quantifies the model uncertainty. In view of the model uncertainty of the USV itself, a 30% model error is selected in the simulation test, that is, the dynamic model value in the controller is 70% of the actual value.

[0346] Ocean current disturbance

[0347] The random external interference that USV may encounter during navigation is defined as:

[0348] w i (t) = [w i1 (t),w i2 (t),w i3 (t)] T (93)

[0349] In the formula, w i1 (t) and w i2 (t) is Gaussian white noise with mean 3 and variance 1; w i3 (t) is Gaussian white noise with mean 0.2 and variance 1.

[0350] Communication topology

[0351] The multi-USV system consists of 6 followers (numbered 1-6) and a leader (numbered 0). The communication topology between the leader USV and the follower USV is as follows: Figure 1 shown.

[0352] Controller Parameters

[0353] Control parameter selection: k i =1.7, K i =2.01, k i1 =0.2, k i2 =22,d i1 =35,d i2 =0.5,Λi =10,β i =1.8. Event trigger mechanism parameter selection: m = 0.2, ε i =0.01, n i =[0.1,0.1,0.1] T , n i =[0.05,0.05,0.05] T . Saturation limit selection: τ i1max =500, τ i2max =500, τ i3max = 100. Saturated auxiliary variable χ i The initial value of is set to 0.

[0354] The upper and lower limits of the error constraints are set to

[0355]

[0356] Select 11 neural network nodes, and the activation function used in the simulation is:

[0357]

[0358] In the formula The center c of the activation function ij Evenly distributed in the area [-4,4] 6 , width b ij Select b ij =30; Neural network estimation value The initial value is

[0359] Simulation analysis:

[0360] The multi-USV system consists of 6 followers (numbered 1, ..., 6) and 1 leader (numbered 0). The trajectory (angle) tracking curve of the follower USV is as follows: Figure 2 shown.

[0361] For trajectory error constraints, follower USV 3 is used as an example to show the change of error variables in three degrees of freedom, as shown in Figures 3 to 5 shown.

[0362] Without loss of generality, the controller input is shown in the example of follower USV 3. The simulation results are as follows: Figure 6 and Figure 7 shown.

[0363] Under the event trigger mechanism, the event triggering time of each follower USV within 10 seconds is as follows: Figure 8 shown.

[0364] For each follower USV, the event triggering time interval of the controller within 10s is as follows Figures 9 to 14 shown.

[0365] The event triggering times and triggering ratios of the follower USV are shown in Table 4.

[0366] Table 4 Event triggering times and triggering ratios of follower USVs

[0367]

[0368] Depend on Figure 2 It can be seen that in about 2 seconds, the follower USV achieves trajectory (angle) tracking of the three-degree-of-freedom direction of the leader USV. Figures 3 to 5 The trajectory tracking error curve of the multi-USV system is given. It can be seen from the figure that under the action of the exponential BLF, the error variable of the USV is limited to the specified constraint range (94), which improves the transient performance and steady-state accuracy of the system. Figures 2 to 5 It shows that under the control law (58) and event trigger mechanism (55)-(57), the follower USV can track the reference trajectory formed by the leader USV in a relatively short time, thus realizing the coordinated tracking control of the multi-USV system. Figure 6 and Figure 7 It shows that the control force and control torque of the follower USV are large in the initial stage. After the system stabilizes, the control force amplitude is within the range of 100N and the control torque is within the range of 1Nm. From the partial enlarged diagram, it can be seen that the event-triggered control signal curve is step-shaped, which means that the controller is updated only when the event triggering conditions are met, and remains unchanged between two adjacent triggering moments.

[0369] Figure 8 The moment when the USV updates the controller within 10 seconds. It can be seen from the figure that the controller of the follower USV is updated only when the trigger condition is met. Compared with the traditional periodic update, the event-triggered update has fewer trigger times, and its trigger ratio is between 30.46% and 35.63%.

[0370] Based on the above analysis, under the action of control law (58) and event trigger mechanism (55)-(57), a multi-USV distributed error constraint cooperative tracking control law is proposed based on the event trigger mechanism to address the model uncertainty, environmental interference and input saturation problems in the multi-USV cooperative control process. It ensures that the trajectory error variable of the system can converge within the specified range, the event trigger time interval is greater than zero, and the system is stable and does not have Zeno behavior. It proves that the control algorithm not only realizes the distributed error constraint tracking control of the multi-USV system, but also reduces the trigger frequency of the system, realizes the intermittent update of the controller, and thus reduces the consumption of the controller.

[0371] If the control requirements of multi-USV system trajectory tracking in the presence of input saturation, current disturbances and model uncertainty are to be achieved, in addition to the present invention, there are also event-triggered solutions, error constraint control and other solutions. The following briefly introduces these two solutions and compares them with the present invention.

[0372] (1) Event-triggered solutions

[0373] 《Distributed dynamic edge-based event-triggered formation control for multiple underactuated unmanned surface vessels》 combines the adaptive algorithm and the minimum learning parameter algorithm to propose a distributed event-triggered control method based on dynamic edge. This method introduces dynamic variables in the trigger function, which can obtain a larger time trigger interval while completing the expected multi-USV system formation control task, effectively reducing the communication burden. 《Cooperative trajectory tracking control of MUSVs with periodic relative threshold event-triggered mechanism and safe distance》 adopts an adaptive control strategy to compensate for the uncertainty and external interference of the system model, and proposes an event-triggered adaptive sliding mode control method in combination with a nonlinear tracking differentiator and a relative threshold event trigger mechanism, which solves the input saturation problem and realizes the cooperative trajectory tracking control of multiple USVs.

[0374] However, compared with the present invention, this solution does not take into account that the actuators of the USV, such as the motor and the steering gear, are constrained by their own physical characteristics, cannot provide control input without range restrictions, and does not further consider error constraints.

[0375] Therefore, the present invention has been improved by further considering the error constraints and input saturation problems, and by regarding the ocean current disturbance and model uncertainty as the overall uncertainty of the system, and using a radial basis function neural network to approximate the uncertainty, thereby incorporating several factors affecting the USV control accuracy into the design of the controller, which is closer to actual engineering needs.

[0376] (2) Error Constrained Control-Based Scheme

[0377] In actual sea conditions, constraining the trajectory of the USV is an important consideration. Constraining the trajectory of the USV can prevent it from colliding with obstacles during navigation, which is of great help to the performance and safety of the system itself.

[0378] "Bioinspired neurodynamics based formation control for unmanned surface vehicles with line-of-sight range and angle constraints" uses a time-varying tan-type BLF to deal with the line-of-sight range and angle tracking error constraint problems, introduces neural network technology to eliminate the differential term of the virtual control input, limits the output within a certain range, and ensures that the multi-USV system meets the constraints while achieving formation control. For underactuated USVs with model uncertainty and interference, "Singularity-free continuous adaptive control of uncertain underactuated surface vessels with prescribed performance" combines adaptive technology with a predetermined performance control method, and imposes constraints on position errors and auxiliary variables, on the one hand, eliminating the defects of the system model, and on the other hand, achieving the predetermined performance based on the singularity-free continuous control action. However, compared with the present invention, this solution does not consider the use of event triggering mechanism to reduce communication burden, reduce energy consumption, and ensure tracking performance and stability.

[0379] Therefore, the present invention designs event trigger conditions based on the relationship between the controller's real-time signal and the trigger signal. By combining event triggering with error constraints, the number of communications of the multi-USV system in the control process is reduced, the communication burden and energy consumption are reduced, and it is closer to actual engineering needs.

[0380] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-USV event-triggered error constraint control method considering input saturation, characterized in that: For each USV in a multi-USV system, the kinematic and dynamic equations of the USV are established; the multi-USV system includes a leader and N followers, the follower USVs are numbered 1, 2, ..., N, and the leader USV is numbered 0; the communication mode of the multi-USV system is a directed communication topology; The smooth hyperbolic tangent function is used to approximate the saturation function for the actuator of the USV; the saturation input estimation model of the i-th USV is constructed: p i (t i )=[p i (t ik )] p i (τ i ) is the saturation input estimate of the i-th follower, with τ = [τ1, τ2, τ3] T represents the desired forces τ1, τ2 and torque τ3 acting on the USV, then τ i =[τ i1 ,τ i2 ,τ i3 ] represents the control force τ generated by the propulsion system of the i-th follower i1, τ i2 and torque τ i3 , τ ik Represents τ i1 ,τ i2 ,τ i3 ; τ imax =[τ i1max ,τ i2max ,τ i3max ] T is the saturation control force τ i1max, τ i2max and torque τ i3max The amplitude of Based on p i (τ i ), the input saturation of the i-th follower USV is expressed as sat(t i )=p i (t i )+q i (t i ) (3) In the formula, sat(τ i )=[sat(τ i1 ),sat(τ i2 ),sat(τ i3 )] T , sat(·) represents the saturation function; q i (τ i ) is the estimated model error for saturated input; Based on the kinematic and dynamic equations of USV, the kinematic and dynamic equations of the i-th follower USV are transformed into In the formula, x i1 =η i , η i is the η corresponding to the i-th follower, η=[x,y,ψ] T represents the position x, y and attitude ψ of USV in the inertial coordinate system; i2 =v i , v i is the v corresponding to the ith follower, v = [u, v, r] T represents the velocity u, v and angular velocity r in the motion coordinate system; f i The model itself is nonlinear; is the inverse of the mass inertia matrix corresponding to the i-th follower; J i is the transformation matrix between the inertial coordinate system and the motion coordinate system corresponding to the i-th follower; w i is the unknown external interference corresponding to the i-th follower; Then design the input saturation auxiliary variable χ i for Among them, k i2 is the normal amount; The unknown nonlinearity f of the i-th USV is i Represented as f i =W i T φ i +ε i ;in, represents the weight matrix, represents the activation function, is the approximation error; Then transform formula (4) into In the formula, x i1 =η i , x i2 =v i , d i =ε i +w i represents the overall interference corresponding to the i-th follower; Design the following disturbance observer: In the formula, δ i is the auxiliary system state quantity of the disturbance observer; k i is a positive constant; It is W i The estimated value of Yes i Estimated value of M i is the mass inertia matrix corresponding to the i-th follower; Use RBF neural network to approximate f i , and determine the neural network estimation law as follows: In the formula, Λ i and β i For normal amount, is the speed compensation error, where is the speed error, So it is the virtual control law α i1 The output value of the command filter obtained as the command filter input; the compensation signal β i2 satisfy Based on the designed disturbance observer and neural network estimation law, the USVs in the multi-USV system are controlled by using multi-USV distributed event-triggered error constraint controller. The multi-USV distributed event-triggered error constraint controller is designed based on a radial basis function neural network disturbance observer and an event trigger mechanism, as follows: Among them, b i is the element of the communication topology matrix between the follower and the leader. If node i can receive the information from the leader, then b i =1, otherwise b i =0; η0(t) represents the trajectory of the leader USV; is the output value of the command filter; i is the input saturation auxiliary variable; m i is the event trigger mechanism parameter, 0<m i <1; is a constant; α i1 is the virtual control law, which is expressed as in, a ij is the element of the weighted adjacency matrix of the directed graph. For nodes i and j, when node j can receive information from node i, a ij =1, otherwise a ij =0; k i1 , k i2 is a normal quantity; x j1 =η j , η j is the η corresponding to the jth follower, η=[x,y,ψ] T represents the position x, y and attitude ψ of USV in the inertial coordinate system; j2 =v j , v j is the v corresponding to the jth follower, v = [u, v′, r] T Represents the velocity u, v′ and angular velocity r in the motion coordinate system; adjustment parameters k bi (t)>0 is a time-varying continuous equation that is differentiable to the second order and is used to constrain the compensation of trajectory tracking error. have ι i is a positive constant; is the trajectory compensation error, is the trajectory error; β i1 is the trajectory error compensation signal, satisfying 2. A multi-USV event-triggered error constraint control method considering input saturation according to claim 1, characterized in that: The kinematic and dynamic equations of the USV are as follows: Where η = [x, y, ψ] T Represents the position x, y and attitude ψ of the USV in the inertial coordinate system, v = [u, v′, r] T represents the velocity u, v′ and angular velocity r in the motion coordinate system, J(η) is the transformation matrix between the inertial coordinate system and the motion coordinate system; M is the mass inertia matrix, C(v) is the Coriolis force and centripetal force matrix, D(v) is the hydrodynamic damping matrix, g(η) is the restoring force and torque vector generated by gravity and buoyancy, τ=[τ1,τ2,τ3] T are the control forces τ1, τ2 and torque τ3 generated by the propulsion system, and w is the unknown external disturbance.

3. A multi-USV event-triggered error constraint control method considering input saturation according to claim 2, characterized in that: The input saturation of the i-th follower USV is represented as sat(τ ik )=p i (τ ik )+q i (τ ik ), the saturation function of the USV system needs to be determined; the saturation function of the USV system is as follows: Among them, τ1, τ2 represent the desired forces acting on the USV, τ3 represents the torque acting on the USV; τ 1max ,τ 2max ,τ 3max is the actuator amplitude; sat(τ)=[sat(τ1),sat(τ2),sat(τ3)] T is the saturated output matrix of the USV system; sign(·) represents the sign function.

4. A multi-USV event-triggered error constraint control method considering input saturation according to claim 3, characterized in that: The kinematic and dynamic equations of the i-th follower USV are transformed into When the model itself is nonlinear, f i =-C i (x i2 )x i2 -D i (x i2 )x i2 -g i (x i1 ), where C i is the Coriolis force and centripetal force matrix corresponding to the ith follower, D i is the hydrodynamic damping matrix corresponding to the ith follower, g i (x i1 ) represents the restoring force and torque vector generated by the gravity and buoyancy corresponding to the i-th follower.

5. A multi-USV event-triggered error constraint control method considering input saturation according to any one of claims 1 to 4, characterized in that: The output value of the command filter Determined by the following formula: In the formula, So it is the virtual control law α i1 The output value of the command filter obtained as the command filter input satisfies h i (0) = 0; d i1 and d i2 are all normal numbers, satisfying d i1 >0,0<d i2 ≤1.

6. A multi-USV event-triggered error constraint control method considering input saturation according to claim 5, characterized in that: The event triggering mechanism corresponding to the multi-USV distributed event-triggered error constraint controller is as follows: Δe i ′(t)=u i (t)-τ i (t) (15) In the formula, is the current controller update time; is the next update time of the controller; Δe i ′(t) is the measurement error of the controller; the event trigger mechanism parameter m i The value of is 0<m i <1; n i =[n i1 ,n i2 ,n i3 ] T is a constant, satisfying n ij >0; inf represents the infimum; τ i (t) represents the τ corresponding to time t i ,u i (t) represents the u corresponding to time t i .

7. A multi-USV event-triggered error constraint control method considering input saturation according to claim 6, characterized in that: The constant and constant n i Needs to be satisfied 8. The method for controlling a multi-USV event-triggered error constraint considering input saturation according to claim 7, characterized in that: In the process of designing the multi-USV distributed event-triggered error constraint controller, the exponential barrier Lyapunov function is selected to constrain the trajectory compensation error in the system to complete the design and proof process of the multi-USV distributed event-triggered error constraint controller.

Images