An unmanned helicopter fixed time trajectory tracking switching control method

Abstract

The application belongs to the technical field of unmanned aerial vehicle control, and particularly relates to a fixed time trajectory tracking switching control method for unmanned helicopters, which comprises the following steps: establishing a system model of the unmanned helicopter and considering the influence of external disturbance; obtaining a safe expected tracking trajectory of the unmanned helicopter under real-time trajectory constraints based on a switching boundary protection algorithm, and generating a controller switching rule; establishing a fixed time fuzzy disturbance observer to estimate the compound disturbance in the system; designing a position loop fixed time switching backstepping control scheme; and designing an attitude loop fixed time switching backstepping control scheme; according to the switching boundary protection algorithm, the controller switching rule is obtained, and the switching controller is designed to enable the unmanned helicopter to have expected fixed time tracking performance and disturbance suppression capability under real-time trajectory constraints.

Description

Technical Field

[0001] The present invention belongs to the technical field of flight control, and in particular relates to a fixed-time trajectory tracking and switching control method for an unmanned helicopter. Background Art

[0002] An unmanned helicopter is an aircraft that can perform tasks without a pilot and has the ability to be unmanned or remotely controlled. With the continuous development and maturity of unmanned technology, the application scope of unmanned helicopters in military, civil and commercial fields is expanding. Unmanned helicopters have the following characteristics: (1) They can take off and land vertically in a small space without the need for a long runway or flat ground, so they are suitable for performing tasks in complex terrain or confined spaces; (2) They can hover stably in the air, which makes them suitable for applications that require long-term observation or the performance of specific tasks, such as surveillance, search and rescue, and traffic control; (3) Due to the flexibility and maneuverability of unmanned helicopters, they can quickly adjust the flight direction and altitude in a short period of time to respond to emergencies or changing mission requirements.

[0003] However, unmanned helicopters also face several technical challenges. The difficulties are: First, in specific mission environments, the external geographical environment is often unpredictable. Unmanned helicopters are subject to real-time trajectory constraints, and the ideal trajectory will change with these constraints. A single controller cannot guarantee effective tracking near the boundaries. By designing a fixed-time switching controller, response time can be reduced, tracking accuracy can be improved, and the tracking trajectory can always be guaranteed to remain within the safety boundary, better achieving rapid and accurate tracking of the desired trajectory. Second, unmanned helicopters are subject to combined interference from multiple factors during flight. Accurately estimating and suppressing these combined interferences can enhance the robustness of the system and further improve the trajectory tracking accuracy of unmanned helicopters.

[0004] The paper (O Halbe and H Oza. Robust continuous finite-time control of ahelicopter in turbulence. IEEE Control Systems Letters, 2021, 5: 37-42) designed a finite-time output tracking control method for full-size helicopters. However, the convergence time in finite-time control depends on the initial conditions and may increase with larger initial errors. The paper (Chen L, Li T, Liu L, et al. Trajectory tracking anti-disturbance control for unmanned aerial helicopter based on disturbance characterization index [J]. Control Theory Technology, 2023, 21: 233–245) studied the trajectory tracking control problem of the unmanned helicopter system and proposed a set of finite-time disturbance observers to estimate the mismatched disturbance. However, none of the above results comprehensively considered the design of fuzzy fixed-time disturbance observers for the outer and inner loops of the unmanned helicopter, and only concluded that the closed-loop system converges within a finite time. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a fixed-time trajectory tracking switching control method for an unmanned helicopter.

[0006] In order to achieve the purpose of the present invention, the present invention will be implemented by adopting the following technical solutions.

[0007] A fixed-time trajectory tracking switching control method for an unmanned helicopter comprises the following steps:

[0008] S1. Establishing a system dynamics model of the unmanned helicopter while taking into account the influence of external interference; wherein the system dynamics model of the unmanned helicopter includes a dynamics model of a position loop subsystem and a dynamics model of an attitude loop subsystem;

[0009] S2, based on the preset expected tracking trajectory, when the real-time trajectory tends to cross the constraint conditions, the switching boundary protection algorithm is used to switch to obtain the constrained trajectory, which is filtered by a first-order filter to obtain the safe expected trajectory and generate the controller switching rules;

[0010] S3, establishing a position loop fixed-time fuzzy disturbance observer and an attitude loop fixed-time fuzzy disturbance observer based on the dynamic models of the position loop subsystem and the dynamic models of the attitude loop subsystem, respectively; wherein: the position loop fixed-time fuzzy disturbance observer estimates the position loop composite disturbance through a fuzzy logic system with an adaptive update law for velocity estimation error; and the attitude loop fixed-time fuzzy disturbance observer estimates the attitude loop composite disturbance through a fuzzy logic system with an adaptive update law for angular velocity estimation error;

[0011] S4, using a fixed-time position loop switching control strategy to design the input safe desired trajectory and position loop composite disturbance as the system switching control input, and by inversely solving the system switching control input, obtain the desired tail rotor thrust, desired roll angle, and desired pitch angle; wherein: the position loop fixed-time switching control strategy is based on a position loop switching virtual control law designed by combining the dynamic model of the position loop subsystem with the controller switching rule, and the system switching control input is designed by filtering the position loop switching virtual control input obtained by the nonlinear filter;

[0012] S5. Use a fixed-time attitude loop switching control strategy to design the desired roll angle, desired pitch angle, preset desired yaw angle, and attitude loop composite interference as torque switching control inputs; wherein: the fixed-time attitude loop switching control strategy is based on an attitude loop switching virtual control law designed based on the desired attitude angle and attitude loop composite interference obtained after filtering by a nonlinear filter, and the torque switching control input is designed based on the attitude loop switching virtual control input obtained after filtering by the nonlinear filter.

[0013] Furthermore, the system dynamics model is expressed as follows:

[0014]

[0015] Where: P e =[X,Y,Z] T Represents the position of the ground coordinate system, X, Y, and Z are the positions of the x-axis, y-axis, and z-axis in the ground coordinate system respectively, and T represents the matrix transpose; V e =[V ex ,V ey ,V ez ] T Indicates the flight speed in the ground coordinate system, V ex 、V ey and V ez are the flight speeds in the x-axis, y-axis, and z-axis directions of the ground coordinate system; α = [φ, θ, ψ] T represents the attitude angle, φ is the roll angle, θ is the pitch angle, and ψ is the yaw angle; ω = [p, q, r] TIndicates attitude angular velocity, p is roll angular velocity, q is pitch angular velocity, r is yaw angular velocity; F = [0,0,-T r ] T represents the net external force, T r is the tail rotor thrust; G1=[0,0,g] T Represents the gravitational acceleration vector, g is the gravitational acceleration; M=[M x ,M y ,M z ] T Represents the net external torque, M x 、M y and M z are the components of the total external moment M in the x-axis, y-axis and z-axis directions of the body coordinates; d1=[d 11 ,d 12 ,d 13 ] T and d2=[d 21 ,d 22 ,d 23 ] T They represent the composite interference in the position loop and attitude loop of the unmanned helicopter, d 11 and d 21 Acting on the x-axis, d 12 and d 22 Acting on the y-axis, d 13 and d 23 Acting on the z-axis; m is the mass of the unmanned helicopter;

[0016] Represents the attitude angular rate matrix, where: p is the roll angular velocity, q is the pitch angular velocity, and r is the yaw angular velocity;

[0017] represents the inertia matrix, where: J x 、J y 、J z The moment of inertia of the unmanned helicopter around the x-axis, y-axis and z-axis of the body coordinate respectively;

[0018] represents the attitude kinematic matrix;

[0019] Represents the coordinate transformation matrix.

[0020] Furthermore, the constraint condition includes the lower boundary P l =[X l ,Y l ,Z l ] T and the upper boundary P u =[X u ,Y u,Z u ] T ; Among them: X l 、Y l and Z l The lower boundaries of the real-time track constraint paths in the X, Y and Z directions respectively; u 、Y u and Z u These are the upper boundaries of the real-time track constraint path in the X, Y, and Z directions respectively.

[0021] Furthermore, the controller switching rule is specifically described using the x direction as an example:

[0022] Switching Case 1: If X r ≥X u -ρ(X u -X l ), then X c =X u -ρ(X u -X l );

[0023] Switching Case 2: If X r ≤X l +ρ(X u -X l ), then X c =X l +ρ(X u -X l );

[0024] Switching Case 3: If X l +ρ(X u -X l )<X r <X u -ρ(X u -X l ), then X c =X r ;

[0025] Where: X r 、Y r and Z r are the preset expected tracking tracks in the X, Y, and Z directions respectively; ρ is a positive constant to be designed, and the size of the distance between the generated safe expected tracking signal and the boundary can be adjusted by selecting different ρ; the switching rules in the y and z directions are the same as those in the x direction, and both determine whether to switch by judging the real-time distance to the boundary; X c is the restricted desired trajectory subject to upper and lower bound constraints.

[0026] Furthermore, the constraint trajectory is:

[0027] P c =[X c ,Y c ,Z c ] T ,

[0028] Where: X c 、Y c and Z c are the restricted desired trajectories in the X, Y, and Z directions subject to upper and lower boundary constraints.

[0029] Furthermore, the safety expectation trajectory P s =[X s ,Y s ,Z s ] T is the constraint path P c =[X c ,Y c ,Z c ] T Obtained after filtering by a first-order filter; where: X s 、Y s and Z s These are the safe expected trajectories in the X, Y, and Z directions subject to upper and lower boundary constraints.

[0030] Furthermore, the controller switching rules are described as:

[0031] σ(P, t):R 3 ×R + →Θ={1,...,G1};

[0032] Where: σ(P,t) is the switching rule, Θ is the number of possible switching modes, R 3 For three-dimensional state, R + Is a positive state quantity.

[0033] Furthermore, the establishment process of the position loop fixed time fuzzy disturbance observer and the attitude loop fixed time fuzzy disturbance observer is as follows:

[0034] (1) The establishment process of the fixed-time fuzzy disturbance observer of the position loop:

[0035] The dynamic model of the position loop subsystem is described as:

[0036]

[0037] Where: u is the position loop control input, u=R bi F;

[0038] Design the position loop fuzzy logic system to estimate the composite disturbance d1 of the position loop:

[0039] d1=W1 *T η1(P e ,V e )+σ1;

[0040] Of which: W1 *T is the optimal weight matrix of the position loop fuzzy logic system; η1(P e ,V e ) is the basis function of the position loop fuzzy logic system, σ1 is the estimation error of the position loop fuzzy logic system and satisfies the inequality in: is the upper bound of σ1;

[0041] Select the following adaptive update law for the position loop fuzzy logic system:

[0042]

[0043] in: is the optimal weight matrix W1 of the position loop *T The estimated value of is the estimated value of the optimal weight matrix of the position loop The derivative of is the adaptive update law of the position loop fuzzy logic system; χ1 and χ2 are positive constants; is the estimated error of the flight speed in the ground coordinate system, is the ground coordinate system flight speed V e estimated value of;

[0044] For any vector ζ=[ζ1,...,ζ n ] T , define sig(ζ) r The function is sig(ζ) r =|ζ| r sign(ζ); where |ζ| r =diag(|ζ1| r ,...,|ζ n | r ), sign(ζ)=[sign(ζ1),...,sign(ζ n )] T , sign(·) is the sign function;

[0045] Therefore, the fixed-time fuzzy disturbance observer of the position loop is designed as:

[0046]

[0047] Where: V f ∈R 3 is an auxiliary variable; is the estimated value of d1; is the estimated error of attitude angular velocity, is the estimated value of the attitude angular velocity ω; f1 and f2 are constants satisfying 0<f1<1 and f2>1 respectively; z1=diag{z 11 z 12 z 13} and z2=diag{z 21 z 22 z 23} is a parameter matrix, satisfying and λ min (z1) and λ min (z2) are the minimum eigenvalues ​​of matrices z1 and z2 respectively;

[0048] (2) The establishment process of the attitude loop fixed time fuzzy disturbance observer:

[0049] The dynamic model of the attitude subsystem is described as:

[0050]

[0051] Where: Ω(ω)=J -1 ο(ω)J means Ω(ω) is J -1 The simplified form of the o(ω)J matrix;

[0052] Design the attitude loop fuzzy logic system to estimate the composite disturbance d2 of the attitude loop:

[0053]

[0054] in: is the optimal weight matrix of the attitude loop fuzzy logic system, η2(α,ω) is the basis function of the attitude loop fuzzy logic system, σ2 is the estimation error of the attitude loop fuzzy logic system and satisfies the inequality in: is the upper bound of σ2;

[0055] Select the following adaptive update law for the attitude loop fuzzy logic system:

[0056]

[0057] in: is the optimal weight matrix of the attitude loop The estimated value of is the optimal weight matrix estimate The derivative of is the adaptive update law of the attitude loop fuzzy logic system; χ3 and χ4 are positive constants;

[0058] Therefore, the attitude loop fixed-time disturbance observer is designed as:

[0059]

[0060] Where: f ∈R 3 is an auxiliary variable, is the estimated value of d2, z3=diag{z 31 z 32 z 33} and z4=diag{z 41 z 42 z 43} is the disturbance observer parameter matrix, satisfying and

[0061] Furthermore, based on the dynamic model of the position loop subsystem of the unmanned helicopter and combined with the switching rules, the position loop switching virtual control law V is designed. c :

[0062]

[0063] Where: r p =diag{r p1 r p2 r p3} and s p =diag{s p1 s p2 s p3} is the position tracking error control parameter matrix, satisfying and Position tracking error e1 = P e -P s ; scalars κ1 and κ2 satisfy 0<κ1<1 and κ2>1 respectively; r p1 、r p2 and r p3 are the position tracking error control parameters in the X, Y and Z directions respectively; p1 、s p2 and s p3 These are the position tracking error control parameters in the X, Y and Z directions respectively;

[0064] In order to avoid repeated differentiation of the position loop switching virtual control law, the nonlinear filter is designed as follows:

[0065]

[0066] Where: Λ=diag{Λ1Λ2Λ3} is the filter control parameter matrix, satisfying Λ j >0, where: j = 1, 2, 3; V s ∈R 3is the virtual control input after position loop filtering; Λ1, Λ2, and Λ3 are the filter control parameters in the X, Y, and Z directions, respectively;

[0067] According to the controller switching rules, the system switching control input u is further designed:

[0068]

[0069] Where: r v =diag{r v1 r v2 r v3} and s v =diag{s v1 s v2 s v3} is the velocity tracking error parameter matrix, satisfying and p 1i is the control switching parameter matrix, p 1i =diag{p 11i p 12i p 13i}>0,i∈Θ,p 11i 、p 12i and p 13i are the control switching parameters for the position tracking errors e1 in the X, Y and Z directions respectively; the speed tracking error is e2 = V e -V s ; r v1 、r v2 and r v3 are the speed tracking error control input parameters in the X, Y and Z directions respectively; v1 、s v2 and s v3 They are the input parameters for velocity tracking error control in the X, Y and Z directions respectively.

[0070] Furthermore, considering the underactuated characteristics of the unmanned helicopter system, we define u=[u1,u2,u3] T , where: u1 is the position loop x-axis direction control input, u2 is the position loop y-axis direction control input, and u3 is the position loop z-axis direction control input;

[0071] The desired attitude angle α is obtained by the following formula r =[φ r ,θ r ,ψ r ] T and the desired tail rotor thrust T r as follows:

[0072]

[0073] Where: φ r is the desired roll angle, θ r is the desired pitch angle, ψ r is the desired yaw angle;

[0074] To avoid repeated differentiation of the attitude loop switching virtual control law and ensure fixed-time convergence, the filtered desired attitude angle α s ∈R 3 is defined as:

[0075]

[0076] Where: Λ = diag{Λ1 Λ2 Λ3}, satisfying Λ j > 0, where j = 1, 2, 3; the scalars k1 and k2 satisfy 0 < k1 < 1 and k2 > 1 respectively;

[0077] Thus, the attitude loop virtual control law ω c is defined as:

[0078]

[0079] Where: r α = diag{r α1 r α2 r α3} and s α = diag{s α1 s α2 s α3} are the attitude angle tracking error control parameter matrices, satisfying <00​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​w1 r w2 r w3} and s w =diag{s w1 s w2 s w3} is the attitude angular velocity tracking error control parameter matrix, satisfying and r w1 、r w2 and r w3 They are the attitude angular velocity tracking error control parameters in the X, Y and Z directions, s w1 、s w2 and s w3 are the attitude angular velocity tracking error control parameters in the X, Y and Z directions respectively; p 2i is the attitude angular velocity tracking error control switching parameter matrix, p 2i =diag{p 21i p 22i p 23i}>0,i∈Θ,p 21i 、p 22i and p 23i The control switching parameters of the attitude angular velocity tracking error e3 in the three directions of X, Y and Z respectively; attitude angular velocity tracking error e4 = ω-ω s ,ω s is the expected attitude angular velocity after filtering.

[0085] Beneficial effects

[0086] 1. This paper combines the arbitrary precision approximation characteristics of fuzzy logic systems and proposes a fixed-time fuzzy disturbance observer, which can estimate the system's composite disturbance within a fixed time, thereby improving the system's robustness.

[0087] 2. According to the track generation controller switching rules, the present invention adopts a fixed-time switching backstepping control method to design a fixed-time switching controller, so that the unmanned helicopter can accurately track the desired trajectory within a fixed time under the real-time track constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 This is the overall structure diagram of the fixed-time adaptive trajectory tracking control method for an unmanned helicopter of the present invention;

[0089] Figure 2 A switching rule curve diagram of an unmanned helicopter controller obtained by using the flight control method of the present invention;

[0090] Figure 3The safe track tracking response curve in the X-axis direction under the track constraint of the unmanned helicopter obtained by the flight control method of the present invention is as follows;

[0091] Figure 4 The safe track tracking response curve in the Y-axis direction under the track constraint of the unmanned helicopter obtained by the flight control method of the present invention is as follows;

[0092] Figure 5 The safe track tracking response curve in the Z-axis direction under the track constraint of the unmanned helicopter obtained by the flight control method of the present invention is as follows;

[0093] Figure 6 The figure is a graph showing the attitude angle response of an unmanned helicopter obtained by using the flight control method of the present invention. DETAILED DESCRIPTION

[0094] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific examples. It should be understood that the specific implementation described herein is only for explaining the present invention and is not intended to limit the present invention. The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0095] For feedback systems, fixed-time backstepping control ensures that the system state converges within a fixed time. Furthermore, due to system uncertainties and external disturbances inherent in the modeling process, a fixed-time fuzzy disturbance observer is designed to estimate the composite disturbance. Therefore, the switching backstepping control method based on the fixed-time fuzzy disturbance observer in this invention enables an unmanned helicopter to quickly and accurately track its desired trajectory within real-time trajectory constraints.

[0096] As an embodiment of the present invention, Figures 1 to 2 As shown, a fixed-time trajectory tracking switching control method for an unmanned helicopter includes the following specific steps:

[0097] S1, first establish the unmanned helicopter system model and consider the impact of external interference.

[0098] The dynamic model of the unmanned helicopter is established, and the expression is as follows:

[0099]

[0100] Where: P e =[X,Y,Z] T Represents the position of the ground coordinate system, X, Y, and Z are the positions of the x-axis, y-axis, and z-axis in the ground coordinate system respectively, and T represents the matrix transpose; V e =[V ex ,V ey ,V ez ]T Indicates the flight speed in the ground coordinate system, V ex 、V ey and V ez are the flight speeds in the x-axis, y-axis, and z-axis directions of the ground coordinate system; α = [φ, θ, ψ] T represents the attitude angle, φ is the roll angle, θ is the pitch angle, and ψ is the yaw angle; ω = [p, q, r] T Indicates attitude angular velocity, p is roll angular velocity, q is pitch angular velocity, r is yaw angular velocity; F = [0,0,-T r ] T represents the net external force, T r is the tail rotor thrust; G1=[0,0,g] T Represents the gravitational acceleration vector, g is the gravitational acceleration; M=[M x ,M y ,M z ] T Represents the net external torque, M x 、M y and M z are the components of the total external moment M in the x-axis, y-axis and z-axis directions of the body coordinates; d1=[d 11 ,d 12 ,d 13 ] T and d2=[d 21 ,d 22 ,d 23 ] T They represent the composite interference in the position loop and attitude loop of the unmanned helicopter, d 11 and d 21 Acting on the x-axis, d 12 and d 22 Acting on the y-axis, d 13 and d 23 Acting on the z-axis; m is the mass of the unmanned helicopter;

[0101] Represents the attitude angular rate matrix;

[0102] represents the inertia matrix, J x 、J y 、J z The moment of inertia of the unmanned helicopter around the x-axis, y-axis and z-axis of the body coordinate respectively;

[0103] represents the attitude kinematic matrix;

[0104] Represents the coordinate transformation matrix.

[0105] S2, track the track P according to the preset expectation r =[X r ,Y r ,Z r ] T , combined with the real-time trajectory constraint lower boundary P l =[X l ,Y l ,Z l ] T and the upper boundary P u =[X u ,Y u ,Z u ] T When the helicopter tends to cross the upper or lower boundary, the ideal trajectory will switch to meet the safety requirements; when the helicopter remains within the safe distance from the upper and lower boundaries, the ideal trajectory will not switch and the helicopter will fly along the original ideal trajectory. Taking the x direction as an example, the trajectory switching rules are explained. Figure 2 shown.

[0106] Switching Case 1: If X r ≥X u -ρ(X u -X l ), then X c =X u -ρ(X u -X l );

[0107] Switching Case 2: If X r ≤X l +ρ(X u -X l ), then X c =X l +ρ(X u -X l );

[0108] Switching Case 3: If X l +ρ(X u -X l )<X r <X u -ρ(X u -X l ), then X c =X r ;

[0109] Where: X r 、Y r and Z rare the preset expected tracking tracks in the X, Y, and Z directions respectively; ρ is a positive constant to be designed, and the size of the distance between the generated safe expected tracking signal and the boundary can be adjusted by selecting different ρ; the switching rules in the y and z directions are the same as those in the x direction, and both determine whether to switch by judging the real-time distance to the boundary; X c is the restricted desired trajectory subject to upper and lower bound constraints.

[0110] In summary, the constraint path is P c =[X c ,Y c ,Z c ] T , where: X c 、Y c and Z c The restricted desired trajectory in the three directions of X, Y and Z is subject to upper and lower boundary constraints. A first-order filter is further used to obtain a smoother flight path P s =[X s ,Y s ,Z s ] T , where: X s 、Y s and Z s These are the safe expected trajectories in the X, Y, and Z directions subject to upper and lower boundary constraints.

[0111] According to the designed switching boundary protection algorithm, the expected trajectory will produce switching characteristics, and the number of switching patterns is G = 27. In order to obtain better tracking performance, a switching controller needs to be designed. The switching rule of the controller can be described as σ(P, t): R 3 ×R + →Θ={1,...,G1}, where: σ(P,t) is the switching rule, Θ is the number of possible switching modes, R 3 For three-dimensional state, R + Is a positive state quantity.

[0112] S3, simplifies the dynamic model of the unmanned helicopter. The dynamic model of the position loop subsystem of the unmanned helicopter is described as:

[0113]

[0114] Where: u is the position loop control input, u=R bi F.

[0115] Design the position loop fuzzy logic system to estimate the composite disturbance d1 of the position loop:

[0116] d1=W1 *T η1(P e ,Ve )+σ1; (3)

[0117] Of which: W1 *T is the optimal weight matrix of the position loop fuzzy logic system; η1(P e ,V e ) is the basis function of the position loop fuzzy logic system, σ1 is the estimation error of the position loop fuzzy logic system and satisfies the inequality in: is the upper bound of σ1;

[0118] Select the following adaptive update law for the position loop fuzzy logic system:

[0119]

[0120] in: is the optimal weight matrix W1 of the position loop *T The estimated value of is the estimated value of the optimal weight matrix of the position loop The derivative of is the adaptive update law of the position loop fuzzy logic system; χ1 and χ2 are positive constants; is the estimated error of the flight speed in the ground coordinate system, is the ground coordinate system flight speed V e estimated value of;

[0121] For any vector ζ=[ζ1,...,ζ n ] T , define sig(ζ) r The function is sig(ζ) r =|ζ| r sign(ζ); where |ζ| r =diag(|ζ1| r ,...,|ζ n | r ), sign(ζ)=[sign(ζ1),...,sign(ζ n )] T , sign(·) is the sign function.

[0122] Therefore, the fixed-time fuzzy disturbance observer of the position loop is designed as:

[0123]

[0124] Where: V f ∈R 3 is an auxiliary variable; is the estimated value of d1; is the estimated error of attitude angular velocity, is the estimated value of the attitude angular velocity ω; f1 and f2 are constants satisfying 0<f1<1 and f2>1 respectively; z1=diag{z 11 z 12 z 13} and z2=diag{z 21 z 22 z 23} is a parameter matrix, satisfying and λ min (z1) and λ min (z2) are the smallest eigenvalues ​​of matrices z1 and z2 respectively.

[0125] The dynamic model of the unmanned helicopter attitude subsystem is described as:

[0126]

[0127] Where: Ω(ω)=J -1 ο(ω)J means Ω(ω) is J -1 The simplified form of the o(ω)J matrix;

[0128] Design the attitude loop fuzzy logic system to estimate the composite disturbance d2 of the attitude loop:

[0129]

[0130] in: is the optimal weight matrix of the attitude loop fuzzy logic system, η2(α,ω) is the basis function of the attitude loop fuzzy logic system, σ2 is the estimation error of the attitude loop fuzzy logic system and satisfies the inequality in: is the upper bound of σ2;

[0131] Select the following adaptive update law for the attitude loop fuzzy logic system:

[0132]

[0133] in: is the optimal weight matrix of the attitude loop The estimated value of is the optimal weight matrix estimate The derivative of is the adaptive update law of the attitude loop fuzzy logic system; χ3 and χ4 are positive constants;

[0134] Therefore, the attitude loop fixed-time fuzzy disturbance observer is designed as:

[0135]

[0136] Where: f ∈R 3is an auxiliary variable, is the estimated value of d2, z3=diag{z 31 z 32 z 33} and z4=diag{z 41 z 42 z 43} is the disturbance observer parameter matrix, satisfying and

[0137] S4. Design a fixed time switching control strategy for the position loop.

[0138] According to the dynamic model of the position loop subsystem of the unmanned helicopter and the controller switching rules, the position loop switching virtual control law is designed:

[0139]

[0140] Where: r p =diag{r p1 r p2 r p3} and s p =diag{s p1 s p2 s p3} is the position tracking error control parameter matrix, satisfying and Position tracking error e1 = P e -P s ; scalars κ1 and κ2 satisfy 0<κ1<1 and κ2>1 respectively; r p1 、r p2 and r p3 are the position tracking error control parameters in the X, Y and Z directions respectively; p1 、s p2 and s p3 These are the position tracking error control parameters in the X, Y and Z directions respectively;

[0141] In order to avoid repeated differentiation of the position loop switching virtual control law, the nonlinear filter is designed as follows:

[0142]

[0143] Where: Λ=diag{Λ1Λ2Λ3} is the filter control parameter matrix, satisfying Λ j >0, where: j = 1, 2, 3; V s ∈R 3 is the virtual control input after position loop filtering; Λ1, Λ2, and Λ3 are the filter control parameters in the X, Y, and Z directions, respectively;

[0144] According to the controller switching rules, the system switching control input is further designed:

[0145]

[0146] Where: r v =diag{r v1 r v2 r v3} and s v =diag{s v1 s v2 s v3} is the velocity tracking error parameter matrix, satisfying and p 1i is the control switching parameter matrix, p 1i =diag{p 11i p 12i p 13i}>0,i∈Θ,p 11i 、p 12i and p 13i are the control switching parameters for the position tracking errors e1 in the X, Y and Z directions respectively; the speed tracking error is e2 = V e -V s ; r v1 、r v2 and r v3 are the speed tracking error control input parameters in the X, Y and Z directions respectively; v1 、s v2 and s v3 They are the input parameters for velocity tracking error control in the X, Y and Z directions respectively.

[0147] S5, design the attitude loop fixed time switching control strategy.

[0148] Considering the underactuated characteristics of the unmanned helicopter system, define u=[u1,u2,u3] T , where: u1 is the position loop x-axis direction control input, u2 is the position loop y-axis direction control input, and u3 is the position loop z-axis direction control input;

[0149] The desired attitude angle α is obtained by formula (13): r =[φ r ,θ r ,ψ r ] T and the desired tail rotor thrust T r as follows:

[0150]

[0151] Among them, φr is the desired roll angle, θ r is the desired pitch angle, ψ r is the desired yaw angle.

[0152] To avoid repeated differentiation of the attitude loop switching virtual control law and ensure fixed-time convergence, the filtered desired attitude angle α s ∈R 3 is defined as:

[0153]

[0154] where: Λ = diag{Λ1 Λ2 Λ3}, satisfying Λ j > 0, where j = 1, 2, 3; the scalars k1 and k2 satisfy 0 < k1 < 1 and k2 > 1 respectively;

[0155] Thus, the designed attitude loop switching virtual control law is:

[0156]

[0157] where: r α = diag{r α1 r α2 r α3} and s α = diag{s α1 s α2 s α3} are the attitude angle tracking error control parameter matrices, satisfying and The attitude angle tracking error e3 = α - α s ; r α1 、r α2 and r α3 are the attitude angle tracking error control parameters in the X, Y, and Z directions respectively; s α1 、s α2 and s α3 are the attitude angle tracking error control parameters in the X, Y, and Z directions respectively;

[0158] After filtering ω c , we get:

[0159]

[0160] Furthermore, the designed total external torque M as the switching control input is:

[0161]

[0162] where: r w = diag{r w1 r w2 rw3} and s w =diag{s w1 s w2 s w3} is the attitude angular velocity tracking error control parameter matrix, satisfying and r w1 、r w2 and r w3 They are the attitude angular velocity tracking error control parameters in the X, Y and Z directions, s w1 、s w2 and s w3 are the attitude angular velocity tracking error control parameters in the X, Y and Z directions respectively; p 2i is the attitude angular velocity tracking error control switching parameter matrix, p 2i =diag{p 21i p 22i p 23i}>0,i∈Θ,p 21i 、p 22i and p 23i The control switching parameters of the attitude angular velocity tracking error e3 in the three directions of X, Y and Z respectively; attitude angular velocity tracking error e4 = ω-ω s ,ω s is the expected attitude angular velocity after filtering.

[0163] In order to verify the effectiveness of the trajectory tracking method of the present invention under real-time trajectory constraints, the following simulation experiments are carried out.

[0164] Assume that the composite interference to the position loop and attitude loop of the unmanned helicopter is:

[0165]

[0166] Preset expected tracking track P r =[X r ,Y r ,Z r ] T , combined with the real-time trajectory constraint lower boundary P l =[X l ,Y l ,Z l ] T and the upper boundary P u =[X u ,Y u ,Z u ] T The changes with time t are:

[0167]

[0168] like Figure 1 As shown in the figure, the overall structure diagram of the control method implemented in this example is constructed. The simulation time of the flight control process is set to 120s, and the flow chart of the switching rules generated according to the switching boundary protection algorithm is shown in the figure. Figure 2 As shown. Simulating an unmanned helicopter traveling through a narrow cave, the position tracking response and attitude angle tracking response of the unmanned helicopter are obtained as shown in Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 shown.

[0169] from Figure 3 、 Figure 4 、 Figure 5 It can be seen that the fixed-time switching backstepping control method adopted by the present invention can make the closed-loop system signal converge in a fixed time. Under the real-time trajectory constraint, the unmanned helicopter can quickly and accurately track the ideal signal, and the trajectory tracking effect is good. Figure 6 The response curve of the attitude angle is shown in Figure 2. It can be seen that the roll angle, pitch angle, and yaw angle can all track the desired signal well. The above simulation results show that the fixed-time trajectory tracking switching control method for unmanned helicopters can effectively solve the trajectory tracking problem of unmanned helicopters under real-time trajectory constraints.

Claims

1. A fixed-time trajectory tracking switching control method for an unmanned helicopter, comprising the following steps: S1. Considering the influence of external interference, establish a system dynamics model of the unmanned helicopter; where: The unmanned helicopter system dynamics model includes a dynamics model of a position loop subsystem and a dynamics model of an attitude loop subsystem; S2, based on the preset expected tracking trajectory, when the real-time trajectory tends to cross the constraint conditions, the switching boundary protection algorithm is used to switch to obtain the constrained trajectory, which is filtered by a first-order filter to obtain the safe expected trajectory and generate the controller switching rules; It is characterized in that it also includes the following steps: S3, establishing a position loop fixed-time fuzzy disturbance observer and an attitude loop fixed-time fuzzy disturbance observer based on the dynamic models of the position loop subsystem and the dynamic models of the attitude loop subsystem, respectively; wherein: the position loop fixed-time fuzzy disturbance observer estimates the position loop composite disturbance through a fuzzy logic system with an adaptive update law for velocity estimation error; and the attitude loop fixed-time fuzzy disturbance observer estimates the attitude loop composite disturbance through a fuzzy logic system with an adaptive update law for angular velocity estimation error; S4, using a fixed-time position loop switching control strategy to design the input safe desired trajectory and position loop composite disturbance as the system switching control input, and by inversely solving the system switching control input, obtain the desired tail rotor thrust, desired roll angle, and desired pitch angle; wherein: the position loop fixed-time switching control strategy is based on a position loop switching virtual control law designed by combining the dynamic model of the position loop subsystem with the controller switching rule, and the system switching control input is designed by filtering the position loop switching virtual control input obtained by the nonlinear filter; S5. Use a fixed-time attitude loop switching control strategy to design the desired roll angle, desired pitch angle, preset desired yaw angle, and attitude loop composite interference as torque switching control inputs; wherein: the fixed-time attitude loop switching control strategy is based on an attitude loop switching virtual control law designed based on the desired attitude angle and attitude loop composite interference obtained after filtering by a nonlinear filter, and the torque switching control input is designed based on the attitude loop switching virtual control input obtained after filtering by the nonlinear filter.

2. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 1, characterized in that: The system dynamics model is expressed as follows: Where: P e =[X,Y,Z] T Represents the position of the ground coordinate system, X, Y, and Z are the positions of the x-axis, y-axis, and z-axis in the ground coordinate system respectively, and T represents the matrix transpose; V e =[V ex ,V ey ,V ez ] T Indicates the flight speed in the ground coordinate system, V ex 、V ey and V ez are the flight speeds in the x-axis, y-axis, and z-axis directions of the ground coordinate system; α = [φ, θ, ψ] T represents the attitude angle, φ is the roll angle, θ is the pitch angle, and ψ is the yaw angle; ω=[p,q,r] T Indicates attitude angular velocity, p is roll angular velocity, q is pitch angular velocity, r is yaw angular velocity; F = [0,0,-T r ] T represents the net external force, T r is the tail rotor thrust; G1=[0,0,g] T Represents the gravitational acceleration vector, g is the gravitational acceleration; M=[M x ,M y ,M z ] T Represents the net external torque, M x 、M y and M z are the components of the total external moment M in the x-axis, y-axis and z-axis directions of the body coordinates; d1=[d 11 ,d 12 ,d 13 ] T and d2=[d 21 ,d 22 ,d 23 ] T They represent the composite interference in the position loop and attitude loop of the unmanned helicopter, d 11 and d 21 Acting on the x-axis, d 12 and d 22 Acting on the y-axis, d 13 and d 23 Acting on the z-axis; m is the mass of the unmanned helicopter; Represents the attitude angular rate matrix; represents the inertia matrix, J x 、J y 、J z The moment of inertia of the unmanned helicopter around the x-axis, y-axis and z-axis of the body coordinate respectively; represents the attitude kinematic matrix; Represents the coordinate transformation matrix.

3. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 2, characterized in that: The constraints include the lower bound P l =[X l ,Y l ,Z l ] T and the upper boundary P u =[X u ,Y u ,Z u ] T ; Among them: X l 、Y l and Z l The lower boundaries of the real-time track constraint paths in the X, Y and Z directions respectively; u 、Y u and Z u These are the upper boundaries of the real-time track constraint path in the X, Y, and Z directions respectively.

4. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 3, wherein: The controller switching rule is specifically described using the x direction as an example: Switching Case 1: If X r ≥X u -ρ(X u -X l ), then X c =X u -ρ(X u -X l ); Switching Case 2: If X r ≤X l +ρ(X u -X l ), then X c =X l +ρ(X u -X l ); Switching Case 3: If X l +ρ(X u -X l )<X r <X u -ρ(X u -X l ), then X c =X r ; Where: ρ is a positive constant to be designed. By selecting different ρ, the size of the distance between the generated safety expectation tracking signal and the boundary can be adjusted. The switching rules in the y and z directions are the same as those in the x direction. They all determine whether to switch by judging the real-time distance to the boundary. X r 、Y r and Z r The preset expected tracking tracks in the three directions of X, Y and Z respectively; c is the restricted desired trajectory subject to upper and lower bound constraints.

5. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 4, characterized in that: The constraint trajectory is: P c =[X c ,Y c ,Z c ] T , Where: X c 、Y c and Z c are the restricted desired trajectories in the X, Y, and Z directions subject to upper and lower boundary constraints.

6. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 5, characterized in that: Safety expectation trajectory P s =[X s ,Y s ,Z s ] T is the constraint path P c =[X c ,Y c ,Z c ] T Obtained after filtering by a first-order filter; where: X s 、Y s and Z s These are the safe expected trajectories in the X, Y, and Z directions subject to upper and lower boundary constraints.

7. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 6, characterized in that: The controller switching rules are described as: σ(P,t):R 3 ×R + →Θ={1,...,G1}; Where: σ(P,t) is the switching rule, Θ is the number of possible switching modes, R 3 For three-dimensional state, R + Is a positive state quantity.

8. The unmanned helicopter fixed time trajectory tracking switching control method according to claim 7, characterized in that: The establishment process of the position loop fixed-time fuzzy disturbance observer and the attitude loop fixed-time fuzzy disturbance observer is as follows: (1) The establishment process of the fixed-time fuzzy disturbance observer of the position loop: The dynamic model of the position loop subsystem is described as: Where: u is the position loop control input, u=R bi F; Design a fuzzy logic system to estimate the composite disturbance d1 of the position loop: d1=W1 *T η1(P e ,V e )+σ1; Of which: W1 *T is the optimal weight matrix of the position loop fuzzy logic system; η1(P e ,V e ) is the basis function of the position loop fuzzy logic system, σ1 is the estimation error of the position loop fuzzy logic system and satisfies the inequality in: is the upper bound of σ1; Select the following adaptive update law for the position loop fuzzy logic system: in: is the optimal weight matrix W1 of the position loop *T The estimated value of is the estimated value of the optimal weight matrix of the position loop The derivative of is the adaptive update law of the position loop fuzzy logic system; χ1 and χ2 are positive constants; is the estimated error of the flight speed in the ground coordinate system, is the ground coordinate system flight speed V e estimated value of; For any vector ζ=[ζ1,…,ζ n ] T , define sig(ζ) r The function is sig(ζ) r =|ζ| r sign(ζ); where |ζ| r =diag(|ζ1| r ,...,|ζ n | r ), sign(ζ)=[sign(ζ1),...,sign(ζ n )] T , sign(·) is the sign function; Therefore, the fixed-time fuzzy disturbance observer of the position loop is designed as: Where: V f ∈R 3 is an auxiliary variable; is the estimated value of d1; is the estimated error of attitude angular velocity, is the estimated value of the attitude angular velocity ω; f1 and f2 are constants satisfying 0<f1<1 and f2>1 respectively; z1=diag{z 11 z 12 z 13 } and z2=diag{z 21 z 22 z 23 } is a parameter matrix, satisfying and λ min (z1) and λ min (z2) are the minimum eigenvalues ​​of matrices z1 and z2 respectively; (2) The establishment process of the attitude loop fixed time fuzzy disturbance observer: The dynamic model of the attitude subsystem is described as: Where: Ω(ω)=J -1 ο(ω)J means Ω(ω) is J -1 The simplified form of the o(ω)J matrix; Design the attitude loop fuzzy logic system to estimate the composite disturbance d2 of the attitude loop: in: is the optimal weight matrix of the attitude loop fuzzy logic system, η2(α,ω) is the basis function of the attitude loop fuzzy logic system, σ2 is the estimation error of the attitude loop fuzzy logic system and satisfies the inequality in: is the upper bound of σ2; Select the following adaptive update law for the attitude loop fuzzy logic system: in: is the optimal weight matrix of the attitude loop The estimated value of is the optimal weight matrix estimate The derivative of is the adaptive update law of the attitude loop fuzzy logic system; χ3 and χ4 are positive constants; Therefore, the attitude loop fixed-time disturbance observer is designed as: Where: f ∈R 3 is an auxiliary variable, is the estimated value of d2, z3=diag{z 31 z 32 z 33 } and z4=diag{z 41 z 42 z 43 } is the disturbance observer parameter matrix, satisfying and 9. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 8, characterized in that: According to the dynamic model of the position loop subsystem of the unmanned helicopter, combined with the switching rules, the position loop switching virtual control law V is designed. c : Where: r p =diag{r p1 r p2 r p3 } and s p =diag{s p1 s p2 s p3 } is the position tracking error control parameter matrix, satisfying and Position tracking error e1 = P e -P s ; scalars κ1 and κ2 satisfy 0<κ1<1 and κ2>1 respectively; r p1 、r p2 and r p3 are the position tracking error control parameters in the X, Y and Z directions respectively; p1 、s p2 and s p3 These are the position tracking error control parameters in the X, Y and Z directions respectively; In order to avoid repeated differentiation of the position loop switching virtual control law, the nonlinear filter is designed as follows: Where: Λ=diag{Λ1Λ2Λ3} is the filter control parameter matrix, satisfying Λ j >0, where: j = 1, 2, 3; V s ∈R 3 is the virtual control input after position loop filtering; Λ1, Λ2, and Λ3 are the filter control parameters in the X, Y, and Z directions, respectively; According to the controller switching rules, the system switching control input u is further designed: Where: r v =diag{r v1 r v2 r v3 } and s v =diag{s v1 s v2 s v3 } is the velocity tracking error parameter matrix, satisfying and p 1i is the control switching parameter matrix, p 1i =diag{p 11i p 12i p 13i }>0,i∈Θ,p 11i 、p 12i and p 13i are the control switching parameters for the position tracking errors e1 in the X, Y and Z directions respectively; the speed tracking error is e2 = V e -V s ; r v1 、r v2 and r v3 are the speed tracking error control input parameters in the X, Y and Z directions respectively; v1 、s v2 and s v3 They are the input parameters for velocity tracking error control in the X, Y and Z directions respectively.

10. The method for controlling the fixed-time trajectory tracking and switching of an unmanned helicopter according to claim 9, characterized in that: Considering the underactuated characteristics of the unmanned helicopter system, define u=[u1,u2,u3] T , where: u1 is the position loop x-axis direction control input, u2 is the position loop y-axis direction control input, and u3 is the position loop z-axis direction control input; Get the desired attitude angle α r =[φ r ,θ r ,ψ r ] T and the desired tail rotor thrust T r as follows: Where: φ r is the desired roll angle, θ r is the desired pitch angle, ψ r is the desired yaw angle; In order to avoid repeated differentiation of the virtual control law for attitude loop switching and ensure fixed time convergence, the filtered expected attitude angle α is introduced s ∈R 3 for: where: Λ = diag{Λ1 Λ2 Λ3}, satisfying Λ j > 0, where j = 1, 2, 3; the scalars k1 and k2 satisfy 0 < k1 < 1 and k2 > 1 respectively; Therefore, the virtual control law of the attitude loop is designed c for: Where: r α =diag{r α1 r α2 r α3 } and s α =diag{s α1 s α2 s α3 } is the attitude angle tracking error control parameter matrix, satisfying and Attitude angle tracking error e3 = α - α s ; r α1 、r α2 and r α3 are the attitude angle tracking error control parameters in the X, Y and Z directions respectively; s α1 、s α2 and s α3 are the attitude angle tracking error control parameters in the X, Y and Z directions respectively; Right c After filtering, we get: Furthermore, the total external torque M is designed as the switching control input: Where: r w =diag{r w1 r w2 r w3 } and s w =diag{s w1 s w2 s w3 } is the attitude angular velocity tracking error control parameter matrix, satisfying and r w1 、r w2 and r w3 They are the attitude angular velocity tracking error control parameters in the X, Y and Z directions, s w1 、s w2 and s w3 are the attitude angular velocity tracking error control parameters in the X, Y and Z directions respectively; p 2i is the attitude angular velocity tracking error control switching parameter matrix, p 2i =diag{p 21i p 22i p 23i }>0,i∈Θ,p 21i 、p 22i and p 23i The control switching parameters of the attitude angular velocity tracking error e3 in the three directions of X, Y and Z respectively; attitude angular velocity tracking error e4 = ω-ω s ,ω s is the expected attitude angular velocity after filtering.

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