Four-rotor unmanned aerial vehicle pose control method based on global sliding mode

Abstract

The invention relates to a four-rotor unmanned aerial vehicle pose control method based on a global sliding mode. The invention relates to the technical field of unmanned aerial vehicle control, and the method comprises the steps: carrying out the modeling of a dynamic model of a quad-rotor unmanned aerial vehicle, and obtaining the nonlinear state space description of the quad-rotor unmanned aerial vehicle; secondly, respectively designing global sliding mode control laws for the position subsystem and the attitude subsystem according to the nonlinear model; according to the output of a position subsystem controller, the expected acceleration is mapped into expected lift force and attitude angle by designing control distribution; and finally, constructing a nonlinear programming problem corresponding to a nonlinear model prediction controller by taking a previously designed global sliding mode control law as a contraction constraint, and solving the problem to obtain a control quantity. According to the method, the quadrotor unmanned aerial vehicle can effectively perform trajectory tracking under the conditions of output constraint and convergence guarantee, and the control precision, the response speed and the safety in the flight process are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle control, and is a method for attitude control of a quadrotor unmanned aerial vehicle based on global sliding mode. Background Art

[0002] Due to its high flexibility and low cost, quadrotor unmanned aerial vehicles have been widely used in military, agricultural, surveying and mapping, industrial and other fields. However, the model of a quadrotor unmanned aerial vehicle has strong coupling and nonlinear characteristics, and it is difficult for traditional linear control methods to achieve precise trajectory tracking control. In recent years, nonlinear control methods such as sliding mode control and backstepping method have been widely used in the control of quadrotor unmanned aerial vehicles, but these methods still have certain limitations when dealing with the output constraints of actual controllers. The nonlinear model predictive control method can effectively handle output constraints, so it has received extensive attention from relevant scholars.

[0003] Currently, typical nonlinear model predictive control methods mainly perform direct optimization solution including state and output constraints in a specified time domain. For example, Li Yuxi in the literature "Research on Model Predictive Control Algorithm Based on State Estimation" sets the allowable control output as a set and performs optimization solution with this set as the output constraint; another example is Yun Xingyu in the literature "Nonlinear Model Predictive Control of Perception-Driven Quadruped Robots", where the joint constraints and collision avoidance constraints of the robot are used as equality and inequality state constraints, and on this basis, the nonlinear programming problem is solved.

[0004] In the process of controller design for the above literature, since the action time domain is a finite time domain, the obtained results may not ensure the convergence of the system state. The present invention proposes a method for attitude control of a quadrotor unmanned aerial vehicle based on global sliding mode, and on the basis of conventional constraints, by using the global sliding mode control law as a contraction constraint, the trajectory tracking problem of the quadrotor unmanned aerial vehicle is solved. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to enable the quadrotor unmanned aerial vehicle to effectively perform trajectory tracking under output constraints and ensure convergence, and improve the control accuracy, response speed and safety during flight. The present invention provides a method for attitude control of a quadrotor unmanned aerial vehicle based on global sliding mode.

[0006] The present invention provides the following technical solutions:

[0007] A method for attitude control of a quadrotor unmanned aerial vehicle based on global sliding mode, the method comprising the following steps:

[0008] Step 1: Construct a quadrotor unmanned aerial vehicle model and obtain a nonlinear state space description of the quadrotor unmanned aerial vehicle;

[0009] Step 2: Design a global sliding mode auxiliary control law according to the constructed model;

[0010] Step 3: Establish a nonlinear model predictive controller based on the output of the position subsystem controller to control the pose of the quadrotor UAV;

[0011] Step 4: Evaluate the control effect of the quadrotor UAV pose.

[0012] Preferably, the specific content of the said Step 1 is:

[0013] Construct a quadrotor UAV motion model, which is expressed by the following formula:

[0014]

[0015] Among them, the state and input quantities of the quadrotor UAV dynamic model include: p = [x y z] T is the UAV position vector; is the UAV velocity vector in the ground coordinate system; Θ = [φ θ ψ] T is the UAV attitude angle vector; b ω = b ω x b ω y b ω z T is the UAV attitude angular velocity vector; U L is the lift provided by the four rotors; τ = [τ x τ y τ z T is the torque vector provided by the rotors; m is the mass of the quadrotor UAV, g is the gravitational acceleration, and J = diag(J x , J y , J z ) is the inertia matrix of the airframe.

[0016] Preferably, convert Formula 1 into vector form and decompose it into a position subsystem and an attitude subsystem, which is expressed by the following formula:

[0017]

[0018] Among them, G = [0 0 g] T , and for the matrix W(Θ), C( b ω) and the virtual control vector u, they are respectively:

[0019]

[0020] Preferably, the specific content of the said Step 2 is: ​​

[0021] Step 2.1: The control law of the position subsystem is designed as follows:

[0022]

[0023] where \(u\) is the virtual control vector of the position subsystem corresponding to Equation (7); \(G\) is a known parameter vector; is the desired acceleration vector; \(e\) p = p - p d is the position deviation vector is the velocity deviation vector; is the sliding mode surface of the position subsystem, where \(\lambda\) p = diag(\(\lambda\) x , \(\lambda\) y , \(\lambda\) z ), where the elements \(\lambda\) x , \(\lambda\) y , \(\lambda\) z are designable parameters and satisfy \(\lambda\) x , \(\lambda\) y , \(\lambda\) z > 0; \(\Lambda\) p = diag(\(a\) x , \(a\) y , \(a\) z ), where the elements \(a\) x , \(a\) y , \(a\) z are designable parameters and satisfy \(a\) x , \(a\) y , \(a\) z > 0; \(k\) p = diag(\(k\) x , \(k\) y , \(k\) z ); Similarly, \(k\) x , \(k\) y , \(k\) z are designable parameters and satisfy \(k\) x , \(k\) y , \(k\) z > 0; For the sign function sgn(·), it is expressed as follows:

[0024]

[0025] Step 2.2: The control law expression of the attitude subsystem is designed as follows:

[0026]

[0027] where \(\tau = [\tau\) x \(\tau\) y \(\tau\) z T ​is the torque vector; J is a known parameter matrix; is the second derivative vector of the desired attitude angle; e a = Θ - Θ d is the attitude angle deviation vector; is the attitude angle derivative deviation vector; is the attitude subsystem sliding mode surface, where λ a = diag(λ φ , λ θ , λ ψ ), where the elements λ φ , λ θ , λ ψ are designable parameters and satisfy λ φ , λ θ , λ ψ > 0; Λ a = diag(a φ , a θ , a ψ ), where the elements a φ , a θ , a ψ are designable parameters and satisfy a φ , a θ , a ψ > 0; k a = diag(k φ , k θ , k ψ ), similarly, k φ , k θ , k ψ are designable parameters and satisfy k φ , k θ , k ψ > 0. For the matrices W -1 (Θ), are respectively:

[0028]

[0029] Preferably, step 3 is specifically:

[0030] Step 3.1: Describe the NMPC of the position subsystem as a nonlinear programming problem, represented by the following formula:

[0031]

[0032] p and Q p are designable positive definite matrices, and T is the prediction horizon;

[0033] Due to the virtual control quantity and The physical meaning of is the acceleration provided by the rotor in the three-axis directions in the ground coordinate system. Since 0 ≤ U L ≤ U Lmax , and according to Newton's second law, we can obtain:

[0034]

[0035] We get As an inequality constraint, under the action of the global sliding mode auxiliary control law formula 8 of the position subsystem, the position subsystem satisfies:

[0036]

[0037] Among them, is the Lyapunov function, is its derivative; β is the minimum element of the set composed of all diagonal elements of λ p and Λ p ;

[0038] Step 3.2: Since the output of the position subsystem controller is the virtual control quantity It is mapped to the desired lift U Ld , the desired pitch angle θ d and the desired roll angle φ d through control allocation. Let The control allocation expression is:

[0039]

[0040] Through control allocation, while obtaining the desired lift U Ld , the desired pitch angle θ d and the desired roll angle φ d can also be obtained. Combining the desired yaw angle ψ d provided by the external non-linear model predictive controller, the desired attitude angle vector Θ d =[φ d θ d ψ d T ;

[0041] Step 3.3: Describe the NMPC of the attitude subsystem as a non-linear programming problem, which is expressed by the following formula:

[0042]

[0043] Among them, P a and Q a are designable positive definite matrices;

[0044] ​Under the action of the attitude subsystem global sliding mode auxiliary control law formula (10), the attitude subsystem satisfies:

[0045]

[0046] Wherein, is the Lyapunov function, is its derivative; α is the minimum element of the set composed of all diagonal elements of λ a and Λ a

[0047] Preferably, the Lyapunov function V p exponentially converges to 0. To enable the position subsystem nonlinear model predictive controller to make the Lyapunov function V p converge at a speed not slower than the auxiliary control law, and since the obtained only retains as the control quantity at the current moment, add as the obtained contraction constraint.

[0048] Preferably, the Lyapunov function V a will exponentially converge to 0. To enable the attitude subsystem nonlinear model predictive controller to make the Lyapunov function V a converge at a speed not slower than the auxiliary control law, and since the obtained only retains as the control quantity at the current moment, add as the obtained contraction constraint.

[0049] A four-rotor UAV pose control system based on global sliding mode, the system includes:

[0050] A model construction module, which constructs a four-rotor UAV model and obtains a nonlinear state space description of the four-rotor UAV;

[0051] An auxiliary control law module, which designs a global sliding mode auxiliary control law according to the constructed model;

[0052] A predictive controller module, which establishes a nonlinear model predictive controller according to the output of the position subsystem controller to control the pose of the four-rotor UAV;

[0053] An evaluation module, which evaluates the pose control effect of the four-rotor UAV.

[0054] ​A computer-readable storage medium, on which a computer program is stored, and the program is executed by a processor to implement a pose control method for a quadrotor UAV based on global sliding mode.

[0055] A computer device, including a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, a pose control method for a quadrotor UAV based on global sliding mode is implemented.

[0056] The present invention has the following beneficial effects:

[0057] Compared with the prior art, the present invention:

[0058] The method proposed by the present invention combines the convergence of the global sliding mode control method and the optimization ability of the nonlinear model predictive control method, and can achieve high-precision trajectory tracking control under complex nonlinear models and actual controller output constraints. By taking the global sliding mode control law as a contraction constraint and combining the stability analysis of the Lyapunov function, the present invention ensures the stability of the system under complex nonlinear models and avoids the distortion problem of traditional linearization methods in large-angle control. At the same time, the optimization ability of the nonlinear model predictive control enables the system to optimize the control input in each control time domain, ensuring the optimal trajectory tracking effect while satisfying the constraint conditions. Description of the Drawings

[0059] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0060] Figure 1 Shown as a flowchart of the method of the present invention;

[0061] Figure 2 Shown as a structural diagram of the quadrotor UAV of the present invention;

[0062] Figure 3 Shown as a system structure block diagram corresponding to Process 2 of the present invention;

[0063] Figure 4 Shown as a system structure block diagram corresponding to Process 3 of the present invention;

[0064] Figure 5 Shown as a two-dimensional curve graph of trajectory tracking under Simulation Condition 1 of the present invention;

[0065] Figure 6Showing the position-time curve of Simulation Condition 1 of the present invention;

[0066] Figure 7 Showing the three-dimensional curve of trajectory tracking of Simulation Condition 2 of the present invention;

[0067] Figure 8 Showing the position-time curve of Simulation Condition 2 of the present invention. Detailed implementation manners

[0068] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0069] The present invention is described in detail below in conjunction with specific embodiments. Specific Embodiment 1:

[0071] According to Figures 1 to 8 As shown, the specific optimized technical solution adopted by the present invention to solve the above technical problems is: The present invention relates to a method for attitude control of a quadrotor UAV based on global sliding mode.

[0072] The present invention provides a method for attitude control of a quadrotor UAV based on global sliding mode, and the method includes the following steps:

[0073] Step 1: Construct a quadrotor UAV model and obtain the non-linear state space description of the quadrotor UAV;

[0074] Step 2: Design a global sliding mode auxiliary control law according to the constructed model;

[0075] Step 3: Establish a non-linear model predictive controller according to the output of the position subsystem controller to control the attitude of the quadrotor UAV;

[0076] Step 4: Evaluate the attitude control effect of the quadrotor UAV. Specific Embodiment 2:

[0078] The difference between Embodiment 2 and Embodiment 1 of this application is only that:

[0079] The specific content of step 1 is:

[0080] Construct a quadrotor UAV motion model, which is represented by the following formula:

[0081]

[0082] Among them, the states and input variables of the quadrotor UAV dynamic model include: p = [x y z] T is the UAV position vector; is the UAV velocity vector in the ground coordinate system; Θ = [φ θ ψ] T is the UAV attitude angle vector; b ω = b ω x b ω y b ω z T is the UAV attitude angular velocity vector; U L is the lift provided by the four rotors; τ = [τ x τ y τ z T is the torque vector provided by the rotors; m is the mass of the quadrotor UAV, g is the gravitational acceleration, and J = diag(J x , J y , J z ) is the body inertia matrix. Specific Embodiment Three:

[0084] The difference between Embodiment Three and Embodiment Two of this application lies only in:

[0085] Changing Formula 1 to vector form and decomposing it into a position subsystem and an attitude subsystem, which is represented by the following formula:

[0086]

[0087] Among them, G = [0 0 g] T , and for the matrix W(Θ), C( b ω) and the virtual control vector u, they are respectively:

[0088] Specific Embodiment Four:

[0090] The difference between Embodiment Four and Embodiment Three of this application lies only in:

[0091] Step 2 is specifically:

[0092] Step 2.1: Design the position subsystem control law, which is represented by the following formula:

[0093]

[0094] Among them, u is the virtual control vector of the position subsystem corresponding to Formula 7; G is the known parameter vector; is the desired acceleration vector; e p = p - p​​d is the position deviation vector is the velocity deviation vector; is the position subsystem sliding mode surface, where λ p = diag(λ x , λ y , λ z ), where the elements λ x , λ y , λ z are designable parameters and satisfy λ x , λ y , λ z > 0; Λ p = diag(a x , a y , a z ), where the elements a x , a y , a z are designable parameters and satisfy a x , a y , a z > 0; k p = diag(k x , k y , k z ); Similarly, k x , k y , k z are designable parameters and satisfy k x , k y , k z > 0; For the sign function sgn(·), it is expressed by the following formula:

[0095]

[0096] Step 2.2: Design the attitude subsystem control law expression, which is expressed by the following formula:

[0097]

[0098] where, τ = [τ x τ y τ z T is the torque vector; J is a known parameter matrix; is the second derivative vector of the desired attitude angle; e a = Θ - Θ d is the attitude angle deviation vector; is the attitude angle derivative deviation vector; is the attitude subsystem sliding mode surface, where λ a = diag(λ φ , λ θ , λ​ψ ), where the element λ φ , λ θ , λ ψ is a designable parameter and satisfies λ φ , λ θ , λ ψ > 0; Λ a = diag(a φ , a θ , a ψ ), where the element a φ , a θ , a ψ is a designable parameter and satisfies a φ , a θ , a ψ > 0; k a = diag(k φ , k θ , k ψ ), similarly, k φ , k θ , k ψ is a designable parameter and satisfies k φ , k θ , k ψ > 0. For the matrices W -1 (Θ), are respectively:

[0099] Specific Example Five:

[0101] The difference between Example Five and Example Four of the present invention lies only in:

[0102] Step 3 is specifically:

[0103] Step 3.1: Describe the NMPC of the position subsystem as a non-linear programming problem, and represent it by the following formula:

[0104]

[0105] where the superscript "^" represents the variable in the prediction horizon, P p and Q p are designable positive definite matrices, and T is the prediction duration;

[0106] Since the physical meanings of the virtual control variables and are the accelerations provided by the rotors in the three-axis directions in the ground coordinate system, and since 0 ≤ U L ≤ U Lmax , and according to Newton's second law, it can be obtained that:

[0107]

[0108] obtain As an inequality constraint, under the action of the global sliding mode auxiliary control law formula 8 of the position subsystem, the position subsystem satisfies:

[0109]

[0110] wherein, is the Lyapunov function, is its derivative; β is the minimum element of the set composed of all diagonal elements of λ p and Λ p ;

[0111] Step 3.2: Since the output of the position subsystem controller is the virtual control quantity it is mapped to the desired lift U Ld , the desired pitch angle θ d and the desired roll angle φ d through control allocation. Let the control allocation expression be:

[0112]

[0113] Through control allocation, while obtaining the desired lift U Ld , the desired pitch angle θ d and the desired roll angle φ d can also be obtained. Combining with the desired yaw angle ψ d externally provided by the nonlinear model predictive controller, the desired attitude angle vector Θ d =[φ d θ d ψ d can be obtained; T ;

[0114] Step 3.3: Describe the NMPC of the attitude subsystem as a nonlinear programming problem, and represent it by the following formula:

[0115]

[0116] wherein, P a and Q a are designable positive definite matrices;

[0117] Under the action of the global sliding mode auxiliary control law formula 10 of the attitude subsystem, the attitude subsystem satisfies:

[0118]

[0119] wherein, is the Lyapunov function, is its derivative; α is the minimum element of the set composed of all diagonal elements of λ a and Λ a The minimum element of the set composed of all diagonal elements. Specific Embodiment Six:

[0121] The difference between Embodiment Six and Embodiment Five of the present invention lies only in:

[0122] The Lyapunov function V p Exponentially converges to 0. To enable the position subsystem non - linear model predictive controller to make the Lyapunov function V p Converge at a speed not slower than the auxiliary control law, and since the obtained Only retain As the control quantity at the current moment, add As the obtained Contraction constraint. Specific Embodiment Seven:

[0124] The difference between Embodiment Seven and Embodiment Six of the present invention lies only in:

[0125] The Lyapunov function V a Will exponentially converge to 0. To enable the attitude subsystem non - linear model predictive controller to make the Lyapunov function V a Converge at a speed not slower than the auxiliary control law, and since the obtained Only retain As the control quantity at the current moment, add As the obtained Contraction constraint. Specific Embodiment Eight:

[0127] The difference between Embodiment Eight and Embodiment Seven of the present invention lies only in:

[0128] The present invention provides a position and attitude control system for a quadrotor UAV based on global sliding mode. The system includes:

[0129] A model construction module, which constructs a quadrotor UAV model and obtains the non - linear state - space description of the quadrotor UAV;

[0130] An auxiliary control law module, which designs a global sliding mode auxiliary control law according to the constructed model;

[0131] A predictive controller module, which establishes a non - linear model predictive controller according to the output of the position subsystem controller and controls the position and attitude of the quadrotor UAV;

[0132] An evaluation module, which evaluates the position and attitude control effect of the quadrotor UAV. Specific Embodiment Nine:

[0134] The only difference between Embodiment Nine and Embodiment Eight of the present invention lies in:

[0135] The present invention provides a computer-readable storage medium, on which a computer program is stored, and the program is executed by a processor to implement a pose control method for a quadrotor UAV based on global sliding mode. Specific Embodiment Ten:

[0137] The only difference between Embodiment Ten and Embodiment Nine of the present invention lies in:

[0138] The present invention provides a computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, a pose control method for a quadrotor UAV based on global sliding mode is implemented. Specific Embodiment Eleven:

[0140] The only difference between Embodiment Eleven and Embodiment Ten of the present invention lies in:

[0141] The flow chart of the present invention is as Figure 1 shown. First, a dynamic model of the quadrotor UAV is modeled to obtain its non-linear state space description; then, for this non-linear model, global sliding mode control laws are designed for the position and attitude subsystems respectively; then, for the output of the position subsystem controller, by designing control allocation, the desired acceleration is mapped into the desired lift and attitude angles; finally, by taking the previously designed global sliding mode control law as a contraction constraint, a non-linear programming problem corresponding to the non-linear model predictive controller is constructed, and solving this problem can obtain the control quantity.

[0142] The flow chart of the present invention is as Figure 1 shown, and it includes a total of 4 processes. First, by studying the motion mechanism of the quadrotor UAV, a dynamic model of the quadrotor UAV is modeled, and the kinematic model and dynamic model of the pose two subsystems of the quadrotor UAV are described in the form of a set of non-linear differential equations. Secondly, to ensure that the trajectory tracking of the quadrotor UAV can meet the stability in the sense of Lyapunov, based on the non-linear motion model obtained in the previous process, the global sliding mode control method is used to design the global sliding mode control laws for the position and attitude subsystems of the quadrotor UAV respectively. Thirdly, to further improve the dynamic performance of the control system, corresponding finite-time objective functions are designed for the position and attitude subsystems, and the dynamic model of the quadrotor UAV is used as an equality constraint, the saturation limit of the actuator and the global sliding mode contraction constraint are used as inequality constraints, and solving the non-linear programming problem composed of the foregoing objective function and constraints can obtain better dynamic performance on the premise of ensuring the stability of the system in the sense of Lyapunov.

[0143] 1. Construction of a quadrotor UAV model

[0144] Hypothesis 1: The quadrotor UAV is a rigid body with uniform mass distribution, and its center of mass coincides with the origin of the body coordinate system.

[0145] The structure of the quadrotor UAV is as shown in Figure 2 . Among them, 1, 2, 3, and 4 are the labels of the corresponding rotors; O e x e y e z e is the ground coordinate system, the x e axis points due north, the y e axis points due east, and the z e axis points towards the center of the earth; O b x b y b z b is the body coordinate system, φ is the roll angle of the quadrotor UAV, θ is the pitch angle, and ψ is the yaw angle.

[0146] The expression of the quadrotor UAV motion model is as follows:

[0147]

[0148] In the above formula, the states and input variables of the quadrotor UAV dynamic model include: p = [x y z] T is the UAV position vector; is the UAV velocity vector in the ground coordinate system; Θ = [φ θ ψ] T is the UAV attitude angle vector; b ω = b ω x b ω y b ω z T is the UAV attitude angular velocity vector; U L is the lift provided by the four rotors; τ = [τ x τ y τ z T is the torque vector provided by the rotors.

[0149] In addition, the above formula also includes the relevant parameters of the quadrotor UAV: m is the mass of the quadrotor UAV, which can be directly measured by weighing; g is the acceleration due to gravity, which can be experimentally measured by methods such as the free fall method, the simple pendulum method, the inclined plane method, and the optoelectronic gate method; J = diag(J x , J y , J z ) is the inertia matrix of the body rotation, where the moments of inertia J x 、J​​y , J z can be measured separately by methods such as the torsion pendulum method, compound pendulum method, and rotating disk method.

[0150] Furthermore, based on the above definitions of each vector, equation (1) is converted into vector form and decomposed into a position subsystem and an attitude subsystem as follows:

[0151]

[0152]

[0153] where G = [00g] T , and for the matrix W(Θ), C( b ω), and the virtual control vector u, they are respectively:

[0154]

[0155] 2. Design of global sliding mode auxiliary control law

[0156] This section consists of two parts, namely the control law design of the position subsystem of the quadrotor UAV and the control law design of the attitude subsystem of the quadrotor UAV. It should be noted that, as Figure 1 can be seen, the global sliding mode control law designed in this section is an auxiliary control law and will not directly act on the controlled object. Instead, it is used to provide a contraction constraint for the next process. Therefore, it is only necessary to design the control laws for the position and attitude subsystems respectively, without the intermediate control allocation link. The corresponding system structure block diagram of this section is as Figure 3 shown.

[0157] Step 1: Design of the control law for the position subsystem

[0158] This patent uses the global sliding mode control method to design the auxiliary control laws for the position and attitude subsystems. By simultaneously introducing the sliding mode surface and the state deviation into the Lyapunov function, the designed control laws can make both the sliding mode surface and the state deviation converge to 0, ensuring that the sliding mode surface and the state deviation can globally converge on the premise that the system is stable in the sense of Lyapunov.

[0159] The expression of the control law for the position subsystem is designed as:

[0160]

[0161] In the above formula, u is the virtual control vector of the position subsystem corresponding to equation (7); G is the known parameter vector; is the desired acceleration vector, which can be obtained by taking the second-order difference of the desired position; e p = p - p d is the position deviation vector, where the position p can be measured; is the velocity deviation vector, where the velocity vector can be obtained by measurement, while the desired velocity vector can be obtained by differentiating the desired position; is the sliding mode surface of the position subsystem, where λ p = diag(λ x , λ y , λ z ), where the elements λ x , λ y , λ z are designable parameters and satisfy λ x , λ y , λ z > 0; Λ p = diag(a x , a y , a z ), where the elements a x , a y , a z are designable parameters and satisfy a x , a y , a z > 0; k p = diag(k x , k y , k z ), similarly, k x , k y , k z are designable parameters and satisfy k x , k y , k z > 0. For the sign function sgn(·), its expression is:

[0162]

[0163] Step 2: Attitude Subsystem Control Law Design

[0164] Design the expression of the attitude subsystem control law as:

[0165]

[0166] In the above formula, τ = [τ x τ y τ z T is the torque vector; J is a known parameter matrix; is the second derivative vector of the desired attitude angle, which can be obtained by second-order differentiating the desired attitude angle; e a = Θ - Θ d is the attitude angle deviation vector, where the attitude angle Θ can be obtained by measurement; ​is the attitude angle derivative deviation vector, where can be obtained from by calculation. b ω can be measured, while can be obtained by differentiating the desired attitude angle; is the attitude subsystem sliding mode surface, where λ a = diag(λ φ , λ θ , λ ψ ), where the elements λ φ , λ θ , λ ψ are designable parameters and satisfy λ φ , λ θ , λ ψ > 0;

[0167] Λ a = diag(a φ , a θ , a ψ ), where the elements a φ , a θ , a ψ are designable parameters and satisfy a φ , a θ , a ψ > 0;

[0168] k a = diag(k φ , k θ , k ψ ), similarly, k φ , k θ , k ψ are designable parameters and satisfy k φ , k θ , k ψ > 0. For the matrix W -1 (Θ), are respectively:

[0169]

[0170]

[0171] 3. Nonlinear Model Predictive Controller Design

[0172] This section consists of three parts, namely the design of the nonlinear model predictive controller for the position subsystem of the quadrotor UAV, control allocation, and the design of the nonlinear model predictive controller for the attitude subsystem of the quadrotor UAV. Since the only externally given desired value for the controller is the desired position vector p d = [x d y dz d T and the desired yaw angle ψ d , and the output of the position subsystem controller is the virtual control vector u. Therefore, it is necessary to first map u to the desired lift U through control allocation L , the desired pitch angle θ d and the desired roll angle φ d . On this basis, the obtained desired attitude angle Θ d = [φ d θ d ψ d T is sent to the attitude subsystem nonlinear model predictive controller, and the corresponding desired torque is finally solved. The system structure block diagram corresponding to this section is as Figure 4 shown.

[0173] Step 1: Design of the position subsystem nonlinear model predictive controller

[0174] This patent provides actual control quantities for the controlled quadrotor UAV based on the nonlinear model predictive control method. For the nonlinear model predictive control method, first, a cost function is constructed for the prediction horizon, then the system dynamic model and the initial state are used as equality constraints, and the control quantity saturation constraint and the global sliding mode contraction constraint are used as inequality constraints. Finally, the nonlinear programming problem is solved to obtain the optimal control sequence that minimizes the cost function and satisfies all constraints, and the first element of this sequence is taken as the control quantity at the current moment. For the control quantity at each subsequent moment, this solution process is repeated.

[0175] The NMPC of the position subsystem can be described by the following nonlinear programming problem:

[0176]

[0177] In the above formula, the superscript "^" represents the variables in the prediction horizon. For the cost function J p , it is designed as a quadratic form based on the position deviation vector and the virtual control vector . Among them, P p and Q p are designable positive definite matrices, and T is the prediction duration. For the equality constraint conditions, on the one hand, they include the kinematic and dynamic equations of the position subsystem; on the other hand, for each moment t, the above formula should be used for the control law calculation, so the equality constraint includes the initialization of assigning the current moment state to the initial moment of the prediction horizon. For the inequality constraints, on the one hand, since the physical meanings of the virtual control quantities and are the accelerations provided by the rotors in the three-axis directions in the ground coordinate system, and since 0 ≤ U L ​​≤U Lmax , and according to Newton's second law, we can get:

[0178]

[0179] Therefore, we can obtain as an inequality constraint. On the other hand, under the action of the global sliding mode auxiliary control law (8) of the position subsystem, the position subsystem satisfies:

[0180]

[0181] In the above formula, is the Lyapunov function, is its derivative; β is the minimum element of the set composed of all diagonal elements of λ p and Λ p . It can be seen from formula (15) that the Lyapunov function V p will exponentially converge to 0. Therefore, to make the nonlinear model predictive controller of the position subsystem enable the Lyapunov function V p to converge at a speed not slower than the auxiliary control law, and since the obtained only retains as the control quantity at the current moment, therefore, it is necessary to add as the contraction constraint of the obtained .

[0182] Step 2: Control allocation

[0183] Since the output of the position subsystem controller is the virtual control quantity therefore, it is necessary to map it to the desired lift U Ld , the desired pitch angle θ d and the desired roll angle φ d through control allocation. Let The control allocation expression is:

[0184]

[0185] Through control allocation, while obtaining the desired lift U Ld , the desired pitch angle θ d and the desired roll angle φ d can also be obtained. Combining the desired yaw angle ψ d provided externally by the nonlinear model predictive controller, the desired attitude angle vector Θ d =[φ d θ d ψ d T can be obtained.

[0186] ​Step 3: Design of the Nonlinear Model Predictive Controller for the Attitude Subsystem

[0187] The NMPC of the attitude subsystem can be described by the following nonlinear programming problem:

[0188]

[0189] For the objective function J a , similar to the position subsystem, it is designed as a quadratic form based on the attitude angle deviation vector and the torque vector , where P a and Q a are designable positive definite matrices. For the equality constraint conditions, on the one hand, they include the kinematic and dynamic equations of the attitude subsystem; on the other hand, they include the initialization of assigning the current moment state to the initial moment of the prediction time domain. For the inequality constraints, on the one hand, there are saturation constraints on the torque itself. On the other hand, under the action of the global sliding mode auxiliary control law (10) of the attitude subsystem, the attitude subsystem satisfies:

[0190]

[0191] In the above formula, is the Lyapunov function, is its derivative; α is the minimum element of the set composed of all diagonal elements of λ a and Λ a . It can be seen from equation (18) that the Lyapunov function V a will converge exponentially to 0. Therefore, to make the nonlinear model predictive controller of the attitude subsystem enable the Lyapunov function V a to converge at a speed not slower than that of the auxiliary control law, and since the obtained only retains as the control quantity at the current moment, therefore, it is necessary to add as the contraction constraint of the obtained .

[0192] 4. Evaluation of the Pose Control Effect of the Quadrotor UAV

[0193] In this section, simulation experiments will be carried out through two different working conditions to verify the superiority of the method proposed in this patent in terms of dynamic performance and control accuracy compared with the traditional global sliding mode control method.

[0194] The relevant parameters of the quadrotor UAV used in the simulation are shown in Table 1, and the relevant parameters of the auxiliary control law and NMPC are shown in Table 2.

[0195] Table 1 Relevant Parameters of the Quadrotor UAV

[0196]

[0197] Table 2 Parameters related to the global sliding mode auxiliary control law and the non - linear model predictive controller

[0198]

[0199]

[0200] In the above table, h is the prediction period, ΔT is the simulation step size, and the relationship between the prediction duration T and the two is T = h·ΔT. In addition, the initial states of the system are all set to 0.

[0201] For the performance index, the root - mean - square error (RMSE) is used for comparison in this section, and its expression is:

[0202]

[0203] Step 1: Planar figure - eight trajectory tracking

[0204] In this trajectory tracking experiment, the desired trajectory equation and the desired yaw angle are respectively:

[0205]

[0206] The simulation images of working condition 1 are shown by Figure 5 and Figure 6 In the legend, "Desired" represents the desired trajectory; "NMPC" represents the actual trajectory of the quadrotor UAV under the method proposed in this patent; "GSMC" represents the actual trajectory of the quadrotor UAV under the traditional global sliding mode method. It can be seen from Figure 5 and Figure 6 that the use of the method proposed in this patent can significantly improve the response speed. Taking the method proposed in this patent as the controller, the quadrotor UAV's tracking of the trajectory is almost delay - free, while taking the traditional global sliding mode method as the controller, the actual trajectory of the quadrotor UAV converges to near the desired trajectory at 6.7 s. In addition, in terms of accuracy, the RMSE of the method proposed in this patent is 0.0177, while the RMSE of the traditional global sliding mode method is 0.0491, with a 177.4% improvement.

[0207] Step 2: Space helix trajectory tracking

[0208] In this trajectory tracking experiment, the desired trajectory equation and the desired yaw angle are respectively:

[0209]

[0210] The simulation images of working condition 2 are shown by Figure 7 and Figure 8As shown. Similar to the previous set of simulation experiments, using the traditional global sliding mode method as the controller, the quadrotor UAV can converge to the vicinity of the desired trajectory at about 4.5 s, while the method proposed in this patent hardly consumes time. In terms of accuracy, the RMSE of the method proposed in this patent is 0.0271, while the RMSE of the traditional global sliding mode method is 0.1014, an improvement of 274.2%.

[0211] In the description of this specification, the description referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples. Furthermore, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" can explicitly or implicitly include at least one of such features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise specifically and clearly defined. Any process or method description shown in the flowchart or described in other ways herein can be understood to represent a module, segment, or part of code including one or more N executable instructions for implementing a customized logical function or process, and the scope of the preferred embodiments of the present invention includes additional implementations, where the functions can be executed in a substantially simultaneous manner or in a reverse order according to the involved functions, rather than in the order shown or discussed, which should be understood by those skilled in the art to which the embodiments of the present invention belong. The logic and / or steps represented in the flowchart or described in other ways herein, for example, can be considered as a sequenced list of executable instructions for implementing a logical function, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or in combination with these instruction execution systems, apparatuses, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection part (electronic device) having one or N wirings, a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM).In addition, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation or other suitable processing if necessary, and then stored in a computer memory. It should be understood that various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having suitable combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0212] The above is only a preferred embodiment of a global sliding mode based attitude control method for a quadrotor UAV. The protection scope of a global sliding mode based attitude control method for a quadrotor UAV is not limited to the above embodiments. Any technical solutions falling within this concept belong to the protection scope of the present invention. It should be noted that for those skilled in the art, several improvements and variations made without departing from the principle of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A pose control method for a quadrotor UAV based on global sliding mode, characterized in that: The method includes the following steps: Step 1: Construct a quadrotor UAV model and obtain the nonlinear state-space description of the quadrotor UAV; Step 2: Design a global sliding mode auxiliary control law according to the constructed model; Step 3: Establish a nonlinear model predictive controller based on the output of the position subsystem controller to control the pose of the quadrotor UAV; Step 4: Evaluate the control effect of the quadrotor UAV pose.

2. The method according to claim 1, characterized in that: The specific content of Step 1 is as follows: Construct a quadrotor UAV motion model, which is represented by the following formula: Among them, the states and input variables of the quadrotor UAV dynamic model include: p = [x y z] T is the UAV position vector; is the UAV velocity vector in the ground coordinate system; Θ = [φ θ ψ] T is the UAV attitude angle vector; b ω = b ω x b ω y b ω z T is the UAV attitude angular velocity vector; U L is the lift provided by the four rotors; τ = [τ x τ y τ z T is the torque vector provided by the rotors; m is the mass of the quadrotor UAV, g is the acceleration due to gravity, J = diag(J x , J y , J z ) is the body inertia matrix.​​ 3. According to the method described in claim 2, the feature is: Convert formula 1 into vector form and decompose it into a position subsystem and an attitude subsystem, which is represented by the following formula: where G = [00g] T , and for the matrices W(Θ), C( b ω) and the virtual control vector u, they are respectively:

4. The method according to claim 3, characterized in that: The specific content of Step 2 is as follows: Step 2.1: Design the control law of the position subsystem, which is represented by the following formula: where \(u\) is the virtual control vector of the position subsystem corresponding to Equation (7); \(G\) is a known parameter vector; is the desired acceleration vector; \(e\) p = \(p - p\) d is the position deviation vector is the velocity deviation vector; is the sliding mode surface of the position subsystem, where \(\lambda\) p = diag(\(\lambda\) x , \(\lambda\) y , \(\lambda\) z ), where the elements \(\lambda\) x , \(\lambda\) y , \(\lambda\) z are designable parameters and satisfy \(\lambda\) x , \(\lambda\) y , \(\lambda\) z > 0; \(\Lambda\) p = diag(\(a\) x , \(a\) y , \(a\) z ), where the elements \(a\) x , \(a\) y , \(a\) z are designable parameters and satisfy \(a\) x , \(a\) y , \(a\) z > 0; \(k\) p = diag(\(k\) x , \(k\) y , \(k\) z ); Similarly, \(k\) x , \(k\) y , \(k\) z are designable parameters and satisfy \(k\) x , \(k\) y , \(k\) z > 0; For the sign function sgn(·), it is expressed by the following formula: Step 2.2: Design the control law expression of the attitude subsystem, which is represented by the following formula: where τ = [τ x τ y τ z T is the torque vector; J is a known parameter matrix; is the second derivative vector of the desired attitude angle; e a = Θ - Θ d is the attitude angle deviation vector; is the attitude angle derivative deviation vector; is the attitude subsystem sliding mode surface, where λ a = diag(λ φ , λ θ , λ ψ ), where the elements λ φ , λ θ , λ ψ are designable parameters and satisfy λ φ , λ θ , λ ψ > 0; Λ a = diag(a φ , a θ , a ψ ), where the elements a φ , a θ , a ψ are designable parameters and satisfy a φ , a θ , a ψ > 0; k a = diag(k φ , k θ , k ψ ), similarly, k φ , k θ , k ψ are designable parameters and satisfy k φ , k θ , k ψ > 0. For the matrices W -1 (Θ), are respectively:​ 5. The method according to claim 4, wherein: The specific content of Step 3 is as follows: Step 3.1: Describe the NMPC of the position subsystem as a nonlinear programming problem, which is represented by the following formula: where the superscript "^" represents variables in the prediction horizon, and P p and Q p are designable positive definite matrices, and T is the prediction length; Since the virtual control quantity and physically represent the accelerations provided by the rotors in the three-axis directions in the ground coordinate system. Since 0 ≤ U L ≤ U Lmax , and according to Newton's second law, we have: Obtain As an inequality constraint, under the action of the global sliding mode auxiliary control law formula 8 of the position subsystem, the position subsystem satisfies: Among them, is the Lyapunov function, is its derivative; β is the minimum element of the set composed of all diagonal elements of λ p and Λ p ; Step 3.2: Since the output of the position subsystem controller is a virtual control quantity it is mapped to the desired lift force U Ld , the desired pitch angle θ d and the desired roll angle φ d by control allocation. Let the control allocation expression be: By controlling the distribution, while obtaining the desired lift U Ld it is also possible to obtain the desired pitch angle θ d and the desired roll angle φ d . Combining with the desired yaw angle ψ d provided externally by the non - linear model predictive controller, the desired attitude angle vector Θ d =[φ d θ d ψ d T ;​ Step 3.3: Describe the NMPC of the attitude subsystem as a nonlinear programming problem, which is represented by the following formula: Among them, P a and Q a are positive definite matrices that can be designed; Under the action of the global sliding mode auxiliary control law formula 10 of the attitude subsystem, the attitude subsystem satisfies: wherein, is a Lyapunov function, is its derivative; α is the minimum element of the set composed of all diagonal elements of λ a and Λ a .

6. According to the method described in claim 5, the feature is: Lyapunov function V p Exponentially converges to 0. To enable the position subsystem nonlinear model predictive controller to make the Lyapunov function V p Converge at a speed not slower than the auxiliary control law, and since the obtained Only retain As the control quantity at the current moment, add As the obtained Contraction constraint.

7. According to the method described in claim 5, the feature is: Lyapunov function V a will exponentially converge to 0. To enable the attitude subsystem non-linear model predictive controller to make the Lyapunov function V a converge at a speed not slower than the auxiliary control law, and since the only retains as the control quantity at the current moment, add as the contraction constraint obtained by solving.

8. A pose control system for a quadrotor UAV based on global sliding mode, characterized in that: The system includes: A model construction module, which constructs a quadrotor UAV model and obtains the nonlinear state-space description of the quadrotor UAV; An auxiliary control law module, which designs a global sliding mode auxiliary control law according to the constructed model; A predictive controller module, which establishes a nonlinear model predictive controller based on the output of the position subsystem controller to control the pose of the quadrotor UAV; An evaluation module, which evaluates the control effect of the quadrotor UAV pose.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, This program is executed by a processor to implement the method as claimed in claims 1-7.

10. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that: When the processor executes the computer program, it implements the method as claimed in claims 1-7.

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