CN115390574B - Four-rotor unmanned aerial vehicle attitude tracking control method, device, equipment and storage medium - Google Patents
Four-rotor unmanned aerial vehicle attitude tracking control method, device, equipment and storage medium Download PDFInfo
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Abstract
The embodiment of the invention provides a four-rotor unmanned aerial vehicle attitude tracking control method, a device, equipment and a storage medium, and relates to the technical field of unmanned aerial vehicle control. The four-rotor unmanned aerial vehicle attitude tracking control method comprises steps S1 to S3. S1, acquiring a four-rotor unmanned aerial vehicle attitude dynamics model based on improved Rodr igues parameters. S2, acquiring a preset performance model, and combining the preset performance model and the gesture dynamics model to acquire a gesture constraint dynamics model. S3, acquiring a gesture tracking control model of the quadrotor unmanned aerial vehicle based on the robust integral signal error model and the self-adaptive dynamic surface model according to the constraint dynamics model. The invention can have good tracking performance of the attitude control system under the condition that the four-rotor unmanned aerial vehicle encounters interference.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle control, in particular to a four-rotor unmanned aerial vehicle gesture tracking control method, a four-rotor unmanned aerial vehicle gesture tracking control device, four-rotor unmanned aerial vehicle gesture tracking control equipment and a storage medium.
Background
The four-rotor unmanned aerial vehicle is an aircraft with four symmetrical rotors and simple structure. The quadrotor unmanned aerial vehicle can execute various special flight actions such as vertical take-off and landing, hovering and back-off, and the like, and is widely applied to various fields of military and civil use at present. However, a quad-rotor drone is a typical under-actuated system with four inputs and six outputs, making it susceptible to interference during flight.
In order to obtain a better performance flight effect, numerous scientific researchers have designed a series of control schemes, wherein in order to solve the tracking problem of the four-rotor unmanned aerial vehicle, a series of linear control methods including a PID control method, a linear secondary regulator method, a feedback linearization method and the like are designed. However, the performance of the above-described linear control method is drastically reduced when the quadrotor unmanned aerial vehicle performs a trickplay action or encounters a disturbance. In order to solve the problem of insufficient performance of the linear control method, some nonlinear methods such as sliding mode control and backstepping control are applied to the design work of the four-rotor unmanned aerial vehicle controller;
The backstepping control method is very efficient in processing a four-rotor unmanned aerial vehicle system dynamics model with a serial structure; the sliding mode control method has the advantage that disturbances of disturbances can be effectively counteracted. However, the two control methods have disadvantages, for example, the back-step control method can generate a steep increase of items when integrating the virtual controller, resulting in problems of complex algorithm structure, difficult calculation and the like; the sliding mode control method has the problem of flutter due to the switching function item.
In view of the above, the applicant has studied the prior art and has made the present application.
Disclosure of Invention
The invention provides a four-rotor unmanned aerial vehicle attitude tracking control method, a device, equipment and a storage medium, so as to solve the technical problems.
A first aspect,
The embodiment of the invention provides a four-rotor unmanned aerial vehicle attitude tracking control method, which comprises steps S1 to S3.
S1, acquiring a four-rotor unmanned aerial vehicle attitude dynamics model based on improved Rodrigues parameters.
S2, acquiring a preset performance model, and combining the preset performance model and the gesture dynamics model to acquire a gesture constraint dynamics model.
S3, acquiring a gesture tracking control model of the quadrotor unmanned aerial vehicle based on the robust integral signal error model and the self-adaptive dynamic surface model according to the constraint dynamics model.
A second aspect,
The embodiment of the invention provides a four-rotor unmanned aerial vehicle attitude tracking control device, which comprises:
And the gesture dynamics model acquisition module is used for acquiring a gesture dynamics model of the four-rotor unmanned aerial vehicle based on the improved Rodrigues parameter.
The gesture constraint dynamics model acquisition module is used for acquiring a preset performance model, combining the preset performance model with the gesture dynamics model and acquiring the gesture constraint dynamics model.
The attitude tracking control model acquisition module is used for acquiring an attitude tracking control model of the four-rotor unmanned aerial vehicle according to the constraint dynamics model based on the robust integral signal error model and the self-adaptive dynamic surface model.
A third aspect,
The embodiment of the invention provides a four-rotor unmanned aerial vehicle attitude tracking control device, which comprises a processor, a memory and a computer program stored in the memory. The computer program is executable by the processor to implement the four-rotor unmanned aerial vehicle attitude tracking control method as described in the first aspect.
A fourth aspect,
An embodiment of the present invention provides a computer readable storage medium, which includes a stored computer program, where the computer readable storage medium is controlled to execute the gesture tracking control method of the quad-rotor unmanned helicopter according to the first aspect when the computer program runs.
By adopting the technical scheme, the invention can obtain the following technical effects:
According to the embodiment of the invention, the transient performance of the control system is ensured by designing the preset performance function, and the control system can rapidly complete the transition process and enter a steady state under the action of the preset performance function; meanwhile, the tracking error can be limited in a preset range, so that high-precision tracking performance is achieved. The robust integral signal error control method is combined, so that the uncertain quantity and external interference of the model and the buffeting problem are effectively restrained. An adaptive function is designed to further eliminate the error existing in the interference process by the robust integral signal error control method. The four-rotor unmanned aerial vehicle has good attitude control system tracking performance under the condition of encountering interference.
In order to make the above objects, features and advantages of the present invention more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a gesture tracking control method of a quad-rotor unmanned helicopter according to a first embodiment of the present invention.
Fig. 2 is a topology diagram of the control system provided by the first embodiment.
Fig. 3 is a design flow chart of the controller provided in the first embodiment.
Fig. 4-6 are waveform diagrams of tracking results of η 1、η2 and η 3, respectively (i.e., improved Rodrigues parameter output value tracking results in the attitude control system of a quad-rotor unmanned helicopter).
Fig. 7-9 are trace error value waveforms (trace error values that improve the Rodrigues parameter output under a preset performance function) for e 11、e12 and e 13, respectively.
Fig. 10 to 12 are waveform diagrams of output values of angular velocities ω 1、ω2 and ω 3, respectively (i.e., angular velocity output values in a four-rotor unmanned aerial vehicle attitude control system).
Fig. 13-15 are waveform diagrams of control inputs U 1、U2 and U 3, respectively (i.e., control inputs for a four rotor attitude control system).
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For a better understanding of the technical solution of the present invention, the following detailed description of the embodiments of the present invention refers to the accompanying drawings.
It should be understood that the described embodiments are merely some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The terminology used in the embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be understood that the term "and/or" as used herein is merely one relationship describing the association of the associated objects, meaning that there may be three relationships, e.g., a and/or B, may represent: a exists alone, A and B exist together, and B exists alone. In addition, the character "/" herein generally indicates that the front and rear associated objects are an "or" relationship.
Depending on the context, the word "if" as used herein may be interpreted as "at … …" or "at … …" or "in response to a determination" or "in response to a detection". Similarly, the phrase "if determined" or "if detected (stated condition or event)" may be interpreted as "when determined" or "in response to determination" or "when detected (stated condition or event)" or "in response to detection (stated condition or event), depending on the context.
References to "first\second" in the embodiments are merely to distinguish similar objects and do not represent a particular ordering for the objects, it being understood that "first\second" may interchange a particular order or precedence where allowed. It is to be understood that the "first\second" distinguishing aspects may be interchanged where appropriate, such that the embodiments described herein may be implemented in sequences other than those illustrated or described herein.
The invention is described in further detail below with reference to the attached drawings and detailed description:
Embodiment one:
Referring to fig. 1 to 3, a first embodiment of the present invention provides a four-rotor unmanned aerial vehicle gesture tracking control method, which can be executed by a four-rotor unmanned aerial vehicle gesture tracking control device. In particular, the steps S1 to S3 are implemented by one or more processors in the quad-rotor unmanned helicopter attitude tracking control apparatus.
It should be noted that, after a lot of experimental researches, the inventor finds that the tracking problem of the quadrotor unmanned aerial vehicle under the influence of interference has been improved well. However, the back-stepping algorithm and the sliding mode algorithm in the common control algorithm have obvious defects. The backstepping control algorithm has the problem of project expansion in the process of deriving the virtual control; the transfer function in the sliding mode control algorithm causes a buffeting problem.
S1, acquiring a four-rotor unmanned aerial vehicle attitude dynamics model based on improved Rodrigues parameters.
It will be appreciated that quaternions are often applied to attitude kinetic models describing aircraft, and have been applied to practical engineering applications today. Quaternion has many advantages such as high calculation accuracy, no singular points in the calculation, and the like. The quaternion formula is as follows:
Where q 1 denotes a scalar of the quaternion, q v＝[qv2 qv3 qv4]T denotes a vector of the quaternion, σ denotes a rotation angle, and n= [ n 1 n2 n3]T ] denotes a direction vector of the rotation axis.
In describing the attitude power model of an aircraft, quaternion has the following problems: the four quantities of quaternions are constrained and not independent. Only three independent euler angles are needed to describe in the three-dimensional space position, so that the problem of computational redundancy exists when the quaternion is used for carrying out gesture calculation.
Thus, the present invention uses the modified Rodrigues parameter method to implement three independent parameters to describe the pose. Specifically, the attitude dynamics model of the quadrotor unmanned aerial vehicle based on the improved Rodrigues parameter is:
Where η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, q v＝[qv2 qv3 qv4]T represents a vector of quaternions, q 1 represents a scalar of quaternions, σ represents a rotation angle, and n= [ n 1 n2 n3]T ] represents a direction vector of a rotation axis.
It can be appreciated that the model of the attitude dynamics of the four-rotor unmanned aerial vehicle based on the modified Rodrigues parameter method can be modified as follows:
In the method, in the process of the invention, Representing the first derivative of eta, I 3 represents an identity matrix, omega= [ omega 1 ω2 ω3]T ] represents the attitude angular velocity in the body coordinates, J represents the inertial matrix of the quadrotor unmanned aerial vehicle,/>Representing the first derivative of ω, u= [ U 1 U2 U3]T ] represents the control input quantity, d= [ D 1 D2 D3]T ] represents the total disturbance quantity including the parametric perturbation, the non-built modulus and the external disturbance quantity, η × and ω × represent the antisymmetric matrices of η and ω, respectively, as follows:
Defining auxiliary functions Wherein P (η) is bounded.
Then, the first equation of equation (3) can be rewritten as follows:
deriving the formula (5) to obtain:
where p=p (η) is a simplified representation, Is the first derivative of P,/>Representing the second derivative of η.
Multiplying both ends of the second equation in equation (3) by P (η) J -1 at the same time yields:
based on equation (5) and equation (6), equation (7) may be changed to the following form:
wherein P (η) and ω are bounded. Thus, the first and second substrates are bonded together, Is also bounded. The reason is as follows: on the premise that the control input quantity U and the disturbance quantity D are limited. It is known that the right side of equation (8) is bounded. Thus easily get,/>Is bounded.
For convenience of representation, let x 1 =η,The attitude dynamics model of the four-rotor unmanned aerial vehicle based on the improved Rodrigues parameter method can be changed into the following form:
where x 1 = η represents the output of equation (9) (i.e., the modified Rodrigues parameter vector), For the first derivative of the parameter vector,/>For the second derivative of the parameter vector,/>The symbol is abbreviated, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned plane, u= [ U 1 U2U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter disturbance, a non-built modulus, and an external disturbance variable.
In step S1, a model of the attitude dynamics of the quadrotor unmanned aerial vehicle based on the improved Rodrigues parameters is established. The method considers the structural characteristics of the four-rotor unmanned aerial vehicle, factors such as interference in flight and the like, compares the characteristics of a quaternion method and a method for improving the Rodrigues parameter, and obtains a four-rotor unmanned aerial vehicle attitude dynamics model based on the improved Rodrigues parameter.
S2, acquiring a preset performance model, and combining the preset performance model and the gesture dynamics model to acquire a gesture constraint dynamics model.
In particular, ensuring good transient performance is a significant effect in order to achieve high performance tracking performance. Therefore, the transient performance of the control system is ensured by designing a preset performance function for compensating the tracking error of the control system. Under the action of a preset performance function, the control system can rapidly complete the transition process and enter a steady state; meanwhile, the tracking error can be limited in a preset range, so that high-precision tracking performance is achieved.
On the basis of the above embodiment, in an alternative embodiment of the present invention, step S2 specifically includes steps S21 to S25.
S21, acquiring a first tracking error model e 1＝x1-x1d according to the gesture dynamics model.
Specifically, defining the tracking expected value as x 1d, and setting that the first derivative and the second derivative of x 1d exist, the tracking error of the control system can be obtained:
e1＝x1-x1d (10)
Where e 1 is the tracking error, x 1 =η is the output of the gesture dynamics model, and x 1d is the tracking desire.
S22, acquiring a preset performance model, and constructing an error constraint model according to the preset performance model and the first tracking error modelWherein, the preset performance model is: /(I)
Specifically, to ensure that the tracking error e 1 is constrained within a specified performance range, a specific preset performance constraint is defined as follows:
Wherein, rho is more than 0 and less than or equal to 1, the specific numerical value is required to be finally determined after continuous debugging in the simulation process, a numerical value is manually set, a constant value is represented in the formula derivation process, and a coefficient before a certain variable is represented. Representing a monotonically decreasing preset performance function expressed as/>It can be seen that Values representing the preset performance model at t=0,/>The value of the preset performance model when the time approaches infinity is represented, and e -lt represents an exponential function based on e.
S23, converting the first tracking error model with the constraint preset performance into a second tracking error model without the constraint preset performance according to the error constraint modelWherein/>
Specifically, because the preset performance condition (11) has a limitation of complex calculation, in order to avoid the problem, an equivalent unconstrained preset performance condition is used to represent the attitude tracking error of the quadrotor unmanned aerial vehicle, and a specific formula is as follows:
Where e 1 is the tracking error, Representing a monotonically decreasing preset performance function, z 1 representing the conversion error between the constrained preset performance function to the unconstrained performance function, and S (z 1) representing a strictly increasing smooth function, the specific formula is as follows:
Wherein e is a natural base.
The performance condition of the function S (z 1) is set as follows:
S24, obtaining a conversion error from constrained preset performance function to unconstrained performance function conversion according to the second tracking error model
Specifically, based on the equation (12) and the equation (13), the conversion error z 1 can be expressed by the following equation:
Where e 1 is the tracking error, Representing a monotonically decreasing preset performance function,
The derivative calculation is carried out on the formula (14), and the following can be obtained:
S25, combining the conversion error and the attitude dynamics model to obtain an attitude constraint dynamics model:
Specifically, in order to introduce a preset performance function into the control system and to perform tracking performance of the constraint control system, a first formula in the attitude control system (9) may be replaced by an equivalent formula (15), specifically as follows:
In the method, in the process of the invention, The first derivative of the conversion error z 1, e 1, tracking error, p constant,/>For presetting the performance function,/>Representing the first derivative of the parameter vector eta,/>To track the first derivative of the desired x 1d,/>For presetting the first derivative of the performance function,/>Representing the second derivative of the parameter vector eta,/>In short, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned plane, u= [ U 1 U2 U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter disturbance, a non-built modulus, and an external disturbance variable.
In step S2, a preset performance function is designed, so that it is very significant to ensure good transient performance in order to achieve high-performance tracking performance. To ensure that the attitude tracking error can be restricted to a predetermined performance range, a specific performance-defining condition is set. And combining a preset performance function into the four-rotor unmanned aerial vehicle attitude dynamics model through unconstrained conversion.
S3, acquiring a gesture tracking control model of the quadrotor unmanned aerial vehicle based on the robust integral signal error model and the self-adaptive dynamic surface model according to the constraint dynamics model.
Specifically, in order to ensure tracking performance and robust performance of the unmanned aerial vehicle attitude control system under the conditions of uncertain quantity and external interference, a composite control scheme combining a self-adaptive dynamic surface method (dynamic surface technique, DSC) and a robust integral signal error method (robust integral of the sign of the error, RISE) is provided. The dynamic surface control algorithm can effectively avoid the problem of project expansion by applying a first-order filter; the continuous robust integral signal error control method can effectively inhibit interference and ensure gradual stability under the condition of avoiding buffeting.
On the basis of the above embodiment, in an alternative embodiment of the present invention, step S3 specifically includes steps S31 to S34.
S31, constructing a first Lyapunov model according to the conversion error, and constructing a virtual control law by taking the first derivative of the first Lyapunov model as a target that the first derivative is smaller than or equal to zero
In particular, for ease of representation of the Lyapunov function, the conversion error z 1 of the system (16) is defined as,
Z1＝z1 (17)
Deriving the formula Z 1 to obtain
Wherein e 1 is tracking error, ρ is constant,For presetting the performance function,/>Representing the first derivative of the parameter vector eta,/>To track the first derivative of the desired x 1d,/>Is the first derivative of the preset performance function.
Definition of Lyapunov function V 1:
deriving equation (19) to obtain
To ensure Lyapunov functionThe following virtual control laws are defined:
In the method, in the process of the invention, For the input of the first order low pass filter, c 1 represents a constant, Z 1 is a shorthand representation of the conversion error,To track the first derivative of the desired x 1d, e 1 is the tracking error,/>For the preset performance function/>Is a first derivative of (a). The specific numerical value of c 1 is determined finally after continuous debugging according to the initial conditions of simulation and the constraint relation among different design constants in the simulation process; a constant value is represented in the formula derivation process, representing a coefficient before a certain variable.
S32, constructing a first-order low-pass filter according to the virtual control law
Specifically, the output quantity of the first-order low-pass filter is set to be beta 2 and the input quantity is set to beThe expression can be obtained:
Where τ 2 represents a constant, The output of the first order low pass filter is the first derivative of beta 2. The specific numerical value of τ 2 is determined finally after continuous debugging according to the initial simulation condition and the constraint relation among different design constants in the simulation process; a constant value is represented in the formula derivation process, representing a coefficient before a certain variable.
The error of the first order low pass filter is thus:
deriving the formula (23) to obtain:
The design assistance function is as follows:
where L 2 represents a continuous function.
Based on the formula (25) and the formula (24), the following inequality can be obtained:
S33, constructing a third tracking error model Z 2＝x2-β2 according to the first-order low-pass filter and the attitude constraint dynamics model.
Specifically, the tracking error defining the second equation in equation (16) is:
Z2＝x2-β2 (27)
In the method, in the process of the invention, The first derivative of the parameter vector eta, beta 2, represents the output of the first order low pass filter as beta 2
S34, constructing a second Lyapunov model according to the third tracking error model, and constructing a posture tracking control model by taking the first derivative of the second Lyapunov model as a target that is smaller than or equal to zero
Specifically, deriving the formula (27) results in:
Where μ represents the error amount between the error term and the disturbance variable of the robust integral signal, and the first derivative thereof Is bounded, F is expressed as a robust integral signal error method term, and the specific formula is as follows
Where k 1 and k 2 represent constant values, respectively, and Z 2 is the tracking error defining the second equation in equation (16). The specific numerical values of k 1 and k 2 are determined finally after continuous debugging according to the initial conditions of simulation and the constraint relation among different design constants in the simulation process; a constant value is represented in the formula derivation process, representing a coefficient before a certain variable.
Defining Lyapunov function V 2 as
Deriving the formula (30) to obtain
To ensure thatDefine control law U as
Wherein J is an inertial matrix of the quadrotor unmanned aerial vehicle,Is expressed in shorthand, eta= [ eta 1 η2 η3]T ] represents a modified Rodrigues parameter vector, I 3 represents an identity matrix, eta × represents an antisymmetric matrix of eta,Representing the first derivative of the parameter vector eta,/>For robust integral signal error,/>The first derivative of the output beta 2, c 2, is a constant,/>, which is a first order low pass filterAn estimated value expressed as an error amount μ. The specific numerical value of c 2 is determined finally after continuous debugging according to the initial conditions of simulation and the constraint relation among different design constants in the simulation process; a constant value is represented in the formula derivation process, representing a coefficient before a certain variable.
Design ofThe adaptive function of (2) is:
Where k 3 represents a constant value and Z 2 is the tracking error defining the second equation in equation (16). The specific numerical value of k 3 is determined finally after continuous debugging according to the initial simulation conditions and the constraint relation among different design constants in the simulation process; a constant value is represented in the formula derivation process, representing a coefficient before a certain variable.
As shown in fig. 2 and 3, on the basis of the embodiment, in an alternative embodiment of the present invention, the method for controlling posture tracking of a quad-rotor unmanned helicopter further includes step S4.
And S4, combining the gesture tracking controller with the gesture constraint dynamics model, so that gesture tracking control of the four-rotor unmanned aerial vehicle is realized.
Specifically, the gesture tracking controller and the gesture constraint dynamics model are combined to form a topological structure shown in fig. 2 and 3, so that gesture tracking control of the four-rotor unmanned aerial vehicle is realized.
It can be understood that the gesture tracking control method of the four-rotor unmanned aerial vehicle is mainly divided into three parts,
The method comprises the following steps of (1) establishing a four-rotor unmanned aerial vehicle attitude dynamics model based on improved Rodrigues parameters: comparing the characteristics of a quaternion method and a method for improving the Rodrigues parameter by considering the structural characteristics of the four-rotor unmanned aerial vehicle, factors such as interference in flight and the like, and obtaining a four-rotor unmanned aerial vehicle attitude dynamics model based on the improved Rodrigues parameter;
The second part, preset the design of the performance function: in order to achieve high performance tracking performance, it is very significant to ensure good transient performance. To ensure that the attitude tracking error can be restricted to a predetermined performance range, a specific performance-defining condition is set. And combining the preset performance function into the four-rotor unmanned aerial vehicle attitude dynamics model through unconstrained conversion.
And the third part is used for providing a controller design based on the dynamic surface technology and the high-precision tracking of the robust integral signal error by combining with a preset performance function. Deriving a preset performance function conversion error, and combining with a Lyapunov function to derive a virtual control law; the output quantity of the first-order low-pass filter and the Lyapunov function are combined, and a four-rotor unmanned aerial vehicle attitude tracking controller is deduced; in order to further eliminate the influence of the interference quantity on the tracking performance, the four-rotor unmanned aerial vehicle attitude tracking controller is finally obtained by combining an adaptive method and a robust integral signal error technology.
Specifically, a four-rotor unmanned aerial vehicle attitude tracking controller is designed by introducing a dynamic surface control method and a robust integral signal error control method based on a Rodrigues parameter method and combining a preset performance function; ensuring that all signals of the closed loop control system are bounded and that the control system is consistent and ultimately bounded. Meanwhile, the method has good tracking performance and anti-interference capability, and can realize high-precision tracking control of the gesture of the four-rotor unmanned aerial vehicle under the condition that model uncertain items and external interference exist.
Based on the above embodiment, the stability of the controller will be analyzed as follows.
Stability analysis was as follows:
The definition of the tight set is as follows:
Ω2＝{(z1,Z2,y2)：||Z1||2+||Z2||2+||y2||2≤ξ2} (34)
Where ζ 1、ξ2 represents a given positive constant.
Theorem:
Consider the case where the control system (16) encounters disturbances, as well as virtual control amounts (21) and (32) designed. Under bounded constraints, there are constants c i (i=1, 2) and τ 2, when c i (i=12) and τ 2 meet the following conditions,
Wherein γ represents a design constant, wherein the variables are/>
The signals of the overall closed-loop control system can be made bounded and the control system is always ultimately bounded; meanwhile, under the action of a preset performance function, the tracking error can be limited in a preset performance range.
And (3) proving:
Virtual control amount according to tracking error Z 1、Z2 Filter error y 2 and estimation error/>The Lyapunov function is defined as follows:
in the method, the error amount is estimated
When v=ζ 2, it is known that L 2 is bounded and that |l 2 | is at a maximum value L 2 max within the immediate range Ω 1×Ω2. For ease of calculation, the derivative of equation (28) may be obtained as follows:
From the Young's inequality, the following relationship can be obtained
Setting:
substituting equation (37) into equation (36) yields the following inequality:
Wherein V' = ||Z 1||2+||Z2||2+||y2||2
When V' =ζ 1, defineCan be deduced/>Meanwhile, V' (0) is less than or equal to ζ 2,V′(t)≤ξ2, and when t is more than 0, the V is/>The following inequality is available:
Thus, all signals within a closed loop system are bounded; by properly adjusting c i (i=1, 2) and τ 2, the tracking error Z 1 can be converged to an arbitrarily small value; the four-rotor unmanned aerial vehicle attitude control system can be kept stable under the action of the controller designed herein. When c i (i=1, 2) and τ 2 meet the design conditions, it can also be derived that the tracking error e 1＝x1-x1d is always limited within preset performance limits.
Stability analysis shows that the designed control scheme can ensure that all signals of the closed-loop control system are bounded, and the control system is consistent and finally bounded.
Finally:
In order to verify the effectiveness of the four-rotor unmanned aerial vehicle attitude tracking control method based on the Rodrigues parameter method, a four-rotor unmanned aerial vehicle attitude tracking control system is built on a MATLAB simulation platform, the effectiveness of the method in the aspect of attitude tracking is verified through different preset interference amounts and tracking expected values, and the tracking precision of a traditional dynamic surface control method, a traditional sliding mode control method and a dynamic surface sliding mode control method is compared and analyzed, so that the tracking performance and the anti-interference performance of an algorithm are verified.
The invention provides a four-rotor unmanned aerial vehicle attitude tracking control method based on a Rodrigues parameter method, which completes integrated design and verification in a MATLAB environment, and comprises the following specific processes:
(1) Main parameter setting
In order to verify the effectiveness of the four-rotor unmanned aerial vehicle attitude tracking control method based on the Rodrigues parameter method, integrated design is carried out in MATLAB, and main parameters are set as follows:
The expected tracking value of x 1 in the four-rotor unmanned aerial vehicle attitude control system (9) is set to be x 1d＝[0.8sin(t)+0.3cos(t),-0.8sin(t)-0.3cos(t),-0.5sin(t)-0.3cos(t)]T.
The initial values of x 1、x2 in the four-rotor unmanned aerial vehicle attitude control equation (9) are set to be x 1(0)＝[0.4,-0.4,-0.3]T、x2(0)＝[0,0,0]T respectively.
Considering the complexity of interference encountered by the quadrotor unmanned aerial vehicle in the flight process, the interference quantity D is set to be D= [2sin (2 t) +4cos (t), 2sin (2 t) -3cos (t), and 10sin (2 t) cos (2 t ] T.
The preset performance functions to which the control system belongs are defined as shown below (0.5-0.01) ×e -0.1t+0.01,-(0.5-0.01)×e-0.1t-0.01,(0.7-0.05)×e-0.1t +0.05, respectively.
In order to achieve the progressive smoothing tracking effect, the parameter amounts in the control method designed herein also need to be properly selected and set, so that the selected parameter amounts can meet the condition that the inequality (34) is satisfied, thereby achieving the set control target. After proper parameter setting, the main parameters of the obtained controller are as follows: c 1＝[0.1,0.15,0.12]T,c2＝[7.5,7.2,17]T.
(2) Simulation results and performance analysis
The method provided by the invention has the key point that the high-precision tracking of the four-rotor unmanned aerial vehicle gesture can be completed under the constraint of the preset tracking error performance under the condition of interference. And under the condition of setting the interference quantity, the effectiveness of the algorithm is verified through comparative analysis.
Shown in fig. 4-15 are simulation analysis results of a control system under the control method designed herein.
In fig. 4-6, the tracking effect of the improved Rodrigues parameters in the four-rotor unmanned aerial vehicle attitude control system is under the control method designed herein. As shown in the figure, three control outputs of the quadrotor unmanned aerial vehicle can quickly track the set desired value.
The tracking error results for the improved Rodrigues parameter numbers in the control system are presented in fig. 7-9. Under the action of the controller, tracking error is limited to a preset performance functionAnd/>Between them. Wherein the tracking error e 11 fluctuates in a small range between-0.03 and 0.015; tracking error e 12 fluctuates in a small range between-0.025 and 0.01; the tracking error e 13 fluctuates in a small range between-0.1 and 0.15. The tracking error result shows that the tracking effect of the quadrotor unmanned aerial vehicle can reach the set target under the control method designed in the specification. /(I)
As shown in fig. 10 to 12, simulation results of three angular velocity outputs of the quadrotor unmanned aerial vehicle are presented. As can be seen, under the action of the controller, the three angular velocities of the control system can reach around the zero value rapidly after 1 second; at the same time, in the presence of smooth increasing or decreasing disturbances, the angular velocity can be maintained near a zero value, so that the control system remains in a steady state. The control input results of the control system are shown in fig. 13 to 15.
Embodiment II,
The embodiment of the invention provides a four-rotor unmanned aerial vehicle attitude tracking control device, which comprises:
And the gesture dynamics model acquisition module is used for acquiring a gesture dynamics model of the four-rotor unmanned aerial vehicle based on the improved Rodrigues parameter.
The gesture constraint dynamics model acquisition module is used for acquiring a preset performance model, combining the preset performance model with the gesture dynamics model and acquiring the gesture constraint dynamics model.
The attitude tracking control model acquisition module is used for acquiring an attitude tracking control model of the four-rotor unmanned aerial vehicle according to the constraint dynamics model based on the robust integral signal error model and the self-adaptive dynamic surface model.
In an alternative embodiment, the gesture dynamics model is: Where η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, q v＝[qv2 qv3 qv4]T represents a vector of quaternions, q 1 represents a scalar of quaternions, σ represents a rotation angle, and n= [ n 1 n2 n3]T ] represents a direction vector of a rotation axis.
Converting a gesture dynamics model intoWhere x 1 =η is a parameter vector,/>For the first derivative of the parameter vector,/>Is the second derivative of the parameter vector,The symbol is abbreviated, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned plane, u= [ U 1 U2 U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter disturbance, a non-built modulus, and an external disturbance variable.
In an alternative embodiment, the pose constraint dynamics model acquisition module includes:
The first tracking error model obtaining unit is used for obtaining a first tracking error model e 1＝x1-x1d according to the gesture dynamics model.
The error constraint model construction unit is used for acquiring a preset performance model and constructing an error constraint model according to the preset performance model and the first tracking error modelWherein, the preset performance model is:
A second tracking error model conversion unit for converting the first tracking error model with the constraint preset performance into a second tracking error model without the constraint preset performance according to the error constraint model Wherein,
A conversion error acquisition unit for acquiring a conversion error from the constrained preset performance function to the unconstrained performance function according to the second tracking error model/>
The attitude constraint dynamics model acquisition unit is used for combining the conversion error and the attitude dynamics model to acquire an attitude constraint dynamics model:
Where e 1 is the tracking error, x 1 =η is the output of the gesture dynamics model, and x 1d is the tracking desire. For preset performance,/>To set the performance model function/>Initial value,/>For the preset performance model function/>E -lt is an exponential function based on e, 1 is the convergence rate of the preset performance function, t is the time variable, ρ is the constant, z 1 is the conversion error,/>For the first derivative of the conversion error,/>Representing the first derivative of the parameter vector eta,/>To track the desired first derivative,/>Is the first derivative of the preset property. /(I)Representing the second derivative of the parameter vector eta,/>In short, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned plane, u= [ U 1 U2U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter disturbance, a non-built modulus, and an external disturbance variable.
In an alternative embodiment, the gesture tracking control model acquisition module includes:
The virtual control law construction unit is used for constructing a first Lyapunov model according to the conversion error and constructing a virtual control law by taking the first derivative of the first Lyapunov model as a target that the first derivative is smaller than or equal to zero
A first-order low-pass filter construction unit for constructing a first-order low-pass filter according to the virtual control law
And the third tracking error model building unit is used for building a third tracking error model Z 2＝x2-β2 according to the first-order low-pass filter and the attitude constraint dynamics model.
The attitude tracking control model construction unit is used for constructing a second Lyapunov model according to the third tracking error model, and constructing an attitude tracking control model by taking the first derivative of the second Lyapunov model as a target with the first derivative being less than or equal to zero
In the method, in the process of the invention,Input to the first order low pass filter, c 1 is a constant, Z 1 is a simplified representation of the conversion error,/>To track the desired first derivative, e 1 is the tracking error,/>For preset performance,/>Is the first derivative of the preset performance, τ 2 is a constant, β 2 is the output of the first order low pass filter,/>The first derivative, Z 2, being the output of the first order low pass filter is the tracking error of the second equation in the pose-constrained dynamics model,/>First derivative representing parameter vector eta, J is inertial matrix of quadrotor unmanned aerial vehicle,/>In shorthand notation, η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, I 3 represents an identity matrix, η × represents an antisymmetric matrix of η,/>For robust integral signal error, k 1 and k 2 are constant values, c 2 is a constant,/>, respectivelyIs an estimated value of mu,/>Is/>K 3 is a constant.
In an alternative embodiment, the four rotor unmanned aerial vehicle attitude tracking control device further comprises:
and the control module is used for combining the gesture tracking controller and the gesture constraint dynamics model, so that the gesture tracking control of the four-rotor unmanned aerial vehicle is realized.
Third embodiment,
The embodiment of the invention provides a four-rotor unmanned aerial vehicle attitude tracking control device, which comprises a processor, a memory and a computer program stored in the memory. The computer program can be executed by the processor to implement the four-rotor unmanned aerial vehicle attitude tracking control method as described in the first embodiment.
Fourth embodiment,
The embodiment of the invention provides a computer readable storage medium, which comprises a stored computer program, wherein the computer readable storage medium is controlled to execute the four-rotor unmanned aerial vehicle attitude tracking control method according to the embodiment when the computer program runs.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus and method may be implemented in other manners. The apparatus and method embodiments described above are merely illustrative, for example, flow diagrams and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, functional modules in the embodiments of the present invention may be integrated together to form a single part, or each module may exist alone, or two or more modules may be integrated to form a single part.
The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, an electronic device, or a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes. It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The four-rotor unmanned aerial vehicle attitude tracking control method is characterized by comprising the following steps of:
acquiring a gesture dynamics model of the four-rotor unmanned aerial vehicle based on the improved Rodrigues parameter;
Acquiring a preset performance model, and combining the preset performance model and the gesture dynamics model to acquire a gesture constraint dynamics model;
Based on the robust integral signal error model and the self-adaptive dynamic surface model, acquiring a posture tracking control model of the quadrotor unmanned aerial vehicle according to the constraint dynamics model;
the gesture dynamics model is as follows:
Where η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, q v＝[qv2 qv3 qv4]T represents a vector of quaternions, q 1 represents a scalar of quaternions, σ represents a rotation angle, and n= [ n 1 n2 n3]T ] represents a direction vector of a rotation axis;
converting the gesture dynamics model into:
Wherein x 1 = eta is a parameter vector, For the first derivative of the parameter vector,/>Is the second derivative of the parameter vector,A shorthand symbol, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned aerial vehicle, u= [ U 1 U2 U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter disturbance, a non-built modulus, and an external disturbance variable;
acquiring a preset performance model, combining the preset performance model with the gesture dynamics model, and acquiring a gesture constraint dynamics model, wherein the method specifically comprises the following steps of:
acquiring a first tracking error model e 1＝x1-x1d according to the gesture dynamics model;
Acquiring a preset performance model, and constructing an error constraint model according to the preset performance model and the first tracking error model Wherein, the preset performance model is: /(I)
According to the error constraint model, converting the first tracking error model with constraint preset performance into a second tracking error model without constraint preset performanceWherein/>
Obtaining a conversion error from a constrained preset performance function to an unconstrained performance function according to the second tracking error model
Combining the conversion error and the attitude dynamics model to obtain an attitude constraint dynamics model:
Where e 1 is the tracking error, x 1 =η is the output of the gesture dynamics model, x 1d is the tracking desire; For preset performance,/> To set the performance model function/>Initial value,/>For the preset performance model function/>E -lt is an exponential function based on e, l is the convergence rate of the preset performance function, t is the time variable, ρ is the constant, z 1 is the conversion error,/>For the first derivative of the conversion error,/>Representing the first derivative of the parameter vector eta,/>To track the desired first derivative,/>A first derivative of a preset property; /(I)Representing the second derivative of the parameter vector eta,/>In short, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned aerial vehicle, u= [ U 1 U2U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter perturbation, a non-built modulus, and an external disturbance variable;
Based on the robust integral signal error model and the self-adaptive dynamic surface model, acquiring a gesture tracking control model of the quadrotor unmanned aerial vehicle according to the constraint dynamics model specifically comprises the following steps:
according to the conversion error, a first Lyapunov model is built, and a virtual control law is built by taking the first derivative of the first Lyapunov model as a target that the first derivative is smaller than or equal to zero
Constructing a first-order low-pass filter according to the virtual control law
Constructing a third tracking error model Z 2＝x2-β2 according to the first-order low-pass filter and the attitude constraint dynamics model;
Constructing a second Lyapunov model according to the third tracking error model, and constructing a posture tracking control model by taking the first derivative of the second Lyapunov model as a target that is smaller than or equal to zero
In the method, in the process of the invention,Input to the first order low pass filter, c 1 is a constant, Z 1 is a simplified representation of the conversion error,/>To track the desired first derivative, e 1 is the tracking error,/>For preset performance,/>Is the first derivative of the preset performance, τ 2 is a constant, β 2 is the output of the first order low pass filter,/>The first derivative, Z 2, being the output of the first order low pass filter is the tracking error of the second equation in the pose-constrained dynamics model,/>First derivative representing parameter vector eta, J is inertial matrix of quadrotor unmanned aerial vehicle,/>In shorthand notation, η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, I 3 represents an identity matrix, η × represents an antisymmetric matrix of η,/>For robust integral signal error, k 1 and k 2 are constant values, c 2 is a constant,/>, respectivelyIs an estimated value of mu,/>Is/>K 3 is a constant.
2. The method for controlling the attitude tracking of the quadrotor unmanned aerial vehicle according to claim 1, wherein after obtaining the attitude tracking control model of the quadrotor unmanned aerial vehicle according to the constrained dynamics model based on the robust integral signal error model and the adaptive dynamic surface model, further comprising:
And combining the gesture tracking controller with the gesture constraint dynamics model, so that gesture tracking control of the four-rotor unmanned aerial vehicle is realized.
3. Four rotor unmanned aerial vehicle gesture tracking control device, its characterized in that contains:
the gesture dynamics model acquisition module is used for acquiring a gesture dynamics model of the four-rotor unmanned aerial vehicle based on the improved Rodrigues parameter;
The gesture constraint dynamics model acquisition module is used for acquiring a preset performance model, combining the preset performance model with the gesture dynamics model and acquiring a gesture constraint dynamics model;
The attitude tracking control model acquisition module is used for acquiring an attitude tracking control model of the four-rotor unmanned aerial vehicle based on the robust integral signal error model and the self-adaptive dynamic surface model according to the constraint dynamics model;
the gesture dynamics model is as follows:
Where η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, q v＝[qv2 qv3 qv4]T represents a vector of quaternions, q 1 represents a scalar of quaternions, σ represents a rotation angle, and n= [ n 1 n2 n3]T ] represents a direction vector of a rotation axis;
converting the gesture dynamics model into:
Wherein x 1 = eta is a parameter vector, For the first derivative of the parameter vector,/>Is the second derivative of the parameter vector,A shorthand symbol, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned aerial vehicle, u= [ U 1 U2 U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter disturbance, a non-built modulus, and an external disturbance variable;
the attitude constraint dynamics model acquisition module comprises:
the first tracking error model obtaining unit is used for obtaining a first tracking error model e 1＝x1-x1d according to the gesture dynamics model;
an error constraint model construction unit for acquiring a preset performance model and constructing an error constraint model according to the preset performance model and the first tracking error model Wherein, the preset performance model is:
a second tracking error model conversion unit configured to convert the first tracking error model with the constrained preset performance into a second tracking error model with the unconstrained preset performance according to the error constraint model Wherein,
A conversion error acquisition unit for acquiring conversion error from constrained preset performance function to unconstrained performance function according to the second tracking error model
The attitude constraint dynamics model obtaining unit is used for combining the conversion error and the attitude dynamics model to obtain an attitude constraint dynamics model:
Where e 1 is the tracking error, x 1 =η is the output of the gesture dynamics model, x 1d is the tracking desire; For preset performance,/> To set the performance model function/>Initial value,/>For the preset performance model function/>E -lt is an exponential function based on e, l is the convergence rate of the preset performance function, t is the time variable, ρ is the constant, z 1 is the conversion error,/>For the first derivative of the conversion error,/>Representing the first derivative of the parameter vector eta,/>To track the desired first derivative,/>A first derivative of a preset property; /(I)Representing the second derivative of the parameter vector eta,/>In short, I 3 denotes an identity matrix, η × denotes an antisymmetric matrix of η, J denotes an inertial matrix of the quadrotor unmanned aerial vehicle, u= [ U 1 U2U3]T ] denotes a control input amount, and d= [ D 1 D2 D3]T ] denotes a total disturbance variable including a parameter perturbation, a non-built modulus, and an external disturbance variable;
the gesture tracking control model acquisition module comprises:
A virtual control law construction unit, configured to construct a first Lyapunov model according to the conversion error, and construct a virtual control law with a first derivative of the first Lyapunov model being equal to or less than zero as a target
A first-order low-pass filter construction unit for constructing a first-order low-pass filter according to the virtual control law
A third tracking error model building unit, configured to build a third tracking error model Z 2＝x2-β2 according to the first-order low-pass filter and the pose constraint dynamics model;
The attitude tracking control model construction unit is used for constructing a second Lyapunov model according to the third tracking error model, and constructing an attitude tracking control model by taking the first derivative of the second Lyapunov model as a target that is smaller than or equal to zero
In the method, in the process of the invention,Input to the first order low pass filter, c 1 is a constant, Z 1 is a simplified representation of the conversion error,/>To track the desired first derivative, e 1 is the tracking error,/>For preset performance,/>Is the first derivative of the preset performance, τ 2 is a constant, β 2 is the output of the first order low pass filter,/>The first derivative, Z 2, being the output of the first order low pass filter is the tracking error of the second equation in the pose-constrained dynamics model,/>First derivative representing parameter vector eta, J is inertial matrix of quadrotor unmanned aerial vehicle,/>In shorthand notation, η= [ η 1 η2 η3]T ] represents a modified Rodrigues parameter vector, I 3 represents an identity matrix, η × represents an antisymmetric matrix of η,/>For robust integral signal error, k 1 and k 2 are constant values, c 2 is a constant,/>, respectivelyIs an estimated value of mu,/>Is the adaptive function of (a)K 3 is a constant.
4. The four-rotor unmanned aerial vehicle attitude tracking control device is characterized by comprising a processor, a memory and a computer program stored in the memory; the computer program is executable by the processor to implement the four rotor unmanned aerial vehicle attitude tracking control method of any one of claims 1 to 2.
5. A computer readable storage medium, characterized in that the computer readable storage medium comprises a stored computer program, wherein the computer program when run controls a device in which the computer readable storage medium is located to execute the four-rotor unmanned aerial vehicle attitude tracking control method according to any one of claims 1 to 2.
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