CN117590864A - Fixed time self-adaptive formation control method and system for coupled multi-aircraft - Google Patents
Fixed time self-adaptive formation control method and system for coupled multi-aircraft Download PDFInfo
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Abstract
The invention relates to the technical field of self-adaptive control, and provides a fixed time self-adaptive formation control method and a system for coupling multiple aircrafts, wherein the method comprises the following steps: constructing a dynamics model of a coupling four-rotor aircraft formation system node; constructing a state error model of an aircraft node in a formation system; calculating the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft nodes to obtain a coupled aircraft formation system error model; designing a formation system controller containing a fixed time control input item according to the obtained error model of the formation system of the aircraft and combining an adaptive control strategy and a fixed time principle; and solving the controller, and converging according to the set fixed time to obtain the output of the controller. The self-adaptive compensation formation control method is adopted, so that the coupling formation system achieves the expected position and speed targets under the condition of general disturbance and within fixed time.
Description
Technical Field
The invention relates to the technical field of self-adaptive control, in particular to a fixed time self-adaptive formation control method and system for a coupled multi-aircraft.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Quadrotor aircraft are themselves under-actuated, highly nonlinear, strongly coupled, and multivariable complex systems, susceptible to internal structural and external environmental disturbances, and therefore the flying capabilities of a single aircraft system are often limited by high dependency and vulnerability on itself; the multi-aircraft system with formation control coupling can share the flying environment cognition and the flying state, and meanwhile, the formation is dynamically adjusted according to different task requirements and external environment constraints, so that the completion degree and the execution efficiency of the task are greatly improved. Furthermore, in some special application scenarios, such as target monitoring, 3D imaging, weight transportation, etc., multiple quad-rotor aircraft systems are also required to work in concert. For practical multi-aircraft formation, achieving stable operation of the system is critical. In practical applications, stability and robustness of the flight crew are critical requirements due to self-structural limitations such as model uncertainty, nonlinear dynamics, and the large amount of external disturbances present in the real flight environment.
The inventors have found in research that in existing solutions, the disturbance to the formation system has stricter assumptions, such as a norm limitation, which is impractical for the operation of the aircraft formation system in real-world environments. Moreover, the conventional massive formation schemes only consider the asymptotic formation and tracking behavior of the aircraft formation system, and do not consider the factor of the running time, namely the formation system asymptotically reaches a stable running state in an experimental environment which is not limited by time, which obviously is not in agreement with the practical application of the aircraft formation. Finite time theory was introduced into the design of control schemes and has been demonstrated to enable the system to reach steady state faster with a great deal of effort. But limited time control requires determining the initial conditions of the system, and in practical applications the initial state of the system is not always known.
Disclosure of Invention
In order to solve the problems, the invention provides a fixed time self-adaptive formation control method and a system for coupling multiple aircrafts, and the self-adaptive compensation formation control method is adopted to enable the coupling formation system to reach expected positions and speed targets under the condition of general disturbance and within fixed time.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
one or more embodiments provide a method of fixed time adaptive formation control for coupling multiple aircraft, comprising:
constructing a dynamics model of a coupled four-rotor aircraft formation system node by considering the existence of continuous disturbance and control input influence;
according to the set expected track and the constructed dynamic model, constructing a state error model of an aircraft node in a formation system, and establishing a formation communication topological structure;
calculating the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft nodes to obtain a coupled aircraft formation system error model;
designing a formation system controller containing a fixed time control input item according to the obtained error model of the formation system of the aircraft and combining an adaptive control strategy and a fixed time principle; and solving the controller, and converging according to the set fixed time to obtain the output of the controller.
One or more embodiments provide a fixed time adaptive formation control system for coupling multiple aircraft, comprising:
a first construction module: is configured to construct a dynamics model of coupled quad-rotor aircraft formation system nodes in consideration of the presence of continuous disturbance and control input effects;
a state error calculation module: the system comprises a system and a method, wherein the system is configured to construct a state error model of an aircraft node in a formation system according to a set expected track and a constructed dynamic model, and establish a formation communication topological structure;
and a second construction module: the system comprises a coupling aircraft formation system error model, a communication-capable aircraft node and a communication-capable aircraft node, wherein the coupling aircraft formation system error model is configured to calculate the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft node;
and (3) constructing and solving a module by a controller: the system comprises a formation system controller, a control system controller and a control system controller, wherein the formation system controller is configured to design a formation system controller containing a fixed time control input item according to the obtained error model of the formation system of the aircraft in combination with an adaptive control strategy and a fixed time principle; and solving the controller, and converging according to the set fixed time to obtain the output of the controller.
An electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the steps in the method for fixed time adaptive formation control of coupled multi-aircraft described above.
A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the method for fixed time adaptive formation control of coupled multi-aircraft described above.
Compared with the prior art, the invention has the beneficial effects that:
the invention adopts an adaptive control strategy to restrain the negative influence of internal and external disturbance on the system operation in the actual flight process. Meanwhile, the aircraft formation system can reach a stable state more quickly by using a fixed time control strategy, and the fixed time formation controller can effectively prevent the control process of the aircraft formation system from being influenced by the initial state of the system, reach a stable running state in a computable fixed time, and enhance the robustness of the system.
The method designed by the invention has stronger stability and robustness, can process negative effects caused by general disturbance, and ensures that the coupled aircraft formation system performs predetermined track tracking within a computable fixed time, thereby having practical significance.
The advantages of the present invention, as well as additional aspects of the invention, will be described in detail in the following detailed examples.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a flow chart of a formation control method of embodiment 1 of the present invention;
FIG. 2 is a schematic illustration of the location of the aircraft fleet system in a ground coordinate system in accordance with embodiment 1 of the present invention;
figure 3 (a) is a schematic illustration of a coupled quad-rotor aircraft fleet configuration according to embodiment 1 of the present invention;
fig. 3 (b) is a topology of the communication structure of the coupled quad-rotor aircraft queuing system of embodiment 1 of the present invention;
FIG. 4 is a state diagram of the position trajectories of three quad-rotor aircraft followers and one virtual leader in 3D space for a simulation example of embodiment 1 of the present invention;
FIG. 5 is a simulation example of embodiment 1 of the present inventionA position trajectory state diagram of three quad-rotor aircraft followers and one virtual leader in a plane;
FIG. 6 (a) is a view of the position distance between the leader and follower in the queuing system of the simulation example of embodiment 1 of the present inventionA map of position trajectories on the axis;
FIG. 6 (b) is a view of the position distance between the leader and follower in the queuing system of the simulation example of embodiment 1 of the present inventionA map of position trajectories on the axis;
FIG. 6 (c) is a view of the position distance between the leader and follower in the queuing system of the simulation example of embodiment 1 of the present inventionA map of position trajectories on the axis;
FIG. 7 (a) is a system for enqueuing a simulation example of embodiment 1 of the present inventionIrrespective of the distance of position between the leader and followerA map of position trajectories on the axis;
FIG. 7 (b) is a diagram showing a simulation example of embodiment 1 of the present invention in which the position distance between the leader and follower is not considered in the queuing systemA map of position trajectories on the axis;
FIG. 7 (c) is a diagram showing a simulation example of embodiment 1 of the present invention in which the position distance between the leader and follower is not considered in the queuing systemA map of position trajectories on the axis;
figure 8 is a control input diagram of a coupled quad-rotor aircraft queuing system according to a simulation example of embodiment 1 of the present invention;
figure 9 is an estimate of adaptive parameters in a coupled quad-rotor aircraft fleet system controller in accordance with a simulation example of embodiment 1 of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof. It should be noted that, in the case of no conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The embodiments will be described in detail below with reference to the accompanying drawings.
Technical term interpretation:
the self-adaptive control means that the control system can adapt to the changes of dynamic or external disturbance and the like in the system by estimating and adjusting the control parameters of the system on line.
The formation control means that a plurality of single agent systems form a coupling cluster to carry out cooperative control so as to avoid high dependence and vulnerability on the single agent and improve the overall fault tolerance and robustness of the formation system;
the invention provides a robust self-adaptive formation compensation control method for a coupled four-rotor aircraft system within a fixed time, and aims to explore robust fixed time formation control and anti-interference performance of the aircraft formation system. In order to solve the defects of the prior art, the invention adopts the self-adaptive control technology to restrain the negative influence of internal and external disturbance on the system operation in the actual flight process. The use of a distributed leader-follower framework, while using a fixed time control strategy, enables the aircraft queuing system to reach steady state faster, enhancing the robustness of the system. Specific examples are described below.
Example 1
In one or more embodiments, as shown in fig. 1 to 9, a method for controlling a fixed time adaptive formation of a coupled multi-aircraft includes the following steps:
step 1, considering the existence of continuous disturbance and control input influence, constructing a dynamics model of a coupling four-rotor aircraft formation system node;
step 2, constructing a state error model of the aircraft nodes in the formation system according to the set expected track and the constructed dynamic model, and establishing a formation communication topological structure;
step 3, calculating the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft nodes to obtain a coupled aircraft formation system error model;
step 4, designing a coupled aircraft formation system controller containing a fixed time control input item according to the obtained aircraft formation system error model and combining an adaptive method and a fixed time principle; solving the controller, and converging according to the set fixed time to obtain the output of the controller;
specifically, solving the controller to obtain the position and the speed of each aircraft, so that the coupled multi-aircraft formation system performs predetermined track tracking in a fixed time;
the present embodiment employs adaptive control techniques to suppress the negative effects of internal and external disturbances on system operation during actual flight. Meanwhile, the aircraft formation system can reach a stable state more quickly by using a fixed time control strategy, and the fixed time formation controller can effectively prevent the control process of the aircraft formation system from being influenced by the initial state of the system, reach a stable running state in a computable fixed time, and enhance the robustness of the system.
In step 1, a dynamic model of the coupled four-rotor aircraft formation system is established by considering the influence of a nonlinear dynamic system, continuous state-related disturbance and formation control input signals in the coupled Euler-Lagrange system, namely, by consideringThe formation system is formed by the aircraft nodes and has continuous disturbance and control input influence, and a second-order dynamic model of the aircraft nodes is expressed by a kinetic equation:
（1）
wherein,representing the presentation by a leader and +.>A.about.in a queuing system consisting of four-rotor aircraft>A plurality of aircraft nodes; />Representation->Time;
respectively the +.>The individual aircraft nodes are +.>Shaft、/>Shaft、/>Position coordinates in the axial direction;
respectively the +.>The individual aircraft nodes are +.>Shaft、/>Shaft、/>A speed state in the axial direction;
、/>、/>respectively the +.>The individual aircraft nodes are +.>Shaft、/>Shaft、/>A control input in the axial direction;
unmanned aerial vehicle formation system in ground coordinate systemShaft、/>Shaft、/>The axial position is schematically shown in fig. 2, and three follow-up unmanned aerial vehicles are adopted by one leader, and the follower 1, the follower 2 and the follower 3.
、/>、/>Respectively refer to->The individual aircraft nodes are->Shaft、/>Shaft、/>An air resistance coefficient in the axial direction; />Refer to->Mass of individual aircraft->Gravitational acceleration.
It should be noted that it is assumed herein that all four-rotor aircraft considered in the fleet control design have the same air drag coefficient and mass. To facilitate subsequent calculations, the following will be、/>、/>Respectively expressed as->、/>、/>Here use is made of capitalized +.>Thus +.>Shaft、/>Shaft、/>Distinguishing the speed states in the axial direction;
indicate->The individual aircraft nodes are +.>Shaft、/>Shaft、/>Disturbance in the position in the axial direction;
further, according to the speed state of the aircraft and the numerical value of the control input, determining the value range of disturbance to the aircraft:
（2）
wherein,、/>、/>，/>、/>、/>，/>、/>、/>the disturbance parameters to be estimated by the adaptive law are unknown positive constants.
The present embodiment simulates the actual system operating environment by assuming that the disturbance satisfies the more general assumption of control inputs, speed state correlations, and partial norms bounding, and may further design a controller that can eliminate the general disturbance, thus making it more practical.
In step 2, setting a desired track, using a leader-follower framework, setting a virtual aircraft node as a leader, taking the own flight state of the leader as a desired target of other aircrafts in the system, and when the state information of the leader changes, changing the own flight state of the rest of the follower to realize tracking and form a control strategy of formation so as to reduce the number of aircrafts communicating with each other in the system, simplify the formation structure and save communication resources.
The leader-follower formation control scheme of the present embodiment is capable of handling the more general anti-jamming problem of input, state-related disturbances.
In step 2, an error model of the aircraft node in the formation system is constructed, comprising the following steps:
s201, calculating expected position distances between every two aircraft nodes according to the set expected track;
definition of the definition、/>、/>And their derivatives as guiding coupling quadrotor formation systems in the coordinate system, respectively>Shaft、/>Shaft、/>Desired position and velocity signals of the axial run. Set->、/>、/>Two aircraft nodes in formation +.>And->Respectively at->Shaft、/>Shaft、/>The desired positional distance that the axial direction needs to be maintained. The desired position distance is in vector form +.>The representation then represents the desired positional distance between the aircraft nodes in the coupled quad-rotor aircraft fleet in three-dimensional space, as follows:
（3）
wherein,、/>、/>refers to aircraft nodes in formation +.>Respectively at->Shaft、/>Shaft、/>A desired position in the axial direction;
、/>、/>refers to aircraft nodes in formation +.>Respectively at->Shaft、/>Shaft、/>A desired position in the axial direction; />、/>Representing the vector form.
S202, calculating the position error between every two aircraft nodes with a communication relationship according to the position coordinates of the aircraft nodes and the calculated expected position distance; calculating the speed error between every two aircraft nodes with communication relation according to the speed state of the aircraft nodes;
specifically, the position error and the speed error between the aircraft nodes are the aircraft node errors in the set formation system, namely the error model of the aircraft nodes, and the specific formula is as follows:
（4）
wherein,indicate->Aircraft and->Communication relationships between individual aircraft;
representation oftTime of day formation System +.>The individual aircraft nodes are in +.>Position error in the axial direction;
representation oftTime of day formation System +.>The individual aircraft nodes are in +.>Speed error in the axial direction;
representation oftTime of day formation System +.>The individual aircraft nodes are in +.>Position error in the axial direction;
representation oftTime of day formation System +.>The individual aircraft nodes are in +.>Speed error in the axial direction;
representation oftTime of day formation System +.>The individual aircraft nodes are in +.>Position error in the axial direction;
representation oftTime of day formation System +.>The individual aircraft nodes are in +.>Speed error in the axial direction;
s203, establishing a formation system communication topological structure by adopting an undirected graph according to the communication relation among the aircrafts;
the present embodiment contemplates a group of users consisting of a leader andan aircraft formation system consisting of a plurality of followers. Wherein, the leader is taken as a No. 0 node, < ->Representing follower nodes in a formation system, < +.>Representing except nodes in a formation systemiOther nodes than those, including the leader. Taking the aircraft nodes as a node set of the undirected graph, and taking the communication relationship among the nodes as an edge set of the undirected graph, wherein the edges of the undirected graph are used for +.>Refer to.
The communication network structure is composed ofDetermining->=1 means%>System of individual aircraft nodes and->Communication connection is arranged among the aircraft node systems, namely, the nodes are communicated; />=0 denotes an aircraft node system +.>System of nodes with aircraft>There is no communication connection between the nodes, i.e. there is no communication between the nodes. And constructing an undirected graph through the node set and the edge set, namely, establishing a communication topological structure of the formation system. At the same time (I)>=1。
In particular, the connection between the aircraft node systems is arranged in this embodiment to satisfy a balanced topology, i.e=/>。
In step 3, a coupling system position and speed error model is established by coupling the sum of state errors among all the communication aircraft nodes in the four-rotor aircraft formation system:
（5）
wherein,the error vector of the axis is expressed as:
；
；
the gain matrix is expressed as:
；
similarly, the error and gain matrix representation for the other two axes is similar;
，/>，/>respectively +.>Shaft、/>Shaft、/>A control input in the axial direction;
，/>，/>respectively +.>Shaft、/>Shaft、/>Disturbance in the axial position;
，/>，/>is defined as:
（6）
by the definition above, the aircraft system is coupledShaft、/>Shaft、/>The systematic error in the axial direction is expressed by the following formula:
（7）
the error matrix is expressed as:
；
；
；
the control input vector is:
the disturbance vector is expressed as:
；
；
；
and, in addition, the processing unit,，/>，/>，/>representing an identity matrix>The number of nodes for followers in the queuing system.
By considering the error model of the coupled aircraft formation system in the step 3, and combining the adaptive technology, designing a formation system controller, and changing the running state of the aircraft node based on the controller estimation and adjustment system control parameters, thereby eliminating the negative influence caused by disturbance, comprising the following steps:
s401, for aircraft node ，Aircraft nodes in the queuing system +.>Is multiplied by the control gain +.>Multiplying the sum of the speed errors of the aircraft nodes capable of establishing a communication by the adaptive control equation +.>The multiplied products are differenced to obtain the aircraft node +.>Position controller of (2);
specifically, the firstThe individual aircraft nodes are->Shaft、/>Shaft、/>The axial position controller is designed as follows:
（8）
wherein,、/>、/>respectively the +.>Individual aircraft systemtMoment in ground coordinate systemShaft、/>Shaft、/>A control input in the axial direction; />、/>、/>To control gain;
，/>similarly, the position and speed errors of the other two shafts are similar;
s402, substituting the disturbance value range formula in the formula (2) into the Lyapunov function, deriving, and designing an adaptive term, namely an adaptive control equation, with the aim of eliminating the residual term；
Wherein, the redundant term refers to the term related to disturbance factors;
specifically, according to the second stability theorem of Lyapunov, an adaptive control equation is determined, and the influence caused by disturbance is eliminated;
controlling gain、/>、/>Expressed in matrix form as:
；
；
；
and satisfies the following conditions:
（9）
wherein,the matrix is->Shaft、/>Shaft、/>The axial directions are respectively expressed as:
in the axial direction +.>The matrix is:
；
in the axial direction +.>The matrix is:
；
in the axial direction +.>The matrix is:
；
is a positive definite matrix,/->Representing an all 0 matrix,/->Representing the number of follower nodes in the queuing system.
Combining the self-adaptive control technology and the fixed time theory, adding the control input item according to the fixed time、/>Design +.>The items are:
（10）
wherein:
above mentioned、/>Is->Control inputs on the axes set according to a fixed time, control inputs on other axes +.>、/>，/>、/>And the same is done; />，/>Is an exponential parameter and satisfies->，/>；
Is->Maximum eigenvalue of matrix;
，/>；
，/>；
，/>；
in this embodiment, the control input item is increased according to the fixed time、/>And obtaining a controller equation, so that the controller converges to obtain the output of the controller according to the set fixed time.
Wherein, the fixed time theory is:
setting a Lyapunov function, setting a value range of control parameters in the Lyapunov function, and calculating fixed time through the control parameters in the Lyapunov function;
specifically, the Lyapunov function is formulated to satisfy the formulaWherein->Are all normal numbers, and ∈>、/>. The calculation formula for calculating the fixed time by the control parameters is as follows:
；
s403, specific design of an adaptive law: calculating the derivative of the disturbance parameter estimated value according to the position error and the speed error of the aircraft nodes which are mutually communicated in the formation system, the adaptive control equation and the set limiting range of the error, and taking the derivative as an adaptive law, wherein the specific formula is shown in a formula (11);
at the position ofOn the axis, the disturbance parameter is +.>The adaptive law estimates the disturbance parameters asThe adaptive law satisfies the following formula:
（11）
wherein,is a parameter of the set adaptive law, and +.>，/>Is the limit of errors and +.>The method comprises the steps of carrying out a first treatment on the surface of the Similarly, let go of> 、/>The adaptive law design form of the axial direction is the same.
S404, expressing the system controller into a vector form according to the obtained formation controller and the self-adaptive law, wherein the method specifically comprises the following steps:
（12）
wherein,、/>、/>control gains for aircraft formation systems;
（13）
the systematic error is re-expressed as:
（14）
in addition, for lyapunov stability analysis, the error in defining the adaptive parameters is:
（15）
and according to the adaptive law in S403, defineThe error system of the self-adaptive parameter in the axial direction is as follows: the derivative of the estimated error of the disturbance parameter is equal to the derivative of the estimated value of the disturbance parameter, and the method is concretely as follows:
in the same way, the processing method comprises the steps of, 、/>the adaptive parameter error system in the axial direction is:
the method further comprises the step of verifying the stability of the system, and the step of verifying the stability based on the Lyapunov function is further carried out;
specifically, a Lyapunov function is constructed by using a Lyapunov second method, stability verification of the control method is performed according to the Lyapunov stability principle, the fixed time principle and the system error and formation controller formulas in the third and fourth steps, and actual operation is performed through computer simulation software.
By design of adaptive control equationAnd removing redundant terms related to disturbance factors in the function after derivation to obtain the following formula:
to theoretically verify the effectiveness and stability of the controllerThe position in the axial direction is exemplified by the definition of the lisapunov function:
（16）
the derivative of the lyapunov function is:
by design of adaptive control equationAnd removing redundant terms related to disturbance factors in the function after derivation to obtain the following formula:
（17）
as a result of:
the following steps are:
（18）/>
based on the design of the adaptive law in S403 and the adaptive parameter error system in S404, it can be known that，/>Always less than->And->. Thus, the following inequality holds:
according to the definition above, the lyapunov function satisfies:
（19）
by the following inequality:
(/>)
(/>)
wherein the method comprises the steps ofThe normal number is finally obtained:
through the formula, the controller can control the system to be in a fixed timeThe error is reduced to a minimum value, and meanwhile, the control time of the system operation can be calculated.
Similarly, it can be demonstrated thatShaft、/>The position controller in the axial direction is effective and stable.
To illustrate the effect of this embodiment, simulation verification was performed, and specifically, a computer software MATLAB was used to verify the inventive control method. Parameters related to each step in the simulation are selected as follows:
the control parameters of the formation system of the coupled quadrotor in the first step are selected as follows:
，/>，/>，/> ；
in the second step, the formation structure adopted in this example is shown in fig. 3.
The desired trajectory of the virtual leader is selected as:
；
the formation communication network structure is selected as follows:
；
the desired positional distance between the aircraft is set to:
/>
wherein m is a unit of position coordinates, meter; in the present embodiment onlyRepresenting the mass of the aircraft, m without subscript represents a meter;
in the fourth step, the controller is formed 、/> 、/>The adaptive parameters of the axes are the same, in order +.>The shaft is taken as an example, and is selected as follows:
，/>，/>，/>，/>。
in the fifth step, the time control parameter is fixed 、/> 、/>The axes are identical, in->The shaft is known as an exampleOther parameters were selected as: />、/>Then->。
And (3) through the selected parameters in the step five, the formation system reaches a stable running state within about 4.052s, namely can reach the stable state within a fixed time.
As shown in fig. 4 and 5, the coupled quad-rotor aircraft queuing system is capable of tracking a predetermined trajectory and stably operating in a perturbed operating environment, wherein each follower forms a triangular formation, as shown by the arrow lines.
As shown in fig. 6 and 7, the control method adopted by the coupled quadrotor formation system has good robustness and stability to the influence of general disturbance, so that the formation system can track a desired position command at about 2.8 s.
As shown in fig. 8 and 9, the control input and the adaptive parameter estimation of the formation system enable the system to have strong adaptability, and the control strategy ensures that the system can counteract the negative influence of general disturbance on the stable operation of the system.
Example 2
Based on embodiment 1, there is provided in this embodiment a system for fixed time adaptive queuing of coupled multiple aircraft, comprising:
a first construction module: is configured to construct a dynamics model of coupled quad-rotor aircraft formation system nodes in consideration of the presence of continuous disturbance and control input effects;
a state error calculation module: the system comprises a system and a method, wherein the system is configured to construct a state error model of an aircraft node in a formation system according to a set expected track and a constructed dynamic model, and establish a formation communication topological structure;
and a second construction module: the system comprises a coupling aircraft formation system error model, a communication-capable aircraft node and a communication-capable aircraft node, wherein the coupling aircraft formation system error model is configured to calculate the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft node;
and (3) constructing and solving a module by a controller: the system comprises a formation system controller, a control system controller and a control system controller, wherein the formation system controller is configured to design a formation system controller containing a fixed time control input item according to the obtained error model of the formation system of the aircraft in combination with an adaptive control strategy and a fixed time principle; and solving the controller, and converging according to the set fixed time to obtain the output of the controller.
Here, the modules in this embodiment are in one-to-one correspondence with the steps in embodiment 1, and the implementation process is the same, which is not described here.
Example 3
The present embodiment provides an electronic device including a memory and a processor, and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the steps described in the fixed time adaptive formation control method for coupled multiple aircraft of embodiment 1.
Example 4
The present embodiment provides a computer readable storage medium storing computer instructions that, when executed by a processor, perform the steps described in the fixed time adaptive formation control method for coupled multiple aircraft of embodiment 1.
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 (10)
1. The fixed time self-adaptive formation control method for the coupled multi-aircraft is characterized by comprising the following steps of:
constructing a dynamics model of a coupled four-rotor aircraft formation system node by considering the existence of continuous disturbance and control input influence;
according to the set expected track and the constructed dynamic model, constructing a state error model of an aircraft node in a formation system, and establishing a formation communication topological structure;
calculating the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft nodes to obtain a coupled aircraft formation system error model;
designing a formation system controller containing a fixed time control input item according to the obtained error model of the formation system of the aircraft and combining an adaptive control strategy and a fixed time principle; and solving the controller, and converging according to the set fixed time to obtain the output of the controller.
2. The method for fixed time adaptive formation control of coupled multi-aircraft according to claim 1, wherein: and solving the controller to obtain the position and the speed of each aircraft, so that the coupled multi-aircraft formation system performs predetermined track tracking in a fixed time.
3. The method for fixed time adaptive formation control of coupled multi-aircraft according to claim 1, wherein: the method comprises the steps that a formation system which consists of N aircraft nodes and has continuous disturbance and control input influence is used for expressing a second-order dynamic model of the aircraft nodes by using a dynamics equation to serve as a dynamics model; and determining the value range of disturbance of the aircraft according to the speed state of the aircraft and the value of the control input.
4. The method for fixed time adaptive formation control of coupled multi-aircraft according to claim 1, wherein: setting a desired track, adopting a leader-follower framework, setting a virtual aircraft node as a leader, taking the flight state of the leader as a desired target for following the aircraft in the system, and changing the flight state of the follower to realize tracking and form a control strategy of formation when the state information of the leader changes.
5. The method for controlling the fixed time adaptive formation of coupled multiple aircraft according to claim 1, wherein the step of constructing an error model of an aircraft node in a formation system comprises the steps of:
according to the set expected track, calculating the expected position distance between every two aircraft nodes;
calculating position errors between every two aircraft nodes with a communication relationship according to the expected position distance obtained by calculating the position coordinates between the aircraft nodes;
and calculating the speed error between every two aircraft nodes with communication relation according to the speed states of the aircraft nodes.
6. The method for controlling the fixed time adaptive formation of coupled multi-aircraft according to claim 1, wherein the formation system controller construction process comprises the steps of:
multiplying the position error and the speed error of the aircraft node in the formation system by a control gain aiming at the aircraft node, multiplying the speed error of the aircraft node capable of establishing communication by an adaptive control equation, and obtaining a position controller of the aircraft node by the difference of the multiplied products;
according to the second stability theorem of Lyapunov, combining the self-adaptive control and the fixed time theory, adding a control input item according to the fixed time, and designing a self-adaptive control equation in the control input item;
and calculating the derivative of the disturbance parameter estimated value as an adaptive law according to the position error and the speed error of the aircraft nodes which are mutually communicated in the formation system, the adaptive control equation and the set limiting range of the error.
7. The method for controlling the adaptive formation of a plurality of coupled aircrafts according to claim 1, wherein the fixed time theory is: setting a Lyapunov function, setting a value range of a control parameter in the Lyapunov function, and calculating the fixed time through the control parameter in the Lyapunov function.
8. A fixed time adaptive formation control system for coupling multiple aircraft, comprising:
a first construction module: is configured to construct a dynamics model of coupled quad-rotor aircraft formation system nodes in consideration of the presence of continuous disturbance and control input effects;
a state error calculation module: the system comprises a system and a method, wherein the system is configured to construct a state error model of an aircraft node in a formation system according to a set expected track and a constructed dynamic model, and establish a formation communication topological structure;
and a second construction module: the system comprises a coupling aircraft formation system error model, a communication-capable aircraft node and a communication-capable aircraft node, wherein the coupling aircraft formation system error model is configured to calculate the state error sum among the communication-capable aircraft nodes in the formation system based on the state error model of the aircraft node;
and (3) constructing and solving a module by a controller: the system comprises a formation system controller, a control system controller and a control system controller, wherein the formation system controller is configured to design a formation system controller containing a fixed time control input item according to the obtained error model of the formation system of the aircraft in combination with an adaptive control strategy and a fixed time principle; and solving the controller, and converging according to the set fixed time to obtain the output of the controller.
9. An electronic device comprising a memory and a processor and computer instructions stored on the memory and running on the processor, which when executed by the processor, perform the steps in the method of fixed time adaptive formation control of coupled multi-aircraft of any one of claims 1-7.
10. A computer readable storage medium storing computer instructions which, when executed by a processor, perform the steps in the method of fixed time adaptive formation control of coupled multi-aircraft of any of claims 1-7.
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Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20180074520A1 (en) * | 2016-09-13 | 2018-03-15 | Arrowonics Technologies Ltd. | Formation flight path coordination of unmanned aerial vehicles |
| CN107844127A (en) * | 2017-09-20 | 2018-03-27 | 北京飞小鹰科技有限责任公司 | Towards the formation flight device cooperative control method and control system of finite time |
| CN110275542A (en) * | 2019-06-14 | 2019-09-24 | 合肥工业大学 | A kind of quadrotor control method based on adaptive finite-time control |
| CN112578804A (en) * | 2020-12-16 | 2021-03-30 | 南京理工大学 | Four-rotor aircraft formation sliding mode control method based on event trigger mechanism |
| CN112650303A (en) * | 2021-01-20 | 2021-04-13 | 南京航空航天大学 | Unmanned aerial vehicle formation fault-tolerant control method based on fixed time technology |
| US20210403159A1 (en) * | 2018-10-18 | 2021-12-30 | Telefonaktiebolaget Lm Ericsson (Publ) | Formation Flight of Unmanned Aerial Vehicles |
| CN114840027A (en) * | 2022-07-01 | 2022-08-02 | 南京理工大学 | Heterogeneous four-rotor aircraft formation attitude fault-tolerant control method |
| CN116954258A (en) * | 2023-08-14 | 2023-10-27 | 武汉大学 | Hierarchical control method and device for multi-four-rotor unmanned aerial vehicle formation under unknown disturbance |
| CN117055605A (en) * | 2023-09-18 | 2023-11-14 | 齐鲁工业大学(山东省科学院) | Multi-unmanned aerial vehicle attitude control method and system |
-
2024
- 2024-01-19 CN CN202410077252.8A patent/CN117590864B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20180074520A1 (en) * | 2016-09-13 | 2018-03-15 | Arrowonics Technologies Ltd. | Formation flight path coordination of unmanned aerial vehicles |
| CN107844127A (en) * | 2017-09-20 | 2018-03-27 | 北京飞小鹰科技有限责任公司 | Towards the formation flight device cooperative control method and control system of finite time |
| US20210403159A1 (en) * | 2018-10-18 | 2021-12-30 | Telefonaktiebolaget Lm Ericsson (Publ) | Formation Flight of Unmanned Aerial Vehicles |
| CN110275542A (en) * | 2019-06-14 | 2019-09-24 | 合肥工业大学 | A kind of quadrotor control method based on adaptive finite-time control |
| CN112578804A (en) * | 2020-12-16 | 2021-03-30 | 南京理工大学 | Four-rotor aircraft formation sliding mode control method based on event trigger mechanism |
| CN112650303A (en) * | 2021-01-20 | 2021-04-13 | 南京航空航天大学 | Unmanned aerial vehicle formation fault-tolerant control method based on fixed time technology |
| CN114840027A (en) * | 2022-07-01 | 2022-08-02 | 南京理工大学 | Heterogeneous four-rotor aircraft formation attitude fault-tolerant control method |
| CN116954258A (en) * | 2023-08-14 | 2023-10-27 | 武汉大学 | Hierarchical control method and device for multi-four-rotor unmanned aerial vehicle formation under unknown disturbance |
| CN117055605A (en) * | 2023-09-18 | 2023-11-14 | 齐鲁工业大学(山东省科学院) | Multi-unmanned aerial vehicle attitude control method and system |
Non-Patent Citations (1)
| Title |
|---|
| 张;王彦恺;: "航天器编队姿态与轨道耦合协同控制器设计", 新型工业化, no. 08, 20 August 2014 (2014-08-20) * |
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