CN107315421B - A kind of distributed speed sensor fault diagnostic method that time delay unmanned plane is formed into columns - Google Patents
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Abstract
The invention discloses a kind of distributed speed sensor fault diagnostic methods for the unmanned plane fleet system with communication time-delay, belong to unmanned plane fleet system field, including calculate communication topological parameter；Based on communication topological parameter, given trace, formation vector sum preset condition, distributed formation control rule is obtained；It is measured based on fleet system closed loop model and each unmanned plane and the relative status of neighbours, obtains distributed fault detection Residual Generation device and corresponding residual error evaluation function；Further obtain one group of distribution fault reconstruction Residual Generation device and corresponding residual error evaluation function；Open loop models based on unmanned plane obtain distributing fault reconstruction Residual Generation device and corresponding residual error evaluation function；Based on residual error evaluation function and corresponding threshold value, fault detection and separation are carried out.By under the interference of fixed length time delay, this method still is able to the detection and separation that realize each unmanned plane to faults itself and neighbours' unmanned plane failure for communication between unmanned plane.
Description
Technical Field
The invention belongs to the field of unmanned aerial vehicle formation systems, and particularly relates to a distributed speed sensor fault diagnosis method for unmanned aerial vehicle formation with communication time delay.
Background
In recent years, unmanned aerial vehicle formation systems are receiving more and more attention in the fields of forest fire prevention, mapping, personnel search and rescue and the like. The unmanned aerial vehicle formation system can realize the function that a single unmanned aerial vehicle can not realize or has the excellent performance that a single unmanned aerial vehicle can not have through cooperation between unmanned aerial vehicles. Because the communication connection is arranged between the unmanned aerial vehicles, the fault of a single unmanned aerial vehicle can cause that the formation of the whole formation system can not be maintained, thereby further influencing the function and performance of the formation system and even causing the occurrence of crash accidents. The fault diagnosis of the formation system is an important technology for ensuring the safe formation flight of the unmanned aerial vehicles.
At present, fault diagnosis methods of unmanned aerial vehicle formation systems are mainly divided into two types, namely centralized fault diagnosis and distributed fault diagnosis. Under the centralized fault diagnosis framework, the fault diagnosis algorithm is centralized in a single unmanned aerial vehicle or a ground station of the system, and the unmanned aerial vehicle or the ground station carries out fault diagnosis by utilizing the information of all the unmanned aerial vehicles. The method has the disadvantages of low reliability and large communication load. Under the framework of distributed fault diagnosis, fault diagnosis algorithms are distributed in all unmanned aerial vehicles, and the fault diagnosis algorithms in all unmanned aerial vehicles are the same. And each unmanned aerial vehicle carries out fault diagnosis on the unmanned aerial vehicle and the neighbors only by using the information of the unmanned aerial vehicle and the neighbors. The method has low communication load and high reliability.
In the formation of unmanned aerial vehicles, the communication between unmanned aerial vehicles is influenced by factors such as environmental interference and communication bandwidth, so that time delay is easily generated. In the current distributed fault diagnosis method of the unmanned aerial vehicle formation system, the influence of time delay is not considered. The time delay causes large errors and even errors in the results of the current distributed fault diagnosis.
Disclosure of Invention
The invention provides a distributed speed sensor fault diagnosis method for an unmanned aerial vehicle formation system with fixed-length communication time delay, aiming at the problem that the current distributed fault diagnosis method for the unmanned aerial vehicle formation system cannot be suitable for the situation that formation has communication time delay. The method can effectively realize the distributed fault diagnosis of the constant deviation sensor fault or the sensor fault with the period of fixed-length time delay.
In order to achieve the purpose, the invention adopts the following technical scheme:
a distributed speed sensor fault diagnosis method of a time delay unmanned aerial vehicle formation system comprises the following steps:
step 1: calculating communication topology parameters of unmanned aerial vehicle formation, and aiming at a formation system consisting of N unmanned aerial vehicles, G ═ { V, E } is a non-directional communication topology of the formation system, wherein V ═ 1, 2.. and N } is communication topology nodes, and each communication topology node represents one unmanned aerial vehicle;each edge represents communication between a pair of unmanned aerial vehicles, and is an edge of a communication topology;
let matrix Ag＝[aij]For the adjacency matrix of the communication topology, if (i, j) belongs to E, the node i and the node j are called as neighbor nodes, namely, the node i and the node j have communication, aij＝aji1, otherwise aij＝aji＝0；
Let NiIs the neighbor set of the ith UAV, | NiL is the set NiThe number of middle elements;
let matrix Dg＝[dij]Is a degree matrix of communication topology, the off-diagonal elements of the degree matrix are zero, and the diagonal elements areTake a value of
Let matrix LgIs a Laplace matrix of the communication topology, then Lg＝Dg-Ag(ii) a Let 0 be less than or equal to lambda1＜λ2≤...≤λNIs LgN eigenvalues from small to large;
step 2: based on communication topological parameters, given tracks, formation vectors and preset conditions of unmanned aerial vehicle formation, a distributed formation control law is designed, and the method specifically comprises the following steps:
the open-loop model of the ith unmanned aerial vehicle in the x-axis direction of the space coordinate system is as follows:
wherein, i is 1, 2., N,for the displacement of the ith drone,for the speed of the ith drone,for the control law of the ith unmanned aerial vehicle,for the displacement sensor measurement of the ith drone,for the speed sensor measurement of the ith drone,the speed sensor fault of the ith unmanned aerial vehicle is as follows:
wherein,for the moment of occurrence of the fault of the ith drone,is the ith unmanned planeAmplitude of barrier, chii(t) is a constant value or a function of period tau,communication time delay between neighboring unmanned aerial vehicles;
given trajectory of the formation system isOrder d with the 1 st unmanned aerial vehicle as the pilot10 and let the formation vector d ═ d1,d2,...,dN]TWhereinFor the distance between the ith unmanned aerial vehicle and the 1 st unmanned aerial vehicle, the distributed control law of the ith unmanned aerial vehicle is as follows:
wherein, first and second derivatives, k, respectively, of a given trajectory1＞0，k2＞0，k3＞0，k4Is more than 0 and satisfies the following preset conditions:and
and step 3: based on a formation system closed-loop model and relative state measurement of each unmanned aerial vehicle and a neighbor, a distributed fault detection residual error generator and a corresponding fault detection residual error evaluation function are designed, and the method specifically comprises the following steps:
based on the open-loop model and the distributed control law of the ith unmanned aerial vehicle, the closed-loop model of the ith unmanned aerial vehicle can be obtained as follows:
wherein, respectively the displacement and speed of the jth drone,for the jth drone's speed sensor fault,the reference track of the closed-loop model of the ith unmanned aerial vehicle is in the following specific form:
let x be [ ξ ]1,ξ2,...ξN,ζ1,ζ2,...,ζN]T，v＝[v1,v2,...,vN]T，f＝[f1,f2,...,fN]T(ii) a Let yi(t) is the relative state measurement of the ith drone and the neighbors in the form:
wherein i1,i2,...,i|Ni|1,2, of the ith node, respectivelyiL neighborhoods;
based on ith unmanned aerial vehicle closed-loop model and yi(t), the closed-loop model of the entire formation system is as follows:
wherein,
wherein iiAndare respectively unit matrix INAnd I2NThe kth column of (1);
based on a closed-loop model of a formation system and relative state measurement of an ith unmanned aerial vehicle and a neighbor, a distributed fault detection residual error generator of the ith unmanned aerial vehicle is designed as follows:
wherein,for the state of the distributed fault detection residual generator,detecting residuals of a residual generator for distributed faultsDesigning a matrix using pole allocationMake itIs a stable matrix;
based on the distributed fault detection residual error generator of the ith unmanned aerial vehicle, designing a corresponding fault detection residual error evaluation function as follows:
wherein,2 norm of (d);
and 4, step 4: based on a closed-loop model of a formation system and relative state measurement of each unmanned aerial vehicle and a neighbor, in each unmanned aerial vehicle, a group of distributed fault separation residual error generators and a group of corresponding fault separation residual error evaluation functions are designed for all neighbor nodes of the unmanned aerial vehicle, and the method specifically comprises the following steps:
in the ith unmanned aerial vehicle, a distributed fault separation residual error generator is designed for the kth neighbor node, and the specific form is as follows:
wherein k is equal to Ni，To isolate the state of the residual generator for distributed faults,separating stubs for distributed faultsA residual of the difference generator;andis calculated as follows:
wherein,are respectively E1，E2And Γi,2The (c) th column of (a),to make it possible toA stable matrix;
designing a corresponding fault separation residual evaluation function based on a kth distributed fault separation residual generator of the ith unmanned aerial vehicle as follows:
and 5: designing a distributed fault separation residual error generator and a corresponding fault separation residual error evaluation function based on an open loop model of each unmanned aerial vehicle; the specific form of the distributed fault separation residual error generator of the ith unmanned aerial vehicle is as follows:
wherein,for the state of the decentralized fault isolation residual generator of the ith drone,separating the residuals of the residual generator for the ith drone's decentralized failure,for the open loop control input of the ith drone,is the measurement output of the ith drone; wherein,andthe values of (A) are as follows:
design using pole allocation methodMake itIs a stable matrix;
based on the distributed fault separation residual error generator of the ith unmanned aerial vehicle, designing a corresponding fault separation residual error evaluation function as follows:
step 6: fault detection is performed based on a distributed fault detection residual evaluation function and a corresponding fault detection threshold, which specifically comprises the following steps:
order toIs composed ofThe corresponding fault detection threshold value is set to,the method can be obtained according to the requirements of noise, unmodeled dynamics and fault detectability and according to actual experience; the fault detection logic of the ith drone is as follows:
if it is notOne unmanned aerial vehicle in the system breaks down; if it is notNo unmanned aerial vehicle in the system fails;
and 7: fault separation is carried out based on a fault separation residual error evaluation function and a corresponding fault separation threshold value, and the method specifically comprises the following steps:
order toIs composed ofCorresponding fault isolation threshold, where k ∈ NiLet us orderIs composed ofA corresponding fault isolation threshold;andthe method can be obtained according to the requirements of noise, unmodeled dynamics and fault separability and according to actual experience; the fault isolation logic of the ith drone is as follows:
if it is notThe ith unmanned aerial vehicle fails; otherwise, if there is a fault isolation residual evaluation functionk∈NiAnd all other fault isolation residual generatorsp∈NiK, satisfiesAnd isThe kth neighbor of the ith unmanned aerial vehicle fails; otherwise, if the residual evaluation function is separated for all faultsAll satisfyThe unmanned aerial vehicle with the fault is the other unmanned aerial vehicle except the ith unmanned aerial vehicle and the neighbors of the ith unmanned aerial vehicle;
and 8: decoupling the kinematics model of the unmanned aerial vehicle on the x axis, the y axis and the z axis of the space coordinate system, wherein the kinematics model of the ith unmanned aerial vehicle in the y axis direction of the space coordinate system is the same as the kinematics model in the x axis direction in the step 2, and repeating the steps 2 to 7 to obtain the fault diagnosis result of the unmanned aerial vehicle formation system in the y axis;
and step 9: and (3) decoupling the kinematics model of the unmanned aerial vehicle on the x axis, the y axis and the z axis of the space coordinate system, repeating the steps from 2 to 7 to obtain the fault diagnosis result of the unmanned aerial vehicle formation system on the z axis, wherein the kinematics model of the ith unmanned aerial vehicle on the z axis direction of the space coordinate system is the same as the kinematics model on the x axis direction in the step 2.
The invention has the following beneficial technical effects:
in the method, each unmanned aerial vehicle updates the states of all residual error generators only by using the output signal of the unmanned aerial vehicle and the state measurement relative to the neighbor, and the unmanned aerial vehicles can still realize fault detection and fault separation of the unmanned aerial vehicles and the neighbor unmanned aerial vehicles under the interference of fixed-length time delay in communication between the unmanned aerial vehicles, namely, more accurate distributed fault diagnosis is realized.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a communication topology of a formation of three quad-rotor drones of example 1.
Fig. 3 is a schematic view of flight results of three quad-rotor drone formation in embodiment 1.
Fig. 4 is a schematic diagram of the fault detection and separation results of the quad-rotor drone 1 according to embodiment 1.
Fig. 5 is a schematic diagram of the results of the fault detection and separation of the quad-rotor drone 2 according to embodiment 1.
Fig. 6 is a schematic diagram of the result of fault detection and separation of the quad-rotor drone 3 in embodiment 1.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
with reference to fig. 1 to 6, a distributed speed sensor fault diagnosis method of a time delay unmanned aerial vehicle formation system is provided for an unmanned aerial vehicle formation system with fixed-length communication time delay and speed sensor faults, and the fault diagnosis method of the invention is described below for a formation system composed of 3 quadrotors, and the flow of the method is shown in fig. 1.
Example 1
Step 1: and obtaining communication topology parameters aiming at the communication topology of the given unmanned aerial vehicle. And calculating the eigenvalues of the communication topology and the Laplace matrix. For a formation system consisting of 3 drones, the communication topology of a quad-rotor drone is shown in fig. 2. Let G be { V, E } a communication topology of the formation system and be a directed link-free graph. Wherein, V ═ {1,2,3} is a communication topology node, and each communication topology node represents an unmanned aerial vehicle. E { (1,2), (2,3), (3,1) } are edges of the communication topology, each edge representing communication between a pair of drones.
Let matrix Ag＝[aij]Is a contiguous matrix of the communication topology. If the node (i, j) belongs to E, the node i and the node j are called to be neighbors, namely, the node i and the node j have communication, aij＝aji1, otherwise aij＝aji0. Let NiIs a set of neighbors of node i. | NiL is the set NiThe number of the elements in (B). Let matrix Dg＝[dij]The degree matrix of the communication topology has off-diagonal elements of zero and diagonal elements of zeroLet dmIs the maximum element value of the degree matrix. Let matrix LgIs a Laplace matrix of the communication topology, then Lg＝Dg-Ag. Let 0 be less than or equal to lambda1≤λ2≤...≤λNIs LgFrom small to large N ofAnd (4) the characteristic value. The values of the respective parameters can be obtained as follows:
N1＝{2,3},N2＝{1,3},N3＝{1,2},|N1|＝|N2|＝|N3|＝2。
step 2: and obtaining a distributed formation control law based on the communication topological parameters, the given tracks, the formation vectors and preset conditions. The open-loop model of the ith unmanned aerial vehicle in the x-axis direction of the space coordinate system is as follows:
wherein, i is 1,2,3,for the displacement of the ith drone,for the speed of the ith drone,for the control law of the ith unmanned aerial vehicle,for the displacement sensor measurement of the ith drone,is the speed sensor measurement of the ith drone. In embodiment 1, it is set that drone 1 fails at 655.2025s with a constant deviation, and drones 2 and 3 do not fail. The specific form of the fault of the unmanned aerial vehicle 1 is as follows:
the tracking trajectory in the x-axis direction of the formation system is r (t) 43.5-0.5t (m). The formation vector is d ═ 0m, -5m]T. The tracking trajectories in the y-axis and z-axis directions are constant, and the control laws adopted in the y-axis and z-axis directions in this example are similar to those in the x-axis direction, and will not be described in detail in the present invention. The present invention is described in detail only with respect to x-axis directional control and fault diagnosis.
The distributed control law of the ith unmanned aerial vehicle is as follows:
wherein First and second derivatives, respectively, of a given trajectory. k is a radical of1＞0，k2＞0，k3＞0，k40 and satisfies the preset conditions: k is a radical of1＞k2λNAnd
according to the preset conditions, the control law parameter k is selected in the embodiment 11＝3，k2＝0.17，k3＝3，k40.37. The result of the formation is shown in fig. 3. The first subgraph in fig. 3 is the flight trajectory of three unmanned aerial vehicles in formation, 3 diamonds represent 3 unmanned aerial vehicles respectively, a triangle formed by connecting lines between the unmanned aerial vehicles represents formation, and three curves represent the flight trajectory of the unmanned aerial vehicles. The second sub-graph represents the formation tracking error of 3 drones. As can be seen from FIG. 3, in the absence of a fault, the triangle formation is positiveThe formation error is small frequently, namely the control law can realize stable formation; after the fault occurs, the formation forms are deviated, the amplitude of the formation error is remarkably increased, and although the control law cannot guarantee the convergence of the formation error, the formation error can still be kept within a certain range.
And step 3: based on a formation system closed-loop model and relative state measurement of each unmanned aerial vehicle and a neighbor, a distributed fault detection residual error generator and a corresponding fault detection residual error evaluation function are designed, and the method specifically comprises the following steps:
based on the open-loop model and the distributed control law of the ith unmanned aerial vehicle, the closed-loop model of the ith unmanned aerial vehicle can be obtained as follows:
wherein, respectively, the displacement and the speed of the jth drone.Is the speed sensor fault of the jth drone.The reference track of the closed-loop model of the ith unmanned aerial vehicle is in the following specific form:
let x be [ ξ ]1,ξ2,ξ3,ζ1,ζ2,ζ3]T，v＝[v1,v2,v3]T，f＝[f1,f2,f3]T. Relative state observation y of ith unmanned aerial vehicle and neighboriThe specific form of (t) is as follows:
closed loop dynamic model and y based on ith unmanned aerial vehiclei(t), the closed-loop model of the formation system is as follows:
wherein,
in example 1, the values of the parameters are specifically as follows:
based on a closed-loop model of a formation system, a distributed fault detection residual error generator of the ith unmanned aerial vehicle is designed as follows:
wherein,in order to be the state of the residual generator,is the residual of the residual generator. By using the pole allocation method, willAndare respectively configured as [ -3-6-9 [ -3 [ -6 [ -9 ] -12 -15 -18]，[-2 -4 -6 -8 -10-12]And [ -2-4-6-8-10-12 ]]Corresponding matrixAndvalues are as follows:
in example 1, based on the fault detection residual generator of the ith drone, the corresponding fault detection residual evaluation function is designed as follows
Wherein, | | ri 0(t) | | is ri 0(t) 2 norm, i ═ 1,2, 3.
And 4, step 4: based on a closed-loop model of a formation system and relative state measurement of each unmanned aerial vehicle and neighbors, in each unmanned aerial vehicle, a group of distributed fault separation residual error generators and a group of corresponding fault separation residual error evaluation functions are designed for all the neighbors, specifically as follows:
in the ith unmanned aerial vehicle, a distributed fault separation residual error generator is designed for the kth neighbor thereof, specifically as follows:
wherein k is equal to Ni，To isolate the state of the residual generator for distributed faults,the residuals of the residual generator are separated for the distributed fault.Is calculated as follows:
wherein,andare respectively E1，E2And Γi,2The (c) th column of (a),to make it possible toA stable matrix.
In embodiment 1, the parameters of all distributed fault isolation residual generators take the following values:
in embodiment 1, based on each distributed fault isolation residual generator for each drone, the corresponding fault isolation residual evaluation function is designed as follows:
and 5: designing a distributed fault separation residual error generator and a corresponding fault separation residual error evaluation function based on an open loop model of each unmanned aerial vehicle;
the decentralized fault isolation residual generator for the ith drone is of the form:
wherein,for the state of the decentralized fault isolation residual generator of the ith drone,separating the residuals of the residual generator for the ith drone's decentralized failure,for the open loop control input of the ith drone,the measurement output of the ith drone. WhereinAndthe values of (A) are as follows:
in embodiment 1, the pole arrangement method is used to arrangeAndrespectively have poles of [ -1-2 [)]，[-3 -6]And [ -3-6]Corresponding matrixThe values of (A) are as follows:
in embodiment 1, based on the ith unmanned distributed fault separation residual generator, the corresponding fault separation residual evaluation function is designed as follows:
step 6: fault detection is performed based on a distributed fault detection residual evaluation function and a corresponding fault detection threshold, which specifically comprises the following steps:
order toIs composed ofCorresponding fault detection threshold. According to the requirements of noise, unmodeled dynamics and fault detectability and actual experienceThe fault detection logic of the ith drone is as follows:
as can be seen from the first sub-diagram of fig. 4, around 655s, the distributed fault detection residual evaluation function of the drone 1Greater than a corresponding threshold valueTherefore, the unmanned aerial vehicle 1 judges that a node in the formation fails.
As can be seen from the first sub-diagram of fig. 5, around 655s, the distributed fault detection residual evaluation function of the drone 2Greater than a corresponding threshold valueTherefore, the unmanned aerial vehicle 2 judges that a node in the formation fails.
As can be seen from the first sub-diagram of fig. 6, around 655s, the distributed fault detection residual evaluation function of the drone 3Greater than a corresponding threshold valueTherefore, the unmanned aerial vehicle 3 judges that a node in the formation fails.
And 7: and carrying out fault separation based on the distributed fault separation residual error evaluation function and the corresponding fault separation threshold value. Order toIs composed ofCorresponding fault isolation threshold, where k ∈ Ni。Is composed ofA corresponding fault isolation threshold. According to the requirements of noise, unmodeled dynamics and fault separability and actual experienceAndthe values of (a) are as follows:
the fault isolation logic of the ith drone is as follows:
if it is notThe ith nobody fails; otherwise, if there is a fault isolation residual evaluation functionk∈NiAnd all other fault isolation residual evaluation functionsp∈NiK, satisfiesAnd isThe kth neighbor of the ith unmanned aerial vehicle fails; otherwise, if the residual evaluation function is separated for all faultsk∈NiAll satisfyThe failed drone is the other drone excluding the ith drone and its neighbors.
As can be seen from the second sub-diagram of fig. 4, after the fault detection is finished, the distributed fault separation residual evaluation function of the unmanned aerial vehicle 1Greater than a corresponding threshold valueThe unmanned aerial vehicle 1 thus judges that it is malfunctioning. The subsequent fault isolation step is not performed at this time.
As can be seen from the second sub-diagram of fig. 5, after the fault detection is finished, the distributed fault separation residual evaluation function of the unmanned aerial vehicle 2Less than the corresponding thresholdThe drone 2 therefore determines that it is not faulty by itself. As can be seen from the third sub-diagram of fig. 5, the distributed fault isolation residual evaluation function of the drone 2 to the drone 1Less than the corresponding thresholdAnd unmanned aerial vehicle 2 is to unmanned aerial vehicle 3's distributed fault separation residual error evaluation functionGreater than a corresponding threshold valueTherefore, the drone 2 determines that the drone 1 has failed.
As can be seen from the second sub-diagram of fig. 6, after the fault detection is finished, the distributed fault separation residual evaluation function of the unmanned aerial vehicle 3Less than the corresponding thresholdThe unmanned aerial vehicle 3 thus judges that no malfunction has occurred by itself. As can be seen from the third sub-diagram of fig. 6, the distributed fault isolation residual evaluation function of the drone 3 to the drone 1Less than the corresponding thresholdAnd distributed fault separation of unmanned aerial vehicle 3 to unmanned aerial vehicle 2Residual evaluation functionGreater than a corresponding threshold valueTherefore, the unmanned aerial vehicle 3 determines that the unmanned aerial vehicle 1 has failed.
And 8: decoupling the kinematics model of the unmanned aerial vehicle on the x axis, the y axis and the z axis of the space coordinate system, wherein the kinematics model of the ith unmanned aerial vehicle in the y axis direction of the space coordinate system is the same as the kinematics model in the x axis direction in the step 2, and repeating the steps 2 to 7 to obtain the fault analysis result of the unmanned aerial vehicle formation system in the y axis;
and step 9: and (3) decoupling the kinematics model of the unmanned aerial vehicle on the x axis, the y axis and the z axis of the space coordinate system, repeating the steps from 2 to 7 to obtain the fault analysis result of the unmanned aerial vehicle formation system on the z axis, wherein the kinematics model of the ith unmanned aerial vehicle on the z axis direction of the space coordinate system is the same as the kinematics model on the x axis direction in the step 2.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (1)
1. A distributed speed sensor fault diagnosis method of a time delay unmanned aerial vehicle formation system is characterized by comprising the following steps:
step 1: calculating communication topology parameters of unmanned aerial vehicle formation, and aiming at a formation system consisting of N unmanned aerial vehicles, G ═ { V, E } is a non-directional communication topology of the formation system, wherein V ═ 1, 2.. and N } is communication topology nodes, and each communication topology node represents one unmanned aerial vehicle;each edge represents communication between a pair of unmanned aerial vehicles, and is an edge of a communication topology;
let matrix Ag＝[aij]For the adjacency matrix of the communication topology, if (i, j) belongs to E, the node i and the node j are called as neighbor nodes, namely, the node i and the node j have communication, aij＝aji1, otherwise aij＝aji＝0；
Let NiIs the neighbor set of the ith UAV, | NiL is the set NiThe number of middle elements;
let matrix Dg＝[dij]The degree matrix of the communication topology has off-diagonal elements of zero and diagonal elements of zero
Let matrix LgIs a Laplace matrix of the communication topology, then Lg＝Dg-Ag(ii) a Let 0 be less than or equal to lambda1＜λ2≤...≤λNIs LgN eigenvalues from small to large;
step 2: based on communication topological parameters, given tracks, formation vectors and preset conditions of unmanned aerial vehicle formation, a distributed formation control law is designed, and the method specifically comprises the following steps:
the open-loop model of the ith unmanned aerial vehicle in the x-axis direction of the space coordinate system is as follows:
wherein, i is 1, 2., N,for the displacement of the ith drone,for the speed of the ith drone,for the control law of the ith unmanned aerial vehicle,for the displacement sensor measurement of the ith drone,for the speed sensor measurement of the ith drone,the speed sensor fault of the ith unmanned aerial vehicle is as follows:
wherein,for the moment of occurrence of the fault of the ith drone,fault amplitude, χ for ith dronei(t) is a constant value or a function of period tau,communication time delay between neighboring unmanned aerial vehicles;
given trajectory of the formation system isOrder d with the 1 st unmanned aerial vehicle as the pilot10 and let the formation vector d ═ d1,d2,...,dN]TWhereinIs the ith nobodyThe distance between the unmanned aerial vehicle and the 1 st unmanned aerial vehicle, the distributed control law of the ith unmanned aerial vehicle is as follows:
wherein,first and second derivatives, k, respectively, of a given trajectory1＞0，k2＞0，k3＞0，k4Is more than 0 and satisfies the following preset conditions: k is a radical of1＞k2λNAnd
and step 3: based on a formation system closed-loop model and relative state measurement of each unmanned aerial vehicle and a neighbor, a distributed fault detection residual error generator and a corresponding fault detection residual error evaluation function are designed, and the method specifically comprises the following steps:
based on the open-loop model and the distributed control law of the ith unmanned aerial vehicle, the closed-loop model of the ith unmanned aerial vehicle can be obtained as follows:
wherein,respectively the displacement and speed of the jth drone,for the jth drone's speed sensor fault,the reference track of the closed-loop model of the ith unmanned aerial vehicle is in the following specific form:
let x be [ ξ ]1,ξ2,...ξN,ζ1,ζ2,...,ζN]T，v＝[v1,v2,...,vN]T，f＝[f1,f2,...,fN]T(ii) a Let yi(t) is the relative state measurement of the ith drone and the neighbors in the form:
wherein,1,2, of the ith node, respectivelyiL neighborhoods;
based on ith unmanned aerial vehicle closed-loop model and yi(t), the closed-loop model of the entire formation system is as follows:
wherein,
wherein iiAndare respectively unit matrix INAnd I2NThe kth column of (1);
based on a closed-loop model of a formation system and relative state measurement of an ith unmanned aerial vehicle and a neighbor, a distributed fault detection residual error generator of the ith unmanned aerial vehicle is designed as follows:
wherein,for the state of the distributed fault detection residual generator,designing a matrix for residual errors of a distributed fault detection residual error generator by using a pole allocation methodMake itIs a stable matrix;
based on the distributed fault detection residual error generator of the ith unmanned aerial vehicle, designing a corresponding fault detection residual error evaluation function as follows:
wherein, | | ri 0(t) | | is ri 0(t) 2 norm;
and 4, step 4: based on a closed-loop model of a formation system and relative state measurement of each unmanned aerial vehicle and a neighbor, in each unmanned aerial vehicle, a group of distributed fault separation residual error generators and a group of corresponding fault separation residual error evaluation functions are designed for all neighbor nodes of the unmanned aerial vehicle, and the method specifically comprises the following steps:
in the ith unmanned aerial vehicle, a distributed fault separation residual error generator is designed for the kth neighbor node, and the specific form is as follows:
wherein k is equal to Ni，To isolate the state of the residual generator for distributed faults,separating the residual of the residual generator for the distributed fault;andis calculated as follows:
wherein,andare respectively E1，E2And Γi,2The (c) th column of (a),to make it possible toA stable matrix;
designing a corresponding fault separation residual evaluation function based on a kth distributed fault separation residual generator of the ith unmanned aerial vehicle as follows:
and 5: designing a distributed fault separation residual error generator and a corresponding fault separation residual error evaluation function based on an open loop model of each unmanned aerial vehicle; the specific form of the distributed fault separation residual error generator of the ith unmanned aerial vehicle is as follows:
wherein,for the state of the decentralized fault isolation residual generator of the ith drone,separating the residuals of the residual generator for the ith drone's decentralized failure,for the open loop control input of the ith drone,is the measurement output of the ith drone; wherein,andthe values of (A) are as follows:
design using pole allocation methodMake itIs a stable matrix;
based on the distributed fault separation residual error generator of the ith unmanned aerial vehicle, designing a corresponding fault separation residual error evaluation function as follows:
step 6: fault detection is performed based on a distributed fault detection residual evaluation function and a corresponding fault detection threshold, which specifically comprises the following steps:
order toIs composed ofThe corresponding fault detection threshold value is set to,the method can be obtained according to the requirements of noise, unmodeled dynamics and fault detectability and according to actual experience; the fault detection logic of the ith drone is as follows:
if it is notOne unmanned aerial vehicle in the system breaks down; if it is notNo unmanned aerial vehicle in the system fails;
and 7: fault separation is carried out based on a fault separation residual error evaluation function and a corresponding fault separation threshold value, and the method specifically comprises the following steps:
order toIs composed ofCorresponding fault isolation threshold, where k ∈ NiLet us orderIs composed ofA corresponding fault isolation threshold;andthe method can be obtained according to the requirements of noise, unmodeled dynamics and fault separability and according to actual experience; the fault isolation logic of the ith drone is as follows:
if it is notThe ith unmanned aerial vehicle fails; otherwise, if there is a fault isolation residual evaluation functionk∈NiAnd all other fault isolation residual generatorsp∈NiK, satisfiesAnd isThen it is firstThe kth neighbor of the i unmanned aerial vehicles fails; otherwise, if the residual evaluation function is separated for all faultsk∈NiAll satisfyThe unmanned aerial vehicle with the fault is the other unmanned aerial vehicle except the ith unmanned aerial vehicle and the neighbors of the ith unmanned aerial vehicle;
and 8: decoupling the kinematics model of the unmanned aerial vehicle on the x axis, the y axis and the z axis of the space coordinate system, wherein the kinematics model of the ith unmanned aerial vehicle in the y axis direction of the space coordinate system is the same as the kinematics model in the x axis direction in the step 2, and repeating the steps 2 to 7 to obtain the fault diagnosis result of the unmanned aerial vehicle formation system in the y axis;
and step 9: and (3) decoupling the kinematics model of the unmanned aerial vehicle on the x axis, the y axis and the z axis of the space coordinate system, repeating the steps from 2 to 7 to obtain the fault diagnosis result of the unmanned aerial vehicle formation system on the z axis, wherein the kinematics model of the ith unmanned aerial vehicle on the z axis direction of the space coordinate system is the same as the kinematics model on the x axis direction in the step 2.
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