CN115903908B - Bee colony unmanned aerial vehicle fault-tolerant cooperative control method based on rapid terminal sliding mode - Google Patents
Bee colony unmanned aerial vehicle fault-tolerant cooperative control method based on rapid terminal sliding mode Download PDFInfo
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Abstract
The utility model discloses a bee colony unmanned aerial vehicle fault-tolerant cooperative control method based on quick terminal sliding mode, relate to unmanned aerial vehicle technical field, this method obtains nonsingular quick terminal sliding mode face based on fixed wing unmanned aerial vehicle's position tracking error design, and the total unknown item and command control input signal that contain trouble related item and external disturbance item are introduced to the dynamics model of combining fixed wing unmanned aerial vehicle, thereby construct and obtain the fault-tolerant control law of fixed wing unmanned aerial vehicle, utilize the fault-tolerant control law that obtains based on quick terminal sliding mode design to carry out fault-tolerant cooperative control to bee colony unmanned aerial vehicle, still can keep bee colony unmanned aerial vehicle's stable flight when unmanned aerial vehicle meets executor external disturbance, still make each unmanned aerial vehicle can carry out formation tracking to desired position, have fine practical meaning and application prospect on bee colony unmanned aerial vehicle's formation cooperative fault-tolerant control.
Description
Technical Field
The application relates to the technical field of unmanned aerial vehicles, in particular to a bee colony unmanned aerial vehicle fault-tolerant cooperative control method based on a rapid terminal sliding mode.
Background
Along with the rapid development of the unmanned aerial vehicle industry, unmanned aerial vehicles are widely applied to complex dangerous tasks such as agricultural plant protection, power grid detection, forest fire monitoring and the like so as to shorten the task period. In recent years, the problem of cooperative control of the swarm unmanned aerial vehicle attracts more and more researchers' attention, mainly because the swarm unmanned aerial vehicle has the remarkable advantages of distributed functions, high survival rate, low cost and the like,
research on swarm unmanned aerial vehicles is being vigorously developed, and application prospects are quite wide. In order to improve the cooperative control performance of the unmanned aerial vehicle in the task execution process, the safety and the practicability become hot research problems in the field of flight control, and urgent development demands are put forward on reliable flight and fault tolerance technologies of the unmanned aerial vehicle. However, when the swarm unmanned aerial vehicle is in the task execution stage, if a certain unmanned aerial vehicle or a plurality of unmanned aerial vehicles in formation fail and are not processed in time, the failed unmanned aerial vehicle has a risk of out of control, chain reaction can occur under serious conditions, the unmanned aerial vehicles around the collision cause the out of control of the whole flying formation, and the situation is particularly obvious when a large number of unmanned aerial vehicles are concentrated to work, so that the reliable flying of the swarm unmanned aerial vehicle is influenced.
Disclosure of Invention
Aiming at the problems and the technical requirements, the applicant provides a bee colony unmanned aerial vehicle fault-tolerant cooperative control method based on a rapid terminal sliding mode, and the technical scheme of the application is as follows:
a fault-tolerant cooperative control method of a swarm unmanned aerial vehicle based on a rapid terminal sliding mode comprises a leader unmanned aerial vehicle and N fixed wing unmanned aerial vehicles which fly along with the leader unmanned aerial vehicle, wherein a communication topology is established among unmanned aerial vehicles contained in the swarm unmanned aerial vehicle, the method comprises the following steps that for any ith fixed wing unmanned aerial vehicle in the swarm unmanned aerial vehicle, i is a parameter and i is more than or equal to 1 and less than or equal to N:
the expression for determining the position tracking error of the ith fixed wing unmanned aerial vehicle is
p i Is the actual position of the ith fixed wing unmanned plane, p di ＝p 0i +p ri Is the expected position of the ith fixed wing unmanned aerial vehicle, p 0i Is the position information of the leader unmanned aerial vehicle observed by the ith fixed wing unmanned aerial vehicle by using a distributed sliding mode observer, and p ri Is the expected relative position between the ith fixed wing unmanned aerial vehicle and the leader unmanned aerial vehicle;
the method comprises the steps of designing and obtaining a nonsingular rapid terminal sliding mode surface based on a position tracking error of an ith fixed wing unmanned aerial vehicle;
determining an actual position p of the ith fixed wing unmanned aerial vehicle based on a dynamics model of the ith fixed wing unmanned aerial vehicle i And command control input signal u 0i And total unknown item ζ i Combining with the sliding mode surface of the nonsingular rapid terminal to establish and obtain the fault-tolerant control law of the ith fixed wing unmanned aerial vehicle, wherein the fault-tolerant control law reflects the command control input signal u 0i Position information p of leader unmanned aerial vehicle observed by movement parameter and ith fixed wing unmanned aerial vehicle of bee colony unmanned aerial vehicle 0i Zeta of total unknown item i Is the relation of total unknown item ζ i The method comprises fault related items and external disturbance items;
and carrying out fault-tolerant cooperative control on the ith fixed wing unmanned aerial vehicle by using a fault-tolerant control law.
The beneficial technical effects of this application are:
the method is used for carrying out fault-tolerant cooperative control on the swarm unmanned aerial vehicle based on the rapid terminal sliding mode, can still keep stable flight of the swarm unmanned aerial vehicle when the unmanned aerial vehicle encounters an actuator fault or external disturbance, can also enable each unmanned aerial vehicle to carry out formation tracking on an expected position, and has good practical significance and application prospect on formation cooperative fault-tolerant control of the swarm unmanned aerial vehicle.
According to the method, a fixed time disturbance observer is adopted to estimate the fault related items and the total unknown items of external disturbance contained in the fault-tolerant control law, and the faults and the disturbance can be rapidly compensated by introducing an estimated value into the fault-tolerant control law, so that a rapid fault-tolerant effect is ensured.
According to the method, the performance constraint is carried out on the synchronous tracking errors by introducing the preset performance of the fixed time, so that the rapid convergence of the synchronous tracking errors of all unmanned aerial vehicles is ensured and the synchronous tracking errors are stabilized in the constraint boundary.
Drawings
Fig. 1 is a schematic communication topology of a swarm drone in an embodiment of the present application.
FIG. 2 is a schematic information flow diagram of a fault-tolerant control law constructed in one embodiment of the present application.
FIG. 3 is a fault tolerant coordinated control block diagram in one embodiment of the present application.
Fig. 4 is a flight trajectory of each fixed wing drone in one simulation example of the present application.
FIG. 5 is a representation of the application control input signal u for each fixed wing drone in a simulation example of the present application i Delta of (2) ti Is a calendar simulation graph of (a).
Fig. 6 is a calendar simulation graph of the synchronous tracking error of each fixed wing drone in one simulation example of the present application.
FIG. 7 is a graph of a calendar simulation of an estimate of the total unknown term for each fixed wing drone in one simulation example of the present application.
Detailed Description
The following describes the embodiments of the present application further with reference to the accompanying drawings.
Referring to fig. 1, the bee colony unmanned aerial vehicle applicable to the method comprises a leader unmanned aerial vehicle 1 and N fixed wing unmanned aerial vehicles which fly along with the leader unmanned aerial vehicle 1, and fig. 1 is an example of the fixed wing unmanned aerial vehicle 2, 3, 4, 5 and 6. Communication topology is established between unmanned aerial vehicle that this bee colony unmanned aerial vehicle contained, includes: a communication connection is established between the leader unmanned aerial vehicle 1 and the fixed wing unmanned aerial vehicle, and a communication connection is established between the fixed wing unmanned aerial vehicles. Each drone may establish a communication connection with all other drones, or only some of the other drones. In one embodiment, a two-way communication connection is established between the fixed wing drones, while a one-way communication connection is established between the leader drone 1 and the fixed wing drone, where information is transmitted by the leader drone to the fixed wing drone. Referring to the communication topology diagram in an example shown in fig. 1, the leader unmanned aerial vehicle 1 establishes unidirectional communication connection with the fixed wing unmanned aerial vehicle 2 and the fixed wing unmanned aerial vehicle 3 respectively, the fixed wing unmanned aerial vehicle 2 establishes bidirectional communication connection with the fixed wing unmanned aerial vehicles 3, 4 and 5 respectively, the fixed wing unmanned aerial vehicle 3 also establishes bidirectional communication connection with the fixed wing unmanned aerial vehicles 4 and 6, and the fixed wing unmanned aerial vehicle 5 also establishes bidirectional communication connection with the fixed wing unmanned aerial vehicle 6.
The method is used for controlling any ith fixed wing unmanned aerial vehicle in the swarm unmanned aerial vehicle by adopting the following fault-tolerant cooperative control method, wherein i is a parameter and is more than or equal to 1 and less than or equal to N:
1. and constructing a fault-tolerant control law of the ith fixed-wing unmanned aerial vehicle. The method comprises the following steps, please refer to the information flow chart shown in fig. 2:
the method for constructing the fault-tolerant control law is designed based on the expression of the position tracking error of the ith fixed wing unmanned aerial vehicle, wherein the expression of the position tracking error of the ith fixed wing unmanned aerial vehicle is that
Wherein p is i The actual position of the ith fixed wing unmanned aerial vehicle can be expressed as p i ＝[x i ,y i ,z i ] T ，x i 、y i 、z i The positions on three coordinate axes of a virtual coordinate system established in advance are respectively. P is p di ＝p 0i +p ri Is the expected position of the ith fixed wing unmanned aerial vehicle. P is p 0i The position information of the leader unmanned aerial vehicle, which is observed by the ith fixed wing unmanned aerial vehicle through a distributed sliding mode observer. P is p ri ＝[x ri ,y ri ,z ri ] T Is the expected relative position, x, between the ith fixed wing unmanned aerial vehicle and the leader unmanned aerial vehicle 1 ri 、y ri 、z ri The desired relative positions on the three coordinate axes of the virtual coordinate system, respectively.
Then based on the position tracking error of the ith fixed wing unmanned aerial vehicle
The nonsingular rapid terminal sliding die surface is designed. The method comprises the following steps:
(1) Position tracking error of unmanned aerial vehicle according to ith frame fixed wing
Combining the position tracking errors of other fixed wing unmanned aerial vehicles, and processing to obtain the synchronous tracking error e of the ith fixed wing unmanned aerial vehicle i ：
Wherein e i ＝[e i(1) ，e i(2) ，e i(3) ] T ，
β 1i 、β 2i All are positive parameters, a ij Is an element of an unmanned aerial vehicle bee colony adjacent matrix, and is used as an ith fixed wing unmanned aerial vehicle and a jth frameWhen the fixed wing unmanned aerial vehicle establishes communication connection, a ij =1, a when the ith and jth fixed wing drones do not establish a communication connection ij ＝0；。/>
Is the position tracking error of any j-th fixed wing unmanned aerial vehicle, j is a parameter, and j is more than or equal to 1 and less than or equal to N.
(2) Synchronous tracking error e of ith frame of fixed wing unmanned aerial vehicle by adopting fixed time preset performance function i ＝[e i(1) ，e i(2) ，e i(3) ] T Performing performance constraint, and processing to obtain a conversion error E of the ith fixed wing unmanned aerial vehicle i ＝[E i(1) ，E i(2) ，E i(3) ] T . Introducing a fixed time preset performance function to synchronize tracking error e i And performance constraint is carried out, so that the synchronous tracking errors of the unmanned aerial vehicles can be ensured to be converged rapidly and stabilized in a constraint boundary.
Presetting a performance function xi based on a fixed time i ＝[ξ i(1) ,ξ i(2) ,ξ i(3) ] T Determining a synchronous tracking error e of the ith fixed wing unmanned aerial vehicle i The performance constraint to be satisfied at each time t is-delta m ξ i(r) (t)<e i(r) (t)<δ M ξ i(r) (t), r is a parameter and r=1, 2, 3, δ m 、δ M Are positive parameters.
The fixed time preset performance function is:
T (r) the settling time of the performance function is preset for a fixed time. Zeta type toy ∞(r) ＝lim t→∞ ξ i(r) (t)，ξ ∞(r) >0，ξ 0(r) >ξ ∞(r) ，ξ i(r) (t)>ξ ∞(r) . Definition e i(r) (t)＝ξ i(r) (t)Φ i(r) (z i(r) (t)), then the error transfer function
Based on phi i(r) (z i(r) (t))∈(-δ m ,δ M ) Requirement setting of (2)
So that the determination can be switched:
namely there is
After obtaining E i ＝[E i(1) ，E i(2) ，E i(3) ] T After that, further to the conversion error E i Taking the derivative to obtain:
wherein,,
ν i ＝diag{ν i(1) ,ν i(2) ,ν i(3) }. The function diag { } represents taking a diagonal matrix.
Then further to
Taking the derivative to obtain:
wherein,,
is v i Derivative of>
Is e i Derivative of>
Is xi i Derivative of>
Is->
Is a derivative of (a).
(3) Conversion error E based on ith frame of fixed wing unmanned aerial vehicle i ＝[E i(1) ，E i(2) ，E i(3) ] T Design the nonsingular quick terminal sliding die surface as
Wherein p, q, g, h is positive odd number,
K 1i ＝diag{K 1i(1) ,K 1i(2) ,K 1i(3) }，K 2i ＝diag{K 2i(1) ,K 2i(2) ,K 2i(3) }。K 1i(1) 、K 1i(2) 、K 1i(3) are all greater than 0, K 2i(1) 、K 2i(2) 、K 2i(3) Are all greater than 0.Sig (sig) g/h (E i )＝|E i | g/h sign(E i )，/>
Function sign () is a standard sign function.
Design-based non-singular rapid terminal sliding die surface
The fault-tolerant control law of the ith fixed wing unmanned aerial vehicle can be established and obtained. In order to establish the fault-tolerant control law, the actual position p of the ith fixed wing unmanned aerial vehicle needs to be determined i And command control input signal u 0i And total unknown item ζ i Based on the relationship of the ith rackThe dynamic model determination of the fixed-wing unmanned aerial vehicle comprises the following steps:
(1) Firstly, establishing a dynamics model of the ith fixed wing unmanned aerial vehicle comprises the following steps:
state variable x= [ X ] of ith frame of fixed wing unmanned aerial vehicle i ,y i ,z i ,V i ,χ i ,γ i ] T . Wherein the actual position p of the ith fixed wing unmanned aerial vehicle i ＝[x i ,y i ,z i ] T ，
Represents x i Derivative of>
Representing y i Derivative of>
Representing z i Derivative of V i Is the speed of the ith fixed wing unmanned aerial vehicle,/->
Represents V i Is a derivative of (a). Gamma ray i Is the track angle of the ith fixed wing unmanned plane,/->
Representing gamma i Is a derivative of (a). X-shaped articles i Is the heading angle of the ith fixed wing unmanned aerial vehicle,/->
Representing χ i Is a derivative of (a). m is m i The mass of the ith fixed wing unmanned aerial vehicle is shown. d, d i(1) 、d i(2) 、d i(3) Are all external disturbances.
μ i Is the tilt angle alpha of the ith fixed wing unmanned aerial vehicle i Is the attack angle beta of the ith fixed wing unmanned plane i Sideslip angle of ith fixed wing unmanned aerial vehicle。T i Is the thrust force received by the ith fixed wing unmanned plane, D i Is the resistance force applied by the ith fixed wing unmanned aerial vehicle, Y i Is the lateral force applied by the ith fixed wing unmanned aerial vehicle, L i Is the lifting force suffered by the ith fixed wing unmanned aerial vehicle and is provided with
Wherein T is max For the maximum thrust delta of the engine of the ith fixed wing unmanned aerial vehicle ti And setting a thrust throttle for the ith fixed wing unmanned aerial vehicle. s is(s) i Is the wing area of the ith fixed wing unmanned aerial vehicle, < ->
Represents dynamic pressure ρ 0 Represents air density, C iL Is the total lift coefficient, C iD Is the total drag coefficient, C iY Is the total lateral force coefficient, and
C iL0 、C iLα 、C iD0 、C iDα 、C iDα2 、C iY0 、C iYβ are all pneumatic coefficients.
(2) Then based on the established dynamic model transformation, the method obtains
f i 、G i 、d i Respectively, are parameter matrixes, u i ＝[u i(1) ,u i(2) ,u i(3) ] T Is the application control input signal of the ith fixed wing unmanned aerial vehicle and has u i ＝[u i(1) ,u i(2) ,u i(3) ] T ＝[δ ti ,α i sinμ i ,α i cosμ i ] T Wherein:
wherein,,
(3) Establishing an actuator fault model as u i ＝ρ i u 0i +u bi 。
Wherein, command control input signal u of ith fixed wing unmanned aerial vehicle 0i ＝[u 0i(1) ,u 0i(2) ,u 0i(3) ] T 。ρ i ＝diag{ ρ 1i 1,1 represents an efficiency factor, 0<ρ 1i ≤1。 u bi ＝[u bi(1) ,u bi(2) ,u bi(3) ] T Indicating the deviation fault amount.
(4) Combining actuator fault models
Obtain->
(5) Breaking f with butterworth low pass filter i Involving command control input signal u 0i The resulting algebraic loop yields:
wherein f i ＝F i +σ i ，σ i Represents the filtering error, phi i ＝G i (ρ i -I)u 0i +G i u bi I is an identity matrix. Total unknown item ζ i ＝φ i +d i +σ i Thus, the total unknown term ζ in this application i Including fault related terms and external disturbance terms.
The actual position p of the ith fixed-wing unmanned aerial vehicle is determined based on the dynamics model of the ith fixed-wing unmanned aerial vehicle i And command control input signal u 0i And total unknown item ζ i The relation of (2) is that
F i 、G i Respectively a parameter matrix and meaning as above,/>
is the actual position p i Is a second derivative of (c). And then combining the relation with the non-singular quick terminal sliding mode surface obtained by the establishment to obtain a fault-tolerant control law.
Firstly, taking derivative of the established nonsingular rapid terminal sliding mode surface to obtain:
wherein,,
is->
Derivative of>
Then based on what has been obtained above
Expression of (2) synchronous tracking error
Expression of (2), and->
The expression of (2) substitutes the derivative of the non-singular fast termination sliding surface +.>
Is obtained by:
thus, the fault-tolerant control law can be designed to be:
wherein,,
representing total unknown term ζ i Is used for the estimation of the estimated value of (a). k (k) i ＝diag{k i(1) ,k i(2) ,k i(3) }，k i(1) 、k i(2) 、k i(3) Are all greater than 0.τ i >0，/>
sgn(S i )＝[sign(S i(1) )，sign(S i(2) )，sign(S i(3) )] T 。
2. Through the above process, a fault-tolerant control law is established, and the established fault-tolerant control law describes the command control input signal u of the ith fixed wing unmanned aerial vehicle 0i Position information p of leader unmanned aerial vehicle observed by movement parameter and ith fixed wing unmanned aerial vehicle of bee colony unmanned aerial vehicle 0i Zeta of total unknown item i Is a relationship of (3). The motion parameters of the swarm unmanned aerial vehicle comprise the motion parameters of the ith fixed-wing unmanned aerial vehicle, the motion parameters of the leader unmanned aerial vehicle and the motion parameters of other fixed-wing unmanned aerial vehicles, and the motion parameters of each unmanned aerial vehicle at least comprise the state variable X= [ X ] of the unmanned aerial vehicle i ,y i ,z i ,V i ,χ i ,γ i ] T 。
Then, fault-tolerant cooperative control can be performed on the ith fixed wing unmanned aerial vehicle by using a fault-tolerant control law, and please refer to a control block diagram shown in fig. 3.
The fault-tolerant control law includes some unknown parameters in addition to known parameters. In the working process of the swarm unmanned aerial vehicle, the unknown parameters in the fault-tolerant control law are except the position information p of the leader unmanned aerial vehicle observed by the ith fixed wing unmanned aerial vehicle 0i And total unknown item ζ i Besides, the rest can be obtained by using the communication topology of the swarm unmanned aerial vehicle based on the motion parameters of the swarm unmanned aerial vehicle. Next, the embodiment will be described to determine the position information p 0i And total unknown item ζ i Is determined by:
(1) The position information p of the leader unmanned aerial vehicle is obtained by utilizing the following observation of the distributed sliding mode observer 0i 。
Wherein,,
is p 0i Derivative of alpha 1i 、α 2i Two positive parameters. P is p 0j Is the position information of the leader unmanned aerial vehicle observed by any j-th fixed-wing unmanned aerial vehicle, j is a parameter, j is more than or equal to 1 and less than or equal to N, and p 0 Is the actual location of the leader drone. As introduced in the communication topology section above, not all fixed wing drones establish a communication connection with the leader drone, so not all fixed wing drones can obtain the actual position of the leader drone, when the ith fixed wing drone can obtain the actual position of the leader drone c i =1. C when the ith fixed wing unmanned aerial vehicle cannot acquire the actual position of the leader unmanned aerial vehicle i ＝0。
(2) Obtaining a total unknown term ζ using a fixed time disturbance observer i Estimate of (2)
Defining a state variable X 1i ＝p i And
The +.>
Rewritten as
Is X 1i Derivative of>
Is X 2i Is a derivative of (a).
Based on the obtained
Establishing a reference auxiliary system as->
X ei ＝X 2i -X ai ，/>
i Is a positive real parameter.
Then designing a fixed time disturbance observer based on the reference auxiliary system as follows:
wherein,,
is the total unknown item ζ i Is used for the estimation of the estimated value of (a). />
Is an intra-system state estimation error. />
Is X ei Derivative of>
Is X ei Estimated value of ∈10->
Is->
Derivative of eta i(1) 、η i(2) 、η i(3) Are all greater than 0,0<κ i(1) <1，κ i(2) >1。
Then the fixed time disturbance observer obtained by the design can be used for obtaining the actual position p of the fixed wing unmanned aerial vehicle according to the ith frame i Obtaining total unknown term ζ i Estimate of (2)
Please refer to fig. 3, the position information p of the leader unmanned aerial vehicle is obtained by observation 0i Combining a preset expected relative position p between the ith fixed wing unmanned aerial vehicle and the leader unmanned aerial vehicle ri The desired position p can be calculated by means of an addition loop di . The ith fixed wing unmanned plane can acquire the state variable X= [ X ] i ,y i ,z i ,V i ,χ i ,γ i ] T I.e. the motion parameters of the body, the actual position p i ＝[x i ,y i ,z i ] T Is known and therefore according to p di Actual position p of ith fixed wing unmanned aerial vehicle i Can be calculated by a subtraction loop
The j-th fixed wing unmanned aerial vehicle can be obtained based on the motion parameters thereof>
Then based on the communication topology between unmanned aerial vehicles, the ith fixed wing unmanned aerial vehicle can also acquire +.>
Thereby combining->
And->
Can calculate +.>
Further combining with fixed time to preset performance function xi i Calculate and get the conversion error E i ＝[E i(1) ，E i(2) ，E i(3) ] T . Substituting these known parameters into the fault-tolerant control law will result in a total unknown term ζ obtained with a fixed-time disturbance observer i Estimate of +.>
And the command control input signal u of the ith fixed wing unmanned aerial vehicle can be obtained by using the fault-tolerant control law 0i . Then combine the actuator fault model u i ＝ρ i u 0i +u bi Obtaining an application control input signal u of the ith fixed wing unmanned aerial vehicle i The control input signal u will be applied i And outputting the fault-tolerant control result to the ith fixed wing unmanned aerial vehicle, so as to realize fault-tolerant cooperative control of the ith fixed wing unmanned aerial vehicle.
A simulation example is built based on the swarm unmanned aerial vehicle with the communication topology shown in fig. 1, and the values of each structural parameter and the aerodynamic coefficient comprise the following:
all fixed wing unmanned aerial vehicle's wing area is s i ＝1.463m 2 All fixed wing unmanned aerial vehicles's mass is m i =25 kg, air density ρ 0 ＝1.205kg·m -3 Acceleration of gravity g 0 ＝9.8m·s -2 . All aerodynamic coefficient values of the mass of the fixed wing unmanned aerial vehicle are C iL0 ＝0.2153、C iLα ＝4.6333rad -1 、 C iD0 ＝0.0225、C iDα ＝0.1002rad -1 、C iDα2 ＝1.0778、C iY0 ＝0、C iYβ ＝-0.0046rad -1 。
In this simulation example, it is assumed that the fixed-wing unmanned aerial vehicle 2 suffers from an actuator failure at t=20s, the fixed-wing unmanned aerial vehicle 3 suffers from an external disturbance at t=30s, the fixed-wing unmanned aerial vehicle 4 suffers from an actuator failure at t=30s, and suffers from an external disturbance at t=50s. Taking the efficiency factor ρ of the fixed wing unmanned aerial vehicle 2 2 =diag {0.5,1,1}, fixed wing unmanned aerial vehicleEfficiency factor ρ of 4 4 Diag {0.6,1,1}. D for taking out external disturbance of fixed wing unmanned aerial vehicle 3 3 ＝[0.4,0.4,0.4] T D for taking out external disturbance of fixed wing unmanned aerial vehicle 4 4 ＝[0.2,0.2,0.2] T . Taking positive parameter beta 1i ＝9、β 2i =0.4, take k i ＝diag{50,80,30}，ζ i =0.8. Positive parameter alpha of distributed sliding mode observer 1i ＝10、α 2i =0.001. Positive parameter delta of fixed time preset performance function m ＝δ M ＝1，ξ 0(r) ＝1、ξ ∞(r) ＝0.1、T (r) =8. Positive real parameter θ in a fixed time disturbance observer i ＝1、η i(1) ＝η i(2) ＝η i(3) ＝5、κ i(1) ＝0.8、κ i(2) =1.2. Positive odd number p=7, q=5, g=7, h=3, k in the non-singular fast termination slip plane 1i ＝diag{30,30,30}，K 2i ＝diag{10,10,10}。
The initial motion parameters of the bee colony unmanned aerial vehicle are set as follows:
assuming that the speeds of all fixed wing unmanned aerial vehicles are V i =30m/s, track angles are all γ i =0.573° and the heading angle is χ i =0.573°. Actual position p of leader unmanned aerial vehicle 1 at initial time t=0 0 (0)＝[0m,0m,1000m] T . The actual position p of the fixed wing unmanned aerial vehicle 2 at the initial time t=0 2 (0)＝[0m,-15m,1030m] T Desired relative position p with respect to the leader unmanned aerial vehicle 1 r2 ＝[0m,-15m,30m] T . The actual position p of the fixed wing unmanned aerial vehicle 3 at the initial time t=0 3 (0)＝[0m,15m,1030m] T Desired relative position p with respect to the leader unmanned aerial vehicle 1 r3 ＝[0m,15m,30m] T . The actual position p of the fixed wing unmanned aerial vehicle 4 at the initial time t=0 4 (0)＝[0m,0m,1000m] T Desired relative position p with respect to the leader unmanned aerial vehicle 1 r4 ＝[0m,0m,0m] T . The actual position p of the fixed wing unmanned aerial vehicle 5 at the initial time t=0 5 (0)＝[0m,-15m,970m] T Desired relative position p with respect to the leader unmanned aerial vehicle 1 r5 ＝[0m,-15m,-30m] T . The actual position p of the fixed wing unmanned aerial vehicle 6 at the initial time t=0 6 (0)＝[0m,15m,970m] T Desired relative position p with respect to the leader unmanned aerial vehicle 1 r6 ＝[0m,15m,-30m] T 。
The flight trajectory of the leader unmanned aerial vehicle 1 is set to p 0 (t)＝[30*t,0,P 0z ] T The units are m and P 0z Step from 1000m to 1030m at t=20s. Using filters
Generating a smoothed desired signal, wherein ω n ＝0.2、ξ n ＝0.9。
The flight path of each unmanned aerial vehicle in the bee colony unmanned aerial vehicle obtained through simulation is shown in fig. 4, the flight path of the fixed wing unmanned aerial vehicle 2 is 42, the flight path of the fixed wing unmanned aerial vehicle 3 is 43, the flight path of the fixed wing unmanned aerial vehicle 4 is 44, the flight path of the fixed wing unmanned aerial vehicle 5 is 45, and the flight path of the fixed wing unmanned aerial vehicle 6 is 46. Due to the application of the control input signal u i ＝[u i(1) ,u i(2) ,u i(3) ] T ＝[δ ti ,α i sinμ i ,α i cosμ i ] T Thus, in case of other parameter determination, the control input signal u is applied i Actually from delta ti Determining delta of each unmanned aerial vehicle in the bee colony unmanned aerial vehicle ti The time calendar simulation graph of (a) is shown in FIG. 5, delta in FIG. 5 t5 And delta t6 And (5) overlapping. Based on fig. 5 it can be seen that delta of the fixed wing unmanned aerial vehicle 2, 3, 4 ti I.e. applying the control input signal u i Can be quickly adjusted when an actuator fault or external disturbance is encountered. The calendar simulation graphs of the synchronous tracking errors of the fixed wing unmanned aerial vehicle 2, 3, 4 are shown in fig. 6, fig. 6 also shows an enlarged schematic of local fluctuations in the calendar simulation graphs, it can be seen on the basis of fig. 6 that the synchronous tracking errors are rapidly converging and are limited within defined boundaries. Total unknown term ζ obtained by fixed-wing unmanned aerial vehicle 2, 3, 4 using fixed-time disturbance observer i Estimate of (2)
The time calendar simulation graph of (a) is shown in figure 7, and the total unknown item zeta can be rapidly and accurately estimated i Estimate of +.>
What has been described above is only a preferred embodiment of the present application, which is not limited to the above examples. It is to be understood that other modifications and variations which may be directly derived or contemplated by those skilled in the art without departing from the spirit and concepts of the present application are to be considered as being included within the scope of the present application.
Claims (6)
1. The utility model provides a bee colony unmanned aerial vehicle fault-tolerant cooperative control method based on quick terminal slipform, which is characterized in that, including a leader unmanned aerial vehicle and N fixed wing unmanned aerial vehicles that follow the leader unmanned aerial vehicle in the bee colony unmanned aerial vehicle, establish communication topology between the unmanned aerial vehicle that the bee colony unmanned aerial vehicle contains, the method includes to arbitrary i fixed wing unmanned aerial vehicle in the bee colony unmanned aerial vehicle, i is parameter and 1 is less than or equal to i is less than or equal to N:
the expression for determining the position tracking error of the ith fixed wing unmanned aerial vehicle is as follows
p i Is the actual position of the ith fixed wing unmanned aerial vehicle, p di ＝p 0i +p ri Is the expected position, p, of the ith fixed wing unmanned aerial vehicle 0i The position information, p, of the leader unmanned aerial vehicle, observed by the ith fixed wing unmanned aerial vehicle through a distributed sliding mode observer ri Is the desired relative position between the ith fixed wing unmanned aerial vehicle and the leader unmanned aerial vehicle;
the nonsingular rapid terminal sliding mode surface is designed and obtained based on the position tracking error of the ith fixed wing unmanned aerial vehicle;
determining an actual position p of the ith fixed wing unmanned aerial vehicle based on a dynamic model of the ith fixed wing unmanned aerial vehicle i With command control input signalsNumber u 0i And total unknown item ζ i Combining the nonsingular rapid terminal sliding mode surface to establish and obtain the fault-tolerant control law of the ith fixed wing unmanned aerial vehicle, wherein the fault-tolerant control law reflects command control input signals u 0i The motion parameters of the bee colony unmanned aerial vehicle and the position information p of the leader unmanned aerial vehicle, which is observed by the ith fixed wing unmanned aerial vehicle 0i Zeta of total unknown item i Is the relation of total unknown item ζ i The method comprises fault related items and external disturbance items;
performing fault-tolerant cooperative control on the ith frame of fixed wing unmanned aerial vehicle by using the fault-tolerant control law;
the method for designing and obtaining the nonsingular rapid terminal sliding mode surface based on the position tracking error of the ith fixed wing unmanned aerial vehicle comprises the following steps:
according to the position tracking error of the ith fixed wing unmanned aerial vehicle and the position tracking errors of other fixed wing unmanned aerial vehicles, processing to obtain the synchronous tracking error of the ith fixed wing unmanned aerial vehicle
e i ＝[e i(1) ，e i(2) ，e i(3) ] T ，/>
A when the ith fixed wing unmanned aerial vehicle and the jth fixed wing unmanned aerial vehicle establish communication connection ij =1, a when the ith and jth fixed wing unmanned aerial vehicles do not establish communication connection ij ＝0；β 1i 、β 2i All are positive parameters, ++>
Is the position tracking error of any j-th fixed wing unmanned aerial vehicle, j is a parameter, and j is more than or equal to 1 and less than or equal to N;
synchronous tracking error e of the ith frame of fixed wing unmanned aerial vehicle by adopting fixed time preset performance function i Performing performance constraint, and processing to obtain a conversion error E of the ith frame of fixed wing unmanned aerial vehicle i ，E i ＝[E i(1) ，E i(2) ，E i(3) ] T Comprising the following steps: presetting a performance function xi based on a fixed time i(r) (t) determining a synchronous tracking error e of the ith fixed wing unmanned aerial vehicle i The performance constraint to be satisfied at each time t is-delta m ξ i(r) (t)<e i(r) (t)<δ M ξ i(r) (t), r is a parameter and r=1, 2, 3, δ m 、δ M All are positive parameters; the fixed time presets the performance function as
ξ ∞(r) ＝lim t→∞ ξ i(r) (t)，ξ ∞(r) >0，ξ 0(r) >ξ ∞(r) ，ξ i(r) (t)>ξ ∞(r) ，T (r) Presetting the stable time of the performance function for a fixed time, defining e i(r) (t)＝ξ i(r) (t)Φ i(r) (z i(r) (t)), then the error transfer function
Based on phi i(r) (z i(r) (t))∈(-δ m ,δ M ) Requirement setting of (2)
Determination of
Conversion error E based on ith frame of fixed wing unmanned aerial vehicle i Design the nonsingular quick terminal sliding die surface as
Wherein K is 1i ＝diag{K 1i(1) ,K 1i(2) ,K 1i(3) }，K 2i ＝diag{K 2i(1) ,K 2i(2) ,K 2i(3) The function diag { } represents taking a diagonal matrix; k (K) 1i(1) 、K 1i(2) 、K 1i(3) Are all greater than 0, K 2i(1) 、K 2i(2) 、K 2i(3) Are all greater than 0, sig g/h (E i )＝|E i | g/h sign(E i )，/>
Function sign () is a standard sign function, +.>
Is E i Is p, q, g, h is positive odd, < >>
Determination of a kinetic model based on the ith fixed wing unmanned aerial vehicle
F i 、G i The method for establishing and obtaining the fault-tolerant control law of the ith fixed wing unmanned aerial vehicle comprises the following steps of: determining the derivative of the non-singular fast terminal sliding surface to get +.>
Is->
Derivative of>
Based on E i ＝[E i(1) ，E i(2) ，E i(3) ] T And->
Is characterized by conversion error E i Taking the derivative to get +.>
Wherein->
ν i ＝diag{ν i(1) ,ν i(2) ,ν i(3) }，ξ i ＝[ξ i(1) ,ξ i(2) ,ξ i(3) ] T The method comprises the steps of carrying out a first treatment on the surface of the For->
Taking the derivative
Wherein,,
will get +.>
Synchronous tracking error e i And
Substituted into->
Is obtained by:
the fault-tolerant control law is designed as follows:
wherein,,
representing total unknown term ζ i Estimate of k i ＝diag{k i(1) ,k i(2) ,k i(3) }，k i(1) 、k i(2) 、k i(3) Are all greater than 0>
i >0，/>
sgn(S i )＝[sign(S i(1) )，sign(S i(2) )，sign(S i(3) )] T 。
2. The method of claim 1, wherein the determination is based on a kinetic model of the i-th stationary vane unmanned aerial vehicle
The method of (1) comprises:
based on the dynamic model transformation of the ith fixed wing unmanned aerial vehicle
f i 、d i As a parameter matrix, u i ＝[u i(1) ,u i(2) ,u i(3) ] T Is an application control input signal of the ith fixed wing unmanned aerial vehicle;
establishing an actuator fault model as u i ＝ρ i u 0i +u bi Command control input signal u 0i ＝[u 0i(1) ,u 0i(2) ,u 0i(3) ] T ， ρ i ＝diag{ρ 1i 1,1 represents an efficiency factor, 0<ρ 1i ≤1，u bi ＝[u bi(1) ,u bi(2) ,u bi(3) ] T Representing the deviation fault quantity;
combining actuator fault models
Obtain->
Using Butterworth low pass filteringThe device breaks f i Involving command control input signal u 0i The resulting algebraic loop yields:
wherein f i ＝F i +σ i ，σ i Represents the filtering error, phi i ＝G i (ρ i -I)u 0i +G i u bi I is an identity matrix, and the total unknown item ζ i ＝φ i +d i +σ i 。
3. The method of claim 2, wherein the dynamic model transform based on the ith fixed wing unmanned aerial vehicle results in
The method of (1) comprises:
the establishing of the dynamics model of the ith fixed wing unmanned aerial vehicle comprises the following steps:
wherein the actual position p of the ith fixed wing unmanned aerial vehicle i ＝[x i ,y i ,z i ] T ，
Represents x i Derivative of>
Representing y i Derivative of>
Representing z i Derivative of V i Is the speed of the ith fixed wing unmanned aerial vehicle,/>
Represents V i Is a derivative of (2); />
i Is the track angle of the ith fixed wing unmanned aerial vehicle,/the (i)>
Representing gamma i Is a derivative of (2); />
i Is the heading angle of the ith fixed wing unmanned aerial vehicle,/or->
Representation->
i Is a derivative of (2); m is m i Representing the mass of the ith fixed wing unmanned aerial vehicle; d, d i(1) 、d i(2) 、d i(3) All are external disturbance g 0 Representing gravitational acceleration;
μ i is the inclination angle alpha of the ith fixed wing unmanned aerial vehicle i Is the attack angle beta of the ith fixed wing unmanned aerial vehicle i Is the sideslip angle, T of the ith fixed wing unmanned aerial vehicle i Is the thrust force received by the ith fixed wing unmanned aerial vehicle, D i Is the resistance force, Y, received by the ith fixed wing unmanned aerial vehicle i Is the lateral force, L, suffered by the ith fixed wing unmanned aerial vehicle i Is the lifting force received by the ith fixed wing unmanned aerial vehicle and is provided with
Wherein T is max For the maximum thrust delta of the engine of the ith fixed wing unmanned aerial vehicle ti Setting a thrust throttle for the ith fixed wing unmanned aerial vehicle, and s i Is the wing area of the ith fixed wing unmanned aerial vehicle,/or->
Represents dynamic pressure ρ 0 Represents air density, C iL Is the total lift coefficient, C iD Is the total drag coefficient, C iY Is the total lateral force coefficient, and +.>
C iL0 、C iLα 、C iD0 、C iDα 、C iDα2 、C iY0 、C iYβ All are pneumatic coefficients;
based on the established dynamic model transformation
Wherein, the parameter matrix is:
wherein,,
and the application control input signal u of the ith fixed wing unmanned aerial vehicle i ＝[u i(1) ,u i(2) ,u i(3) ] T ＝[δ ti ,α i sinμ i ,α i cosμ i ] T 。
4. The method of claim 2, wherein the fault tolerant coordinated control of the i-th frame fixed wing drone using the fault tolerant control law comprises:
obtaining a command control input signal u of the ith fixed wing unmanned aerial vehicle by using the fault-tolerant control law 0i Combining the actuator fault model u i ＝ρ i u 0i +u bi Obtaining an application control input signal u of the ith fixed wing unmanned aerial vehicle i The application control input signal u i And outputting the data to the ith fixed wing unmanned aerial vehicle.
5. The method according to claim 1, wherein the method further comprises:
defining a state variable X 1i ＝p i And
Based on->
Obtain->
Is X 1i Derivative of>
Is X 2i Is a derivative of (2);
based on
Establishing a reference auxiliary system as->
X ei ＝X 2i -X ai ，/>
i Is a positive real parameter;
designing a fixed time disturbance observer based on the reference auxiliary system is:
wherein,,
is the total unknown item ζ i Estimated value of ∈10->
Is an intra-system state estimationError (S)>
Is X ei Derivative of>
Is X ei Estimated value of ∈10->
Is->
Derivative of eta i(1) 、η i(2) 、η i(3) Are all greater than 0,0</>
i(1) <1，/>
i(2) >1；
The designed fixed time disturbance observer is utilized to obtain the actual position p of the unmanned aerial vehicle according to the ith fixed wing frame i Obtaining total unknown term ζ i Estimate of (2)
And substituted into the fault tolerant control law.
6. The method of claim 1, further comprising observing the position information p of the leader drone with a distributed slipform observer as follows 0i And substituting into the fault-tolerant control law:
wherein,,
is p 0i Derivative of alpha 1i 、α 2i A, when the ith fixed wing unmanned aerial vehicle and the jth fixed wing unmanned aerial vehicle establish communication connection, taking the two parameters as positive parameters ij =1, a when the ith and jth fixed wing unmanned aerial vehicles do not establish communication connection ij ＝0；p 0j Is the position information of the leader unmanned aerial vehicle observed by any j-th fixed wing unmanned aerial vehicle, j is a parameter, j is more than or equal to 1 and less than or equal to N, and p 0 Is the actual location of the leader drone; c) when the ith fixed wing unmanned aerial vehicle can acquire the actual position of the leader unmanned aerial vehicle i =1; c, when the ith fixed wing unmanned aerial vehicle cannot acquire the actual position of the leader unmanned aerial vehicle i ＝0。
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