CN112198893B - Unmanned aerial vehicle cluster area coverage control system and method based on fractional calculus - Google Patents
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Abstract
The invention discloses an unmanned aerial vehicle cluster area coverage control system and method based on fractional calculus. The invention adopts a cluster unmanned aerial vehicle to form a wireless sensor-actuator network, detects the distribution condition of a target object and sends the detection condition to a ground station, the ground station analyzes and processes the detection result, predicts the expected field distribution of the target object, deploys the position of the unmanned aerial vehicle, and the actuator controls the target object to change the distribution of the target object until the target object is completely eliminated. The invention adopts a feedback closed-loop system, so that the unmanned aerial vehicle can carry out coverage deployment according to the distribution of the target object, the control efficiency of the target object is improved, and the dynamic real-time effective control of the target object is realized.
Description
Technical Field
The invention relates to the field of cluster control, in particular to an unmanned aerial vehicle cluster area coverage control system based on fractional calculus.
Background
The movement of many pollutants or insects in life is a diffusion movement, which ideally can be described by Fick's law. The diffusion process described by fick's law is essentially local diffusion, i.e., the flux J at a point in space at each instant is proportional to the concentration gradient in the vicinity of that point, regardless of historical motion and other local particle motion effects. However, in a complex system, the particle motion at different time instants and the particle motion at different spatial points affect each other, which requires that the temporal and spatial correlation, but the spatio-temporal coupling relationship, must be considered when studying the particle motion at a point in space at a time instant.
In order to solve the problem of pollutant diffusion in a local area, the covering type medicine spraying on the area is a way for inhibiting the rapid diffusion of pollutants. At present, a plurality of coverage control methods use random distribution or sequential scanning methods, which have slow coverage speed, cannot realize real-time monitoring of regional pollutants, and cannot find a pollution source in time for control.
Disclosure of Invention
In order to overcome the problems, the inventor of the present invention has made intensive research to design an unmanned aerial vehicle cluster area coverage control system and method based on fractional calculus, wherein the control system includes an unmanned aerial vehicle, a sensor, an actuator and a ground station, the sensor and the actuator are carried on the unmanned aerial vehicle, and the sensor and the actuator are respectively in communication connection with the ground station. The invention adopts a cluster unmanned aerial vehicle to form a wireless sensor-actuator network, detects the distribution condition of a target object and sends the target object to a ground station, the ground station analyzes and processes the detection result, predicts the expected field distribution of the target object, deploys the position of the unmanned aerial vehicle, and simultaneously controls the target object by an actuator to change the distribution of the target object until the target object is completely eliminated. The invention adopts a feedback closed-loop system, so that the unmanned aerial vehicle can carry out coverage deployment according to the distribution of the target object, the control efficiency of the target object is improved, and the dynamic real-time effective control on the target object is realized, thereby completing the invention.
The invention aims to provide an unmanned aerial vehicle cluster area coverage control system based on fractional calculus, which comprises an unmanned aerial vehicle, a sensor, an actuator and a ground station,
the sensor and the actuator are carried on the unmanned aerial vehicle and are respectively in communication connection with the ground station,
the sensor is used for detecting the distribution information of the target object and sending the information to the ground station,
the ground station is used for analyzing and processing the information,
the actuator is used for carrying out operation to control the target object.
The invention aims at providing an unmanned aerial vehicle cluster area coverage control method based on fractional calculus, which comprises the following steps:
step one, obtaining a fractional order diffusion model suitable for a target object;
secondly, controlling the coverage of the target object according to the fractional order diffusion model;
preferably, the first step includes:
and (5) circulating the steps 2-4.
The invention has the following beneficial effects:
(1) the unmanned aerial vehicle cluster area coverage control system based on fractional calculus can realize real-time detection and dynamic coverage control on target distribution, can realize timely control on pollutants, pests and the like in a local area, and has positive significance for protecting personal safety and reducing economic loss;
(2) according to the area coverage control method, a fractional order diffusion model is adopted to predict the evolution of the distribution situation of the target objects in the area, the prediction result is combined with a CVT (constant voltage transformer) division method to determine the expected position of the unmanned aerial vehicle, the distribution of the target objects is changed through the operation of an actuator to form a feedback closed-loop system, and therefore the target objects are eliminated;
(3) the system provided by the invention consists of a common unmanned aerial vehicle, a sensor, an actuator and a ground station, has a simple structure and low cost, and can be widely applied to real-time dynamic coverage control of a target object in different scenes;
(4) the system provided by the invention fills the blank of a coverage control system of a fractional order cluster region, can be used for diffusion control of chemical pollutants, pests and the like in a local region, can adjust the position of the unmanned aerial vehicle according to the distribution of the pollutants, has high coverage speed, can find the pollutants in time for control, and realizes real-time dynamic coverage.
Drawings
Fig. 1 shows a schematic structural diagram of an unmanned aerial vehicle cluster area coverage control system based on fractional calculus according to a preferred embodiment of the present invention;
fig. 2 is a schematic flow chart of an unmanned aerial vehicle cluster area coverage control system based on fractional calculus according to a preferred embodiment of the present invention;
FIG. 3 shows a schematic diagram of the partitioning by density distribution based on the CVT method;
fig. 4 shows a distribution situation of regional pollutants and a deployment situation of an unmanned aerial vehicle when the control system of embodiment 1 of the present invention operates for 1s, fig. 4a is the distribution situation of regional pollutants, and fig. 4b is a schematic diagram of the deployment situation of the unmanned aerial vehicle;
fig. 5 shows a distribution situation of regional pollutants and a deployment situation of an unmanned aerial vehicle when the control system of embodiment 1 of the present invention operates for 5s, where fig. 5a is the distribution situation of regional pollutants, and fig. 5b is a schematic diagram of the deployment situation of the unmanned aerial vehicle;
fig. 6 shows the time-dependent variation of the contaminant concentration using a fractional order diffusion model with different values of α and β according to a preferred embodiment of the present invention.
Detailed Description
The invention is explained in more detail below with reference to the drawings and preferred embodiments. The features and advantages of the present invention will become more apparent from the description.
According to the invention, an unmanned aerial vehicle cluster area coverage control system based on fractional calculus is provided, the system comprises an unmanned aerial vehicle, a sensor, an actuator and a ground station, and the sensor and the actuator are respectively in communication connection with the ground station.
In the invention, for the target object which is not expected to be generated in the region, the problem that the unmanned aerial vehicle needs to detect the target field distribution and the target source position in the region is called as the region coverage control problem.
According to the invention, the target is a substance with diffusion properties, preferably a pollutant, such as a pest, a chemical pollutant, etc., and the target source is a source that produces a substance with diffusion properties.
Fig. 1 is a schematic structural diagram of a coverage control system of a cluster area of an unmanned aerial vehicle based on fractional calculus according to the present invention.
The whole system comprises a plurality of unmanned aerial vehicles and a ground station, wherein each unmanned aerial vehicle is provided with two loads of a sensor and an actuator, the sensor acquires pollutant concentration data, the sensors form a sensor network, the actuator performs operations such as medicine spraying, harmful substance absorption or secondary treatment into harmless substances, and the like, and the ground station performs fractional order system dynamics calculation and CVT region division by combining the outputs of a disturbance source (or a pollution source) and the actuator to obtain system output containing an expected position and an expected distribution field. And the unmanned aerial vehicle moves in the next step according to the expected position, changes the position of the unmanned aerial vehicle and performs the output control of an actuator in the next step according to the expected distribution field.
According to the invention, the sensors and the actuators are mounted on the unmanned aerial vehicles, namely, each unmanned aerial vehicle is mounted with the sensor and the actuator, the sensors and the actuators on the unmanned aerial vehicle cluster form a wireless sensor-actuator network, and the wireless sensor-actuator network can detect and act on the environment in real time by utilizing the speed and height advantages of the unmanned aerial vehicles in the air and combining the characteristics of self-organization and dynamics of the network, namely, the distribution condition of the target objects in the area can be detected in real time and the target objects are removed, so that the coverage deployment and the dynamic control of the area are realized.
According to the invention, the sensors are used for distributing information of the target object, storing the information and sending the information to the ground station.
According to a preferred embodiment of the present invention, the sensors are used to detect the amount of contaminants throughout the target area to obtain area contaminant concentration profile data and transmit the obtained data to the ground station while storing the data.
According to the invention, each sensor can detect the distribution information of the target objects in the detection area, the detection area or the detection range of the sensor is determined by the detection radius of the sensor, each unmanned aerial vehicle detects the distribution information of the target objects in the detection range through the sensor carried on the unmanned aerial vehicle, and the detection range of the unmanned aerial vehicle changes correspondingly when the position of the unmanned aerial vehicle changes.
According to the present invention, the actuator is used for performing work to control the target object and change the distribution of the target object, and preferably, the actuator is used for applying a specific substance to suppress the continuous diffusion of the target object without forming a new target object, for example, the actuator may suppress the diffusion of pests by spraying a medicine which does not pollute the environment.
According to the invention, the ground station is an information processing center of the whole control system, and the ground station receives the target object distribution information sent by the sensor, analyzes and processes the information, and obtains the target object distribution information of the whole target area, namely obtains the target object distribution field of the whole target area, such as the pollutant concentration distribution condition.
According to the invention, the ground station adopts a splicing method to comprehensively process the information sent by each sensor to obtain a target object distribution field of the whole target area.
According to the invention, the ground station estimates the evolution of the distribution of the target object according to the change of the target object distribution field of the whole target area obtained at the moment and the target object distribution field at the last moment, and predicts the distribution of the target object in the next moment area, namely the distribution of the desired field.
According to the invention, when the particle motion of a certain point in a certain time space is researched, the correlation on time and space needs to be considered, the pollutant diffusion problem belongs to the abnormal diffusion problem, and the time and space can be well considered by adopting a fractional order diffusion model, so that the accurate description of the pollutant space-time motion is realized.
According to the invention, the expected field distribution of the target object is obtained according to the change of the target object distribution field at the moment and the target object distribution field at the last moment and according to a fractional order diffusion model, wherein the fractional order diffusion model is shown as the following formula (1):
in the formula (1), the reaction mixture is,
the operator is defined as Caputo, C is defined as Caputo, 0 is initial time of system operation, t is current time (i.e. time t of system operation), ρ (x, y, t) is distribution function of spatial object, x and y respectively represent horizontal and vertical coordinates of the object region in the horizontal plane,
for the total input of the system, k is the diffusion coefficient, and α and β are the orders of the fractional derivative.
According to a preferred embodiment of the present invention,
including a control input representing the amount of a particular substance applied by the actuator (equivalent to the amount of decrease in the target)
And as disturbance input f of the initial target distribution of the system d (x, y, t) (i.e., the interferer, where the variation of the interferer with density is not considered),
preferably, the first and second liquid crystal display panels are,
x and y respectively represent the horizontal and vertical coordinates of the target area in the horizontal plane, t is the time t of the system operation,
represents the measured value of the concentration of the target.
More preferably, the amount of the organic solvent is,
a control input indicative of an amount of drug sprayed by the actuator.
According to the invention, the fractional order diffusion model described by equation (1) is a partial differential equation, the solution of which requires the determination of the boundary conditions of the regions, preferably taking into account only the boundary conditions of the first type and of the second type,
first type boundary conditions:
wherein C is a constant.
Second type boundary condition:
wherein C is 1 And C 2 Is constant and n represents the direction of the normal outside the boundary.
According to a preferred embodiment of the invention, the fractional order diffusion model is solved using a first type of boundary condition.
In the present invention, a first type of boundary condition is used when the density distribution of the region boundary is known, and a second type of boundary condition is used when the rate of change of the density on the region boundary is known.
In the invention, the fractional order diffusion model shown in the formula (1) needs to determine the fractional order derivative orders alpha and beta to determine the fractional order diffusion model, and different target species, target source positions in a target region, target distribution conditions and target diffusion modes need to be applied to the fractional order diffusion model of the target to remove the target.
According to the invention, the control effect of the target object is simulated by changing the fractional order derivative orders alpha and beta, the values of the fractional order derivative orders alpha and beta with the optimal control effect can be determined according to the simulation effect, and then the fractional order diffusion model suitable for the target object is determined.
According to the invention, after the ground station determines the expected field distribution at the next time according to the fractional order diffusion model, the expected position of the unmanned aerial vehicle is determined, the ground station sends an instruction to the unmanned aerial vehicle to deploy the position of the unmanned aerial vehicle, the unmanned aerial vehicle reaches the expected position, and the actuator works to control the target object and change the distribution of the target object.
According to the invention, the ground station preferably adopts a CVT method to divide the target area according to the expected field distribution, and determines the expected position of the unmanned aerial vehicle.
In the present invention, schematic diagrams of the division by the CVT method according to the density distribution are shown in fig. 3a and 3b, the division result shown in fig. 3a is obtained by randomly dividing the target region by the CVT, and the division result of the target region by the CVT method is shown in fig. 3b in combination with the density (concentration) distribution in the target region.
Fig. 3a is a Voronoi diagram obtained by randomly dividing 256 points by randomly sampling the region, and fig. 3b is a centroid Voronoi diagram distributed according to density obtained by performing iterative computation on the region 3a by using a CVT method. The points in the graph are the generator of the Voronoi diagram, i.e., the centroid of each Voronoi cell.
In the invention, the distribution of the target objects in the target area of the fractional order diffusion model and the calculation process of the position of the unmanned aerial vehicle are carried out on the ground station and are not carried out on the unmanned aerial vehicle, thereby reducing the calculation burden of the unmanned aerial vehicle, reducing the energy consumption of the unmanned aerial vehicle and improving the utilization rate.
The unmanned aerial vehicle cluster area coverage control system based on fractional calculus provided by the invention consists of an unmanned aerial vehicle, a sensor, an actuator and a ground station, has a simple system structure, can be widely applied to real-time dynamic coverage control of a target object under different scenes, detects the distribution of the target object in real time through the sensor, comprehensively processes and predicts the expected field distribution through the ground station, deploys the position of the unmanned aerial vehicle, operates through the actuator, changes the distribution of the target object, detects the distribution of the target object again through the sensor, forms a closed-loop feedback system, and improves the control efficiency and the dynamic control of the target object.
The invention provides an unmanned aerial vehicle cluster area coverage control method based on fractional calculus, which is preferably realized by adopting the control system in the first aspect of the invention, and the method comprises the following steps:
step one, obtaining a fractional order diffusion model suitable for a target object.
According to the invention, the fractional order diffusion model suitable for the target object is a fractional order diffusion model with a good control effect on the target object, the fractional order derivative order alpha and beta values of the fractional order diffusion model are determined through simulation so as to determine the fractional order diffusion model suitable for the target object, and the model can be used for eliminating the target object in the target area in a short time, namely reducing the concentration of the target object in the target area to 0.
According to the invention, step one comprises:
According to the invention, in step 1, the control system initialization comprises: and determining the target area information and the parameter information of the unmanned aerial vehicle.
According to the present invention, the target region information includes a range of the target region, the range of the target region is determined by spatial position coordinates of the target region, the shape of the target region may be set to be a rectangle, and the position coordinates of the target region are determined with four end points of the rectangle, for example, the target region coordinates may be set to (0,0), (0, y), (x,0), (x, y).
According to the invention, the parameter information of the unmanned aerial vehicles comprises the number N of the unmanned aerial vehicles, the detection radius of the sensor and the dynamics parameters of the unmanned aerial vehicles, preferably, the dynamics parameters of the unmanned aerial vehicles comprise a proportion parameter k p And a damping parameter k d 。
According to the preferred embodiment of the present invention, particle motion modeling is adopted for the motion of the unmanned aerial vehicle, and preferably, the motion process of the unmanned aerial vehicle satisfies the second order kinetic equation as shown in the following formula (2):
in the formula (2), s i For the location of the ith drone,
for the speed of the ith drone,
the second derivative of the ith drone motion,
desired position, k, for the ith drone p And k d The scale factor and the damping factor are respectively, and the unmanned aerial vehicle can be regarded as a particle controlled by the PD.
According to the present invention, step 1 further comprises: and determining the position and the content of pollutants at the pollution source and determining disturbance input aiming at the target diffusion scene.
According to the invention, in step 1, the initialization of the control system further comprises setting values of the fractional derivative orders α, β, and setting boundary conditions to obtain a set fractional diffusion model.
Setting of values of fractional derivative orders α, β: the initial condition, the boundary condition and the diffusion coefficient of the target area are obtained by estimating the information of the target area, then the numerical simulation is carried out to obtain the fractional order which enables the density (concentration) distribution of the target object to be reduced most quickly, and the order is used as the order of a fractional order system which actually works on the ground station.
According to the invention, the set fractional order diffusion model is shown as formula (1), wherein
The corresponding fractional order diffusion model is determined by setting the values of the fractional order derivative orders alpha and beta, the model is adopted for simulation to obtain the coverage control effect on the target object, and the values of the alpha and the beta are changed to obtain the fractional order diffusion model which has a better control effect and is suitable for the target object.
And 2, monitoring the distribution of the target object by the sensor.
According to the invention, step 2 comprises deploying an initial position of the unmanned aerial vehicles, said unmanned aerial vehicles detecting the distribution information of the target objects within their respective detection areas and sending said information to the ground station.
According to a preferred embodiment of the invention, a CVT method is adopted to uniformly divide a target area according to the range of the target area, parameter information of the unmanned aerial vehicle and the like to obtain N sub-areas, the centroid position of each sub-area is determined, the unmanned aerial vehicle carrying a sensor and an actuator is deployed at the centroid position as the initial position of the unmanned aerial vehicle, and the sensors of the unmanned aerial vehicle cluster form a sensor network.
According to the invention, in step 2, the sensors on each unmanned aerial vehicle detect the distribution of the target object, that is, each sensor detects the distribution information of the target object in the respective detection area, stores the information, and simultaneously transmits the information to the ground station.
In the present invention, the distribution information of the target is the concentration or density distribution information of the target, and is preferably a measured value of the concentration or density of the contaminant.
In the invention, each sensor detects the distribution information of the target object at regular intervals according to the self detection frequency or the set frequency and sends the information to the ground station.
In the present invention, the Sensor is preferably a high-precision toxic and harmful gas concentration detection Sensor such as an NE Sensor 7NE series gas Sensor.
And 3, carrying out information processing by the ground station, and determining the expected position of the unmanned aerial vehicle.
According to the invention, step 3 comprises:
3.1, the ground station processes the collected distribution information of the target object detected by each unmanned aerial vehicle to obtain the distribution information of the target object in the whole target area;
3.2, obtaining an expected distribution field according to the set fractional order diffusion model;
and 3.3, dividing a target area according to the expected distribution field, and determining the expected position of the unmanned aerial vehicle.
According to the invention, in step 3.1, the ground station collects the distribution information of the target object detected by the sensors of each unmanned aerial vehicle, processes the information, preferably processes the collected distribution information of the target object in the detection area of each sensor by using a splicing method to obtain the distribution information of the target object in the whole target area, namely, the distribution field distribution of the target object in the target area at the time t is obtained.
According to the invention, in step 3.2, according to the obtained distribution field distribution of the target object in the target region at the time t and the change of the distribution field distribution of the target object at the time t-1, the expected distribution field of the target object is obtained according to the set fractional order diffusion model (i.e. the fractional order diffusion model set in step 1).
According to the invention, in step 3.3, the target area is divided by combining a CVT method according to the expected distribution field, and the expected position of the unmanned aerial vehicle is determined.
According to the invention, step 3.3 comprises:
step 3.3.1, forming the position of the current cluster unmanned aerial vehicle into an initial generation metaset
Wherein s is i Coordinates (i.e., position) for drone i;
step 3.3.2, constructing Voronoi diagram
Wherein, V i Is the ith sub-region in the Voronoi diagram;
step 3.3.3, determining the centroid position of each Voronoi unit, and taking the centroid position as a new generator set
s i * Is the coordinates of the centroid, i.e. the coordinates of the desired drone i, i is 1,2, … k, k is N;
step 3.3.4, judge
And
to determine the desired position of the drone.
According to the invention, in step 3.3.2, the target region is continuously and iteratively divided based on the CVT division method according to the expected distribution field, and finally a Voronoi diagram matched with the expected distribution field is obtained, wherein the Voronoi diagram comprises k Voronoi units.
According to the property of the Voronoi diagram divided by the CVT, an objective function of an optimization problem can be obtained:
where z is any point in space, s i ρ is the desired density distribution field for the position of the drone. And calculating the target function once after each iteration division is finished, and obtaining the Voronoi graph matched with the expected density distribution field when the target function reaches the minimum value or the deviation of the two calculation results is less than a set threshold (such as 0.001).
According to the invention, in step 3.3.3, each Voronoi cell, i.e. each zone V i The centroid position of (3) is calculated as shown in the following equation (2):
where ρ (z) is the desired density distribution field, z is any point in the space Ω (target region), and s i * Is the coordinates of the centroid, i.e. the coordinates of the desired drone i, i 1,2, … k, k N.
Determining the centroid position of each Voronoi cell as the desired position of the drone.
According to the invention, in step 3.3.4, if
And
if the distance deviation is smaller than a set threshold value (such as 0.01), stopping, namely, the position of the unmanned aerial vehicle does not need to be adjusted; otherwise, it will
Is replaced by
And deploying the position of the unmanned aerial vehicle.
And 4, controlling the target object by the actuator.
According to the invention, in step 4, the unmanned aerial vehicle moves to a desired position, the actuator works, and the target object is controlled.
The ground station deploys the unmanned aerial vehicle cluster according to the calculated expected position of the unmanned aerial vehicle, preferably, the ground station sends an instruction to the unmanned aerial vehicle, the unmanned aerial vehicle moves to the expected position of the unmanned aerial vehicle according to the instruction, the actuator starts to operate, the target object is controlled, namely, the actuator applies a specific substance to reduce the target object and change the distribution of the target object.
And (5) circulating the steps 2-4 until the target object in the target area is completely eliminated.
According to the invention, the steps 2-4 are circulated, after the actuator applies the specific substance, the sensor of each unmanned aerial vehicle detects the distribution information of the target object in the detection area again, the detected information is sent to the ground station, the ground performs information processing, the unmanned aerial vehicle is deployed to the expected position, the unmanned aerial vehicle moves to the expected position, the actuator performs operation to form a closed-loop feedback system until the target object is eliminated, namely the distribution of the target object is 0.
According to the invention, the first step further comprises: changing the set alpha and beta values of the fractional derivative order to obtain different fractional diffusion models, circulating the step 2-4, controlling the distribution of the target by adopting different fractional diffusion models until the target in the target area is completely eliminated to obtain the change curve of the concentration distribution of the corresponding target with time under different alpha and beta values, such as the curve shown in figure 6, firstly adopting a control variable method,using uncontrolled input
The fractional order diffusion model obtains the removal effect of different alpha and beta on the total pollutant concentration, namely the change relation of the target concentration along with time, alpha and beta values which can completely remove the target (namely the target concentration is 0) in a short time are selected to be determined as the fractional order derivative order alpha and beta values applicable to the target, the fractional order diffusion model applicable to the target is obtained, and then control input is added into the fractional order diffusion model
And obtaining the removal effect of the fractional order diffusion model on the target object when control input is included.
And step two, utilizing the fractional order diffusion model to control the coverage of the target object.
According to the present invention, in the second step, the fractional order diffusion model using the target object described in the step 1 is used to perform the area coverage control on the target object in the target area.
According to the invention, step two comprises:
step S1, determining system initialization information;
step S2, detecting the distribution information of the target object in the detection area by the sensor on each unmanned aerial vehicle, and sending the information to the ground station;
step S3, the ground station processes the information, and determines the expected position of the unmanned aerial vehicle according to the fractional order diffusion model applicable to the target object in the step I;
step S4, the unmanned aerial vehicle moves to the expected position, and the actuator performs operation;
looping steps S2-S4.
According to the present invention, the determining of the system initialization information in step S1 includes: and determining target area information, unmanned aerial vehicle parameter information, a target source position and target object content at the target source.
According to the invention, in steps S2-S4, a target area is evenly divided into N sub-areas, the centroid position of each sub-area is determined, unmanned aerial vehicles are deployed at the centroid position, the system starts to operate, each unmanned aerial vehicle detects the distribution information of target objects in each detection area and sends the information to a ground station, the ground station splices the information of each unmanned aerial vehicle to obtain the distribution information of the target objects in the whole target area at the current moment, a fractional order diffusion model applicable to the target object in the step one is utilized, the distribution information of the target objects at the previous moment is combined to predict the distribution information (namely a desired distribution field) of the target objects at the next moment, the desired position of the unmanned aerial vehicle is determined according to the desired distribution field and a CVT method, the unmanned aerial vehicle moves to the desired position, an actuator works, substances are applied, the target objects are controlled, and the steps S2-S4 are circulated, until the target is eliminated, i.e. the target concentration is 0.
According to the unmanned aerial vehicle cluster area coverage control system and method based on fractional calculus, a feedback closed-loop system is adopted, so that the unmanned aerial vehicle can be covered and deployed according to target distribution and gradually approaches a target source until the target is eliminated, the control efficiency of the target is improved, and the target is dynamically and effectively controlled finally.
Examples
The embodiment simulates an unmanned aerial vehicle cluster area coverage control system based on fractional calculus.
And aiming at the pollutant diffusion scene, determining the range of a target area, the number of unmanned aerial vehicles, the kinetic parameters of the unmanned aerial vehicles, the order of a fractional order diffusion model, boundary conditions, the detection radius of a sensor, the position of a pollution source and the pollutant content of the pollution source.
According to the pollutant types and diffusion types, a fractional order diffusion model shown as a formula (1) is adopted, the diffusion coefficient is 0.01, the fractional order derivative order is 0.7, beta is 1.7, the boundary condition is a first type boundary condition and is 0, namely the first type boundary condition is adopted
The diffusion source (contamination source) is taken as an attenuating disturbance f at a fixed point (0.8,0.2) d (t)＝20e -t | (x＝0.8，y＝0.2) The number of drones is 4, the target area coordinates are (0.33 ), (0.33,0.66), (0.66,0.33), (0.66 ), and the kinetic parameter is k p ＝6，k d 1. The simulation region is [0,1 ]]×[0,1]The unit of all position coordinates is meter (m);
uniformly dividing a target area to obtain 4 sub-areas, determining the centroid positions of the 4 sub-areas, wherein the set of centroid coordinates is
The unmanned aerial vehicles are uniformly deployed at the mass center positions of the sub-areas, the sensors carried by the unmanned aerial vehicles start to detect pollutant concentration distribution data information in the detection areas respectively, the detection data information is stored, and meanwhile the detection data information is sent to the ground station.
Fig. 4 shows a distribution situation of regional pollutants and a deployment situation of the unmanned aerial vehicle detected by the unmanned aerial vehicle after the unmanned aerial vehicle operates for 1s initially, fig. 4a shows a distribution situation of the regional pollutants (x and y are respectively a horizontal coordinate and a vertical coordinate of a target region in a horizontal plane, and u is a pollutant concentration), and fig. 4b shows a schematic diagram of the deployment situation of the unmanned aerial vehicle.
In fig. 4, the black circle represents the initial position of the drone, the red circle represents the desired position of the drone, the star represents the source of the contamination, and the green area represents the area of the contamination. Unmanned aerial vehicle evenly deploys in the target area, detects pollutant concentration, and after the initialization operation 1s, it has the region that is greater than 0.2 to detect out pollutant concentration, can calculate the expectation position that obtains unmanned aerial vehicle according to pollutant distribution condition.
and the ground station processes the received detection information data of each unmanned aerial vehicle by a splicing method to obtain the concentration distribution condition of pollutants in the whole area, namely the field distribution of the pollutants at the current moment.
According to the obtained distribution situation of the pollutant concentration in the whole area and the field distribution change at the previous moment, the fractional order diffusion model in the step 1 is utilized to predict the pollutant concentration distribution in the whole area at the next moment, so as to obtain the predicted pollutant concentration distribution in the whole area, namely the expected field distribution of the target object at the next moment,
CVT division is carried out on the target region according to the predicted whole region pollutant concentration distribution, and the method comprises the following steps:
step (1) taking the unmanned aerial vehicle initial position set as an initial generating element
Step (2) constructing a Voronoi diagram according to the expected field distribution
Step (3) determining the centroid of each Voronoi unit, and taking the set of centroids as a new generator
And (4) judging the new generator, stopping if the distance of the initial generator of the new generator is less than 0.01, otherwise, stopping
Is replaced by
the unmanned plane according to the expected position in the step 3
(see the red circles in fig. 4 and 5) and the actuator sprays the medicine for neutralizing the pollutants according to the concentration of the pollutants around, and as shown in fig. 5, the distribution of the pollutants in the area after the system runs for 5sThe deployment situation of the unmanned aerial vehicle, fig. 5a is the distribution situation of the regional pollutants, and fig. 5b is a schematic diagram of the deployment situation of the unmanned aerial vehicle.
In fig. 5, the black circle represents the current position of the drone, the red circle represents the desired position of the drone, the pollution source, and the green area represents the pollution area. After the executor sprays the medicine, unmanned aerial vehicle detects the pollutant concentration in the detection area separately again, and after the system operation 5s, pollutant concentration obviously reduced.
And (5) circulating the step 2-4, and stopping the operation when the regional pollutants are completely eliminated in the step 2.
The invention has been described in detail with reference to the preferred embodiments and illustrative examples. It should be noted, however, that these specific embodiments are only illustrative of the present invention and do not limit the scope of the present invention in any way. Various modifications, equivalent substitutions and alterations can be made to the technical content and embodiments of the present invention without departing from the spirit and scope of the present invention, and these are within the scope of the present invention. The scope of the invention is defined by the appended claims.
Claims (2)
1. An unmanned aerial vehicle cluster area coverage control method based on fractional calculus is characterized by comprising the following steps:
step one, obtaining a fractional order diffusion model suitable for a target object;
the first step comprises the following steps:
step 1, controlling system initialization, comprising: determining target area information and parameter information of the unmanned aerial vehicle,
the target region information includes a range of the target region, determined by spatial position coordinates of the target region, the shape of the target region is set to a rectangle, position coordinates of the target region are determined with four end points of the rectangle, target region coordinates are set to (0,0), (0, y), (x,0), (x, y),
the parameter information of the unmanned aerial vehicle comprises the number N of the unmanned aerial vehicles, the detection radius of the sensor and the kinetic parameters of the unmanned aerial vehicle, wherein the kinetic parameters of the unmanned aerial vehicle comprise a proportional parameter k p And a damping parameter k d ，
Particle motion modeling is adopted for the motion of the unmanned aerial vehicle, and the motion process of the unmanned aerial vehicle meets a second-order kinetic equation shown in the following formula (2):
in the formula (2), s i For the location of the ith drone,
for the speed of the ith drone,
the second derivative of the ith drone motion,
desired position, k, for the ith drone p And k d The proportion coefficient and the damping coefficient are respectively used, and the unmanned aerial vehicle is regarded as a particle controlled by the PD;
in step 1, the control system consists of an unmanned aerial vehicle, a sensor, an actuator and a ground station,
the sensor and the actuator are carried on the unmanned aerial vehicle and are respectively in communication connection with the ground station,
the sensor is used for detecting the distribution information of the target object and sending the information to the ground station,
the ground station is used for analyzing and processing the information,
the actuator is used for carrying out operation to control the target object,
the ground station analyzes and processes the information, obtains an expected distribution field of the target object according to a fractional order diffusion model,
the fractional order diffusion model is as follows:
in the formula (1), the acid-base catalyst,
the method is characterized in that a time fractional order derivative operator under the definition of Caputo is provided, C is the definition of Caputo, 0 is the initial time of system operation, t is the time t of system operation, rho is rho (x, y, t) is a spatial object distribution function, x and y respectively represent the horizontal and vertical coordinates of an object area in a horizontal plane,
is the total input of the system, and the system,
a control input indicative of the amount of drug sprayed by the actuator,
represents the concentration measurement value of the target, k is a diffusion coefficient, alpha and beta are the orders of fractional derivatives,
the fractional order diffusion model described in the formula (1) is a partial differential equation, the solution of the equation needs to determine the boundary condition of the region, only the first type of boundary condition and the second type of boundary condition are considered,
the first type of boundary condition:
wherein C is a constant;
second type boundary conditions:
wherein C 1 And C 2 Is constant, n represents the boundary outer normal direction;
when the density distribution of the region boundary is known, adopting a first type of boundary condition, and when the change rate of the density on the region boundary is known, adopting a second type of boundary condition;
the control system initialization also comprises the steps of setting values of fractional derivative orders alpha and beta to obtain a set fractional order diffusion model;
setting of values of fractional derivative orders α, β: firstly, estimating target area information to obtain initial conditions, boundary conditions and a target diffusion coefficient of a target area, then carrying out numerical simulation to obtain a fractional order which enables the density or concentration distribution of the target to be reduced most quickly, and taking the order as the order of a fractional order system actually working on a ground station;
step 2, detecting the distribution of the target objects by using a sensor, wherein the detection comprises the initial position of deploying the unmanned aerial vehicles, the unmanned aerial vehicles detect the distribution information of the target objects in respective detection areas and send the information to a ground station, and the distribution information of the target objects is the concentration or density measurement value of pollutants;
according to the range of a target area and parameter information of the unmanned aerial vehicle, the target area is uniformly divided by adopting a CVT method to obtain N sub-areas, the mass center position of each sub-area is determined, the unmanned aerial vehicle carrying a sensor and an actuator is deployed at the mass center position and used as the initial position of the unmanned aerial vehicle, the sensor of the unmanned aerial vehicle cluster forms a sensor network, and the sensor is a high-precision toxic and harmful gas concentration detection sensor;
step 3, the ground station processes information and determines the expected position of the unmanned aerial vehicle, and the method comprises the following steps:
step 3.1, the ground station processes the collected distribution information of the target objects detected by each unmanned plane by adopting a splicing method to obtain the distribution information of the target objects in the whole target area, namely the distribution field distribution of the target objects in the target area at the moment t is obtained;
step 3.2, obtaining an expected distribution field of the target object according to the fractional order diffusion model set in the step 1;
3.3, dividing a target area by combining a CVT method according to the expected distribution field, and determining an expected position of the unmanned aerial vehicle;
step 3.3 comprises:
step 3.3.1, forming the position of the current cluster unmanned aerial vehicle into an initial generation element set
Wherein s is i Coordinates of the ith unmanned aerial vehicle;
step 3.3.2, constructing Voronoi diagram
Wherein, V i Is the ith sub-region in the Voronoi diagram;
in step 3.3.2, continuously and iteratively dividing a target region based on a CVT division method according to an expected distribution field to finally obtain a Voronoi diagram matched with the expected distribution field, wherein the Voronoi diagram comprises k Voronoi units;
according to the property of the Voronoi diagram divided by the CVT, an objective function of an optimization problem is obtained:
wherein z is any point in space, s i Rho is the expected density distribution field for the position of the unmanned aerial vehicle; performing primary calculation on the target function after each iterative division is finished, and when the target function reaches a minimum value or the deviation of two calculation results is smaller than a set threshold value, obtaining a Voronoi graph which is matched with the expected density distribution field;
step 3.3.3, determining the centroid position of each Voronoi unit, and taking the centroid position as a new generating element set
Each Voronoi cell, i.e. each region V i The centroid position of (a) is calculated as shown in the following equation (3):
where ρ (z) is the desired density distribution field and z is the space Ω, i.e. any point in the target region, s i * Is the coordinates of the centroid, i.e. the coordinates of the desired drone i, i is 1,2, … k, k is N;
step 3.3.4, judge
And with
Distance deviation to determine the desired position of the drone, if
And with
If the distance deviation is smaller than the set threshold value, stopping, namely, the position of the unmanned aerial vehicle does not need to be adjusted; otherwise, it will
Is replaced by
Deploying the position of the unmanned aerial vehicle;
step 4, the actuator controls the target object,
in step 4, the ground station deploys the unmanned aerial vehicle cluster according to the expected position of the unmanned aerial vehicle obtained by calculation, the ground station sends an instruction to the unmanned aerial vehicle, the unmanned aerial vehicle moves to the respective expected position according to the instruction, the actuator starts to operate and controls the target object, namely, the actuator applies a specific substance to reduce the target object and change the distribution of the target object,
and (4) circulating the step (2-4), after the actuator applies the specific substance, the sensor of each unmanned aerial vehicle detects the distribution information of the target objects in the detection area again, the detected information is sent to a ground station, the ground carries out information processing, the unmanned aerial vehicle is deployed to the expected position, the unmanned aerial vehicle moves to the expected position, the actuator works to form a closed-loop feedback system until the target objects in the target area are completely eliminated, namely the distribution of the target objects is 0,
the first step further comprises the following steps: changing the values of the set fractional order derivative orders alpha and beta to obtain different fractional order diffusion models, and circulating the step 2-4 until the target object in the target area is completely eliminated to obtain the values of the fractional order derivative orders alpha and beta applicable to the target object and obtain the fractional order diffusion model applicable to the target object;
secondly, controlling the coverage of the target object by utilizing the fractional order diffusion model; the second step comprises the following steps:
step S1, determining system initialization information;
step S2, detecting the distribution information of the target objects in the detection area of each unmanned aerial vehicle by the sensor on each unmanned aerial vehicle, and sending the information to the ground station;
step S3, the ground station processes the information, and determines the expected position of the unmanned aerial vehicle according to the fractional order diffusion model applicable to the target object in the step I;
step S4, the unmanned aerial vehicle moves to the expected position, and the actuator performs operation;
looping steps S2-S4; uniformly dividing the target area into N sub-areas, determining the centroid position of each sub-area, deploying the unmanned aerial vehicles at the centroid position, starting the system to operate, detecting the distribution information of the target objects in the respective detection areas by each unmanned aerial vehicle, and the information is sent to a ground station, the ground station splices the information of all unmanned aerial vehicles to obtain the distribution information of the target object in the whole target area at the current moment, the distribution information of the target object at the next moment is predicted by utilizing the fractional order diffusion model applicable to the target object in the step one and combining the distribution information of the target object at the previous moment, namely a desired distribution field, determining a desired position of the unmanned aerial vehicle by combining a CVT method according to the desired distribution field, moving the unmanned aerial vehicle to the desired position, carrying out operation by an actuator, applying a substance, controlling a target object, and circulating the steps S2-S4 until the target object is eliminated, namely the concentration of the target object is 0.
2. The method of claim 1, wherein the ground station divides the target area according to the desired distribution field in combination with the CVT method to determine the desired position of the UAV, the ground station sends a command to the UAV, the UAV reaches the desired position, and the actuator operates to control the target.
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