CN114995512A - Unmanned aerial vehicle swarm formation control method based on prediction model rolling optimization - Google Patents
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Abstract
The invention discloses an unmanned aerial vehicle swarm formation control method based on prediction model rolling optimization, which comprises the step S1 of determining the relative position error of a following unmanned aerial vehicle and a piloting unmanned aerial vehicle by taking a track coordinate system as a reference coordinate system; step S2, dividing formation control into longitudinal control and transverse control, wherein the longitudinal control is completed by a height maintaining channel, and the transverse control adopts a nonlinear model predictive control method to control the yaw rate to achieve the purpose of controlling the transverse distance deviation; the method for controlling the transverse direction comprises the following steps: step S21, establishing a nonlinear prediction model of the flight path; step S22, setting corresponding quadratic form performance index; and step S23, rolling and optimizing quadratic performance indexes by adopting a steepest descent method. The invention can obtain the position of the target again in real time at each sampling moment, does not generate accumulated errors, and the unmanned aerial vehicle can keep formation through real-time adjustment.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicles, in particular to an unmanned aerial vehicle swarm formation shape control method based on prediction model rolling optimization.
Background
The formation control method comprises a following-navigation method (Leader-follow), a behavior-based method, a virtual structure method, an artificial potential field method, distributed control, predictive control, a method of knowledge analysis design by using graph theory and the like. The Leader-Follower is most widely applied, and the Leader-Follower is simple in structure and convenient to understand. However, because the behavior of the whole formation team is determined only by the Leader, there is no team form feedback, and when the Leader fails, the whole system may be paralyzed; the stability of the behavior-based formation method is difficult to analyze mathematically, and the whole formation is difficult to guarantee; the virtual structure method treats the whole formation form as a virtual structure, the method is easy to determine the formation behavior of the whole group, clear formation form feedback exists, but the application range of the formation form is limited because the formation form is required to move like a virtual structure; the artificial potential field method is simple in calculation, convenient for realizing real-time control and particularly effective for processing the collision avoidance problem of the barrier space. However, the design of the potential field function is difficult, and the problem of local extreme points exists; the distributed control can independently consider the characteristics of each robot, and has the advantages of strong flexibility and robustness, high efficiency and fault-tolerant capability of completing tasks and the like. However, the disadvantages are that the design of the controller is complex and difficult, the stability of the closed-loop system is difficult to guarantee, the stability can not be solved by the local stability of each subsystem, and the correlation effect among robots needs to be considered.
The predictive control has the advantages of having a strong theoretical basis, being capable of ensuring the full utilization of information, establishing the optimization at each moment on the basis of the actual process by online rolling optimization and combining the feedback correction of real-time information, and having strong capacity of online processing constraint (control constraint and state constraint). The method has the disadvantages that the stability is difficult to ensure for the distributed model predictive control method, the calculated amount is large, and the aspects of real-time calculation, distribution realization and the like need further research. The above control methods are not necessarily used independently, and in many cases occur simultaneously.
In the process of flying of unmanned aerial vehicle swarm formation, the unmanned aerial vehicle swarm formation faces a complex and variable environment and needs to have certain intelligence, and in order to complete a high-level decision task, a plurality of variables need to be controlled, and coordinated actions are performed to optimize a target and better complete the task.
The unmanned aerial vehicle swarm formation prediction controller can operate on the upper layer of the traditional local loop controller, and can meet the requirement of high-layer intelligent decision as much as possible while meeting the stability. The main research model of the invention is used for predicting and controlling the application of the unmanned aerial vehicle formation flying formation keeping, and provides an idea for more decisions in the future.
In the design process of the unmanned aerial vehicle swarm formation predictive controller, predictive control for establishing a nonlinear system is adopted, the method is basically not different from the linear system, but when a specific algorithm is considered, online rolling optimization of the method becomes remarkably difficult. In the case of quadratic form of the performance indicator, a nonlinear optimization problem is faced due to the model nonlinearity. How to effectively solve the nonlinear rolling optimization problem in real time is still a challenging subject. In recent years, many scholars have made extensive studies on the predictive control of nonlinear systems and have proposed a number of meaningful approaches. The core of these methods is how to overcome the difficulty of solving the non-linear problem. The methods proposed so far are roughly the following:
(1) the linear method is that after the model is linearized, the controller is designed by using the rolling optimization of linear prediction control, and meanwhile, the nonlinear model is reserved for prediction. In order to overcome errors caused by model linearization, the linearized model can be continuously corrected through online identification.
(2) The numerical calculation and analysis are combined, namely, a nonlinear model is utilized to carry out online simulation, optimization is carried out through a gradient method, and the solution of the nonlinear optimization problem is solved through repeated iteration.
(3) The hierarchical method is to convert the nonlinear optimization into linear optimization and coordination two-stage calculation through a hierarchical algorithm, or realize the input and output linearization through nonlinear feedback and then use a linear prediction control algorithm.
(4) The approximation method is that a generalized convolution model or a generalized orthogonal function is used for approximating a nonlinear model, and linear or simple nonlinear predictive control problems are solved after truncation.
(5) And (3) a special nonlinear system, such as Hammerstein (Hammerstein) model and a predictive control algorithm of a bilinear model.
The above prior art does not well solve the optimization problem of the nonlinear prediction model proposed herein, and the present invention is proposed to solve the above-mentioned shortcomings of the prior art.
Disclosure of Invention
In view of the above problems, the invention aims to provide a control method for formation of a swarm of unmanned aerial vehicles based on rolling optimization of a prediction model.
In order to achieve the aim of the invention, the technical scheme provided by the invention is that the unmanned aerial vehicle swarm formation control method based on the prediction model rolling optimization comprises the following steps:
step S1, determining the relative position error of the following unmanned aerial vehicle and the piloting unmanned aerial vehicle by taking a track coordinate system as a reference coordinate system;
in step S1, the calculating of the relative position error includes,
step S11, calculating the relative distance between the following unmanned aerial vehicle and the piloting unmanned aerial vehicle by adopting the GPS value;
and step S12, converting the relative distance error between the piloting unmanned aerial vehicle and the following unmanned aerial vehicle from a ground coordinate system to a track coordinate system of the piloting unmanned aerial vehicle.
Step S2, dividing formation control into longitudinal control and transverse control, wherein the longitudinal control is completed by a height maintaining channel, and the transverse control adopts a nonlinear model predictive control method to control the yaw rate to achieve the purpose of controlling the transverse distance deviation;
the method for controlling the transverse direction comprises the following steps:
step S21, establishing a nonlinear prediction model of the flight path;
the step S21 specifically includes:
the nonlinear prediction model of the flight path is established as follows:
the state space equation of the unmanned aerial vehicle transverse and lateral motion model is as follows:
wherein (x) d ,y d )∈R 2 Is the position of the drone, V is the airspeed, psi is the yaw angle, W x And W y For disturbances of the wind in the x and y directions, u cmd Yaw rate, u mix 、u max Is the range of yaw rate.
The step S22 specifically includes:
step S22, setting corresponding quadratic form performance index;
the quadratic performance index is set as follows:
setting the modeling time domain length N of the controlled object at the moment k for optimization, and calculating an optimized control sequence { u ] at each time interval 1 ,u 2 ...,u N Will control the quantity u immediately 1 Output, save the remaining inputs as { u } 2 ,u 3 ...,u N ,u N Is used in the next time interval,
within a given constraint, the system output value y (k + i | k) is brought as close as possible to the reference given trajectory y r (k + i | k) while avoiding drastic changes in control increments; the quadratic optimization objective function is:
constraint X (k +1) ═ g (X (k), u (k), k) (equation 7)
The yaw rate constraint is-0.2 ≤ u cmd Not more than 0.2, theta (-) terminal state, L i (. to) predict output and input states in the time domain;
the objective function is the deviation of the lateral distance y from the piloted unmanned plane, the deviation of the yaw angle psi and the control input yaw rate u, the weighting matrix is Q, R and S, and the objective function is:
in step S23, the rolling optimization of the quadratic performance index by the steepest descent method specifically includes:
introducing Lagrange multiplier [ lambda ] 1 ,λ 2 ,...,λ N The optimization problem under the constraint of the (formula 3) is an unconstrained optimization,
let Hamilton function H be
The cross-sectional conditions and the adjoint equations are
Optimized output value u at time k k ＝(u(0),u(1),...,u(N-1)) T ，
The direction of the steepest descent, and the steepest descent method comprises the following steps:
While||u k+1 -u k ||＞ε
step 1: according to u k ＝(u(0),u(1),...u(N-1)) T Calculation of X (k +1), … X (k + N)
Step 2: calculating (lambda) N ,λ N-1 ,...λ 1 )
Step3：WhileJ new ＞J
According to u k+1 Calculating X new (k+1),...X new (k+N)
The search step length and the epsilon error threshold are reduced by s-beta s, | beta | < 1.
The beneficial effects of the invention include:
1. the unmanned aerial vehicle formation adopted track coordinate system is obtained through simulation, and the control of the following unmanned aerial vehicle is obtained through coordinate conversion after the error of the relative distance is calculated through the unmanned aerial vehicle position information obtained through a GPS;
2. the stability proves that the method can lead the predicted value and the actual value of the piloting unmanned aerial vehicle to be different to cause errors if the piloting unmanned aerial vehicle is not predicted when the target turns to move flexibly, because the prediction control is real-time rolling optimization, the position of the target can be obtained again in real time at each sampling moment, no accumulated error is generated, and the unmanned aerial vehicle can keep formation through real-time adjustment. In actual engineering, the maneuver of the piloting unmanned aerial vehicle can be generally predicted through a flight line, and the turning process information of the unmanned aerial vehicle is obtained, so that the error can be further reduced.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic diagram of the present invention illustrating the coordinate transformation of the relative position error of formation;
FIG. 2 is a schematic diagram of the analysis of lateral and lateral movement of the unmanned aerial vehicle of the present invention;
FIG. 3 is a control Simulink diagram of the following unmanned aerial vehicle according to the invention through simulation calculation;
FIG. 4 is a diagram showing the X relative distance l in the simulation calculation result of the present invention c (ii) a change;
FIG. 5 is a diagram showing the relative distance f of Y in the simulation calculation result of the present invention c A variation graph;
FIG. 6 is a diagram showing the X-Y relative distance of the straight-line horizontal flight in the simulation calculation result of the present invention;
FIG. 7 is a diagram showing the Z relative distance h in the simulation calculation result of the present invention c A variation graph;
FIG. 8 is a three-dimensional graph of formation control of a formation in a simulation calculation result according to the present invention;
FIG. 9 is a chart of yaw rate variation in the results of simulation calculations according to the present invention.
Detailed Description
The technical solution in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
Step S1, determining the relative position error of the following unmanned aerial vehicle and the piloting unmanned aerial vehicle by taking a track coordinate system as a reference coordinate system;
as shown in fig. 1, two unmanned aerial vehicles are used for formation flying analysis, the following unmanned aerial vehicle keeps the relative distance from the piloting unmanned aerial vehicle as a set value, the reference coordinate system comprises a ground coordinate system and a body coordinate system, but the calculation is relatively complex, the current common speed coordinate system is a speed coordinate system, but uncontrollable points are easy to appear, and the track coordinate system is used as the reference coordinate system to determine the relative position error between the following unmanned aerial vehicle and the piloting unmanned aerial vehicle.
In fig. 1, where "W" denotes following drone, "L" denotes piloting drone, O g X g Y g Z g Ground coordinate axis system, O wk X wk Y wk Z wk Is to follow the track coordinate system of the unmanned aerial vehicle, O lk X lk Y lk Z lk Is the track coordinate system of piloted unmanned aerial vehicle, d w 、d l Is the distance between the following unmanned aerial vehicle, the piloting unmanned aerial vehicle and the origin of the ground coordinate axis system, (f) c ,l c ) The distance between the following unmanned aerial vehicles in the formation and the track coordinate system of the piloting unmanned aerial vehicles. Because in the flight process of the unmanned aerial vehicle, the sideslip angle is very small, in order to simplify the calculation, the unmanned aerial vehicle is supposed to fly without sideslip in formation flight, namely
Psi yaw angle, beta sideslip angle.
For calculating the position error, two steps are divided:
step S11, calculating the relative distance between the following unmanned aerial vehicle and the piloting unmanned aerial vehicle by adopting the GPS value;
and step S12, converting the relative distance error between the piloting unmanned aerial vehicle and the following unmanned aerial vehicle from a ground coordinate system to a track coordinate system of the piloting unmanned aerial vehicle.
The coordinate conversion relation of the relative distance error between the piloting unmanned aerial vehicle and the following unmanned aerial vehicle converted from the ground coordinate system to the track coordinate system of the piloting unmanned aerial vehicle is as follows:
the transverse position error conversion relation is shown as (formula 2), wherein (l, f) is the transverse distance error and the forward distance error of the following unmanned aerial vehicle in the piloting unmanned aerial vehicle track coordinate system, (l) c ,f c ) Is the relative distance of the specified formation.
Step S2, dividing formation control into longitudinal control and transverse control, wherein the longitudinal control is completed by a height maintaining channel, and the transverse control adopts a nonlinear model predictive control method to control the yaw rate to achieve the purpose of controlling the transverse distance deviation;
the method for controlling the transverse direction comprises the following steps:
step S21, establishing a nonlinear prediction model of the flight path;
the step S21 specifically includes:
the nonlinear prediction model of the flight path is established as follows:
the horizontal and lateral motion of the unmanned aerial vehicle is shown in fig. 2, and the state space equation of the horizontal and lateral motion model of the unmanned aerial vehicle is as follows:
wherein (x) d ,y d )∈R 2 For the position of the drone, V is the airspeed, psi is the yaw angle, W x And W y For disturbances of the wind in the x and y directions, u cmd Yaw rate, u mix 、u max Is the range of yaw rate.
The drone speed is usually constant or varies over a small range, thus assuming a fixed airspeed V during flight, windless environment. The simplified discretized kinematic equation is the formula (formula 4), and Δ T is the time interval.
For brevity, this is: x (k +1) ═ f (X (k), u (k)) (formula 5)
The step S22 specifically includes:
step S22, setting corresponding quadratic form performance index;
the quadratic performance index is set as follows:
and setting the modeling time domain length N of the controlled object at the moment k for optimization, wherein when the value of N is large, the calculated amount is correspondingly increased, so that the value of N must be reasonably selected by combining hardware equipment. In selecting the input sequence, some simple structure is usually adopted, so that the number of variables to be parameterized is small. The optimized control sequence u is usually calculated every time interval 1 ,u 2 ...,u N Will control the quantity u immediately 1 And (6) outputting. Because the unmanned aerial vehicle does not have violent maneuverabilityAct so that in a time interval u N The control inputs do not change much, and the remaining inputs are saved as { u 2 ,u 3 ...,u N ,u N And the calculation speed of the optimization algorithm can be increased by using the algorithm in the next time interval.
Within a given constraint, the system output value y (k + i | k) is brought as close as possible to the reference given trajectory y r (k + i | k) while avoiding drastic changes in control increments. Thus, the quadratic optimization objective function is:
constraint X (k +1) ═ g (X (k), u (k), k) (equation 7)
The yaw rate constraint is-0.2 ≤ u cmd Not more than 0.2, theta (-) terminal state, L i (. to) predict output and input states in the time domain;
the objective function is the deviation of the lateral distance y from the piloted unmanned plane, the deviation of the yaw angle psi and the control input yaw rate u, the weighting matrix is Q, R and S, and the objective function is:
in step S23, the rolling optimization of the quadratic performance index by the steepest descent method specifically includes:
introducing Lagrange multiplier [ lambda ] 1 ,λ 2 ,...,λ N The optimization problem under the constraint of the (formula 3) is an unconstrained optimization,
let Hamilton function H be
The cross-sectional conditions and the adjoint equation are
Optimized output value u at time k k ＝(u(0),u(1),...,u(N-1)) T ，
The direction of the steepest descent, and the steepest descent method comprises the following steps:
While||u k+1 -u k ||＞ε
step 1: according to u k ＝(u(0),u(1),...u(N-1)) T Calculation of X (k +1), … X (k + N)
Step 2: calculating (lambda) N ,λ N-1 ,...λ 1 )
Step3：WhileJ new ＞J
According to u k+1 Calculating X new (k+1),...X new (k+N)
And the search step length and the epsilon error threshold are reduced by s-beta s, | beta | < 1.
After the unmanned aerial vehicle swarm formation control completed through the steps, the simulation test result is as follows:
in the simulation, the unmanned aerial vehicle formation adopts a track coordinate system, and the control Simulink diagram of the following unmanned aerial vehicle is obtained by calculating the position information of the unmanned aerial vehicle obtained by the GPS and then carrying out coordinate conversion, as shown in FIG. 3.
In the simulation, the initial conditions of the formation control simulation are as shown in the following table 1, and the front of the navigation unmanned aerial vehicle track coordinate system is defined as positive, the right side is defined as positive, and the upper side is defined as positive. Formation distance in experiment, forward distance f between following unmanned aerial vehicle and piloting unmanned aerial vehicle c -30m, transverse distance l c -40m, height distance h c ＝-10m。
TABLE 1 formation control simulation initial conditions
| Piloting unmanned plane | Following unmanned aerial vehicle | |
| Speed of rotation | 25m/s | 25m/s |
| Longitude (G) | 0.000005 | 0 |
| Latitude | 0.000005 | 0 |
| Height | 500m | 500m |
| Yaw angle | 0deg | 0deg |
And in the straight-line level flight state of the piloting unmanned plane, under the condition that the speed is constant at 25m/s, the yaw angle psi is 45 deg. Mainly controlling the transverse distance l c Reach the formation and the height distance h c Control is accomplished by a height control channel. Fig. 9 shows simulation results when dT is 0.2s, the prediction time domain N is 10, the control time domain m is 1, and dT is 0.2 s.
The formation control stability after the unmanned aerial vehicle swarm formation control completed through the steps is proved as follows:
the formation movement modes are divided into the following two types:
the first motion mode is as follows: two machines formation flies with straight line air route, so the equilibrium state of unmanned aerial vehicle after formation follows unmanned aerial vehicle controlled variable: the drone has the same speed and angle of motion as the target, i.e. v w ＝v l And
and (2) a second motion mode: the two machines are formed into a formation and are flown by the turning machine,
when the target turns and moves flexibly, if the piloting unmanned aerial vehicle is flexible and unpredictable, the predicted value and the actual value of the piloting unmanned aerial vehicle are different, errors can be caused, because the predictive control is to carry out real-time rolling optimization, the position of the target can be obtained again in real time at each sampling moment, accumulated errors can not be generated, and the unmanned aerial vehicle can also keep formation through real-time adjustment. In actual engineering, the maneuver of the piloting unmanned aerial vehicle can be generally predicted through a flight line, and the turning process information of the unmanned aerial vehicle is obtained, so that the error can be further reduced.
To unmanned aerial vehicle bee colony control system, the error mainly comes from following three aspects: firstly, system errors can be generated when the relative motion model of the formation unmanned aerial vehicle is discretized, and secondly, the piloting unmanned aerial vehicle measurement errors are generated. However, since the predictive control is real-time rolling optimization at the sampling time, various information is obtained again at each sampling point, no error accumulation is generated, and the error is within an allowable range.
The described embodiments are only some embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Claims (5)
1. An unmanned aerial vehicle swarm formation control method based on prediction model rolling optimization is characterized by comprising the following steps:
step S1, determining the relative position error of the following unmanned aerial vehicle and the piloting unmanned aerial vehicle by taking a track coordinate system as a reference coordinate system;
step S2, dividing formation control into longitudinal control and transverse control, wherein the longitudinal control is completed by a height maintaining channel, and the transverse control adopts a nonlinear model predictive control method to control the yaw rate to achieve the purpose of controlling the transverse distance deviation;
the method for controlling the transverse direction comprises the following steps:
step S21, establishing a nonlinear prediction model of the flight path;
step S22, setting corresponding quadratic form performance index;
and step S23, rolling and optimizing quadratic performance indexes by adopting a steepest descent method.
2. The method for controlling formation of drone swarm based on predictive model roll optimization according to claim 1, wherein in step S1, the calculation of relative position error includes,
step S11, calculating the relative distance between the following unmanned aerial vehicle and the piloting unmanned aerial vehicle by adopting the GPS value;
and step S12, converting the relative distance error between the piloting unmanned aerial vehicle and the following unmanned aerial vehicle from a ground coordinate system to a track coordinate system of the piloting unmanned aerial vehicle.
3. The unmanned aerial vehicle swarm formation control method based on predictive model roll optimization according to claim 1, wherein the step S21 specifically comprises:
the nonlinear prediction model of the flight path is established as follows:
the state space equation of the unmanned aerial vehicle transverse and lateral motion model is as follows:
wherein (x) d ,y d )∈R 2 For the position of the drone, V is the airspeed, psi is the yaw angle, W x And W y For disturbances of the wind in the x and y directions, u cmd Yaw rate, u mix 、u max Is the range of yaw rate.
4. The unmanned aerial vehicle swarm formation control method based on predictive model rolling optimization according to claim 3, wherein the step S22 specifically comprises:
the quadratic performance index is set as follows:
setting a modeling time domain length N of a controlled object at the moment k for optimization, and calculating an optimized control sequence { u } at each time interval 1 ,u 2 ...,u N Will control the quantity u immediately 1 Output, save the remaining inputs as { u } 2 ,u 3 ...,u N ,u N Is used in the next time interval,
within a given constraint, the system output value y (k + i | k) is brought as close as possible to the reference given trajectory y r (k + i | k) while avoiding drastic changes in control increments; secondary form optimization purposeThe standard function is:
constraint X (k +1) ═ g (X (k), u (k), k) (equation 7)
The yaw rate constraint is-0.2 ≤ u cmd Not more than 0.2, theta (-) terminal state, L i (. to) predict output and input states in the time domain;
the objective function is the deviation of the lateral distance y from the piloted unmanned plane, the deviation of the yaw angle psi and the control input yaw rate u, the weighting matrix is Q, R and S, and the objective function is:
5. the unmanned aerial vehicle swarm formation control method based on predictive model rolling optimization according to claim 4, wherein in the step S23, the quadratic performance index is optimized by rolling by a steepest descent method, specifically:
introducing Lagrange multiplier [ lambda ] 1 ,λ 2 ,...,λ N The optimization problem under the constraint of the (formula 3) is an unconstrained optimization,
let Hamilton function H be
The cross-sectional conditions and the adjoint equations are
Optimized output value u at time k k ＝(u(0),u(1),...,u(N-1)) T ，
The direction of the steepest descent, and the steepest descent method comprises the following steps:
While||u k+1 -u k ||＞ε
step 1: according to u k ＝(u(0),u(1),...u(N-1)) T Calculation of X (k +1), … X (k + N)
Step 2: calculating (lambda) N ,λ N-1 ,...λ 1 )
Step3：WhileJ new ＞J
According to u k+1 Calculating X new (k+1),...X new (k+N)
The search step length and the epsilon error threshold are reduced by s-beta s, | beta | < 1.
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