CN113157000B - Flight formation cooperative obstacle avoidance self-adaptive control method based on virtual structure and artificial potential field - Google Patents

Flight formation cooperative obstacle avoidance self-adaptive control method based on virtual structure and artificial potential field Download PDF

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CN113157000B
CN113157000B CN202110499631.2A CN202110499631A CN113157000B CN 113157000 B CN113157000 B CN 113157000B CN 202110499631 A CN202110499631 A CN 202110499631A CN 113157000 B CN113157000 B CN 113157000B
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许斌
寿莹鑫
马波
唐勇
胡逸雯
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Northwestern Polytechnical University
AVIC Chengdu Aircraft Design and Research Institute
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AVIC Chengdu Aircraft Design and Research Institute
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    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying
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Abstract

The invention relates to a flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field, belongs to the field of formation flight control, and is used for formation obstacle avoidance control of multiple unmanned aerial vehicles and processing the influence of dynamics uncertainty of an unmanned aerial vehicle model. The method adopts a virtual formation structure and an artificial potential field strategy, and combines a target track of a formation reference point and a formation virtual structure mass point kinematics model to obtain a virtual mass point motion track under collision avoidance and obstacle avoidance as an expected instruction of a closed loop system. And the control input of the unmanned aerial vehicle is designed by adopting a backstepping method, so that the target tracking control under formation accurate maintenance and effective obstacle avoidance is realized. The dynamics uncertainty of the neural network estimation model is utilized, a serial-parallel model is established to obtain a parallel estimation state, a learning evaluation index of a prediction error mining system is established, and a neural network weight updating law is designed by combining a tracking error. The invention enhances the accuracy of uncertain estimation and provides a new technical approach for improving the formation flight performance.

Description

Flight formation cooperative obstacle avoidance self-adaptive control method based on virtual structure and artificial potential field
Technical Field
The invention relates to a multi-aircraft tracking control method, in particular to a flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field, and belongs to the field of formation flight control.
Background
With the wide application of unmanned aerial vehicles in military and civil use, the flight control technology for formation of multiple unmanned aerial vehicles has important application value in realizing tasks such as cooperative reconnaissance and battle, pesticide spraying and the like. Aiming at multi-unmanned aerial vehicle cooperative tracking control, the strategy based on the virtual structure integrally describes group behaviors and simplifies task description and distribution, and higher formation control accuracy can be obtained. Aiming at collision avoidance of unmanned aerial vehicles between formation and barrier avoidance control of formation, the formation is accurately kept and effectively avoided by combining an artificial potential field and a virtual structure design cooperative control algorithm. Considering the influence of dynamics uncertainty and nonlinearity existing in an unmanned aerial vehicle system on formation flight tracking performance, an intelligent control algorithm for estimating by using the approximation capability of a neural network is widely researched. However, the current intelligent control can only ensure the stability of the system and neglects the evaluation of the expected nonlinear estimation performance. In order to improve the performance of cooperative tracking control and ensure the nonlinear estimation effect, the research on the compound learning strategy based on parallel estimation has important significance on formation flight safety.
Composite Learning finish-Time Control With Application to Quadrotors (B.xu, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, volume 48, No. 10) designs a Finite-Time neural network Control algorithm aiming at an under-actuated unmanned aerial vehicle, and the research goal of the thesis is to realize the tracking of the unmanned aerial vehicle individual to an expected track instruction. Virtual leaders, intellectual features and coordinated Control of groups (Leonard N E, Fiorelli E, IEEE Conference on Decision and Control, 2001) design a multi-agent formation Control algorithm based on artificial potential fields and Virtual agents. The thesis takes a virtual leader as a reference point, and the formation of the multi-agent is controlled by adjusting the artificial potential field. However, the control algorithm designed by the paper depends on the dynamic characteristics of the model, and the rapid and stable control of the system is difficult to realize.
Disclosure of Invention
Technical problem to be solved
Aiming at maintaining and avoiding control of formation of multiple unmanned aerial vehicles and considering the influence of model dynamics uncertainty on control precision, the invention provides a flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field.
Technical scheme
A flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field is characterized by comprising the following steps:
step 1: adopting a dynamic model of the unmanned aerial vehicle:
Figure BDA0003052981660000021
wherein x, y, z are positions,
Figure BDA0003052981660000022
roll angle, theta pitch angle, psi yaw angle, m mass, g gravitational acceleration, I x ,I y ,I z For the inertial matrix, l is the distance from the center of mass of the unmanned aerial vehicle to the center of the rotor, J r Is the moment of inertia of the motor, omega r ＝ω 2 +ω 4 -ω 1 -ω 3 ，ω i The rotation speed of the ith motor is 1,2,3, 4; u shape 1 ,U 2 ,U 3 ,U 4 The control inputs for vertical, roll, pitch, and yaw motions, respectively, are:
Figure BDA0003052981660000023
wherein b is a lift coefficient, and d is a moment coefficient;
step 2: decoupling the unmanned aerial vehicle dynamic model to obtain a position subsystem and an attitude subsystem; definition of x j，1 ＝z j ，
Figure BDA0003052981660000031
The jth drone altitude subsystem dynamics may be written as:
Figure BDA0003052981660000032
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000033
τ j，1 ＝U j，1 in order to control the input of the electronic device,
Figure BDA0003052981660000034
for the unknown smooth function obtained from equation (1),
Figure BDA0003052981660000035
a known function obtained by the formula (1), wherein j is the number of the unmanned aerial vehicles in the formation, j is 1, … N, and N is the number of the unmanned aerial vehicles in the flying formation;
definition of x j,3 ＝x j ，x j,4 ＝y j ，
Figure BDA0003052981660000036
Figure BDA0003052981660000037
Assuming that the attitude angle near the equilibrium position is small; the jth horizontal motion dynamics of the unmanned aerial vehicle can be simplified as follows:
Figure BDA0003052981660000038
the jth drone attitude subsystem dynamics may be written as:
Figure BDA0003052981660000039
in the formula (I), the compound is shown in the specification,
Figure BDA00030529816600000310
τ j,2 ＝[U j,2 ,U j,3 ,U j,4 ]in order to control the input of the electronic device,
Figure BDA00030529816600000311
for the unknown smooth function obtained from equation (1),
Figure BDA00030529816600000312
a known function derived from formula (1);
and step 3: the positions and the yaw angles of the unmanned aerial vehicle formation particles are designed as follows:
Figure BDA00030529816600000313
in the formula, x j,rd ,y j,rd ,z j,rd Position signal of formation particle for jth drone, psi j,rd Yaw angle signal, x, for the jth drone formation particle d ,y d ,z d For position expectation command of formation reference point, # d An instruction is expected for the yaw angle of the formation,
Figure BDA00030529816600000314
for the relative position of the jth drone formation particle and the reference point,
Figure BDA00030529816600000315
forming a relative yaw angle of a particle and a reference point for the jth unmanned aerial vehicle;
the virtual structure particle model is described as:
Figure BDA0003052981660000041
in the formula, x j,d ,y j,d ,z j,d Is the position signal of the jth virtual dot, μ j,1 ,μ j,2 ,μ j,3 A control input signal of the jth virtual dot;
the virtual particle control inputs are designed as:
Figure BDA0003052981660000042
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000043
is a negative gradient term of the artificial potential field, V (-) is a total potential energy function of the particle,
Figure BDA0003052981660000044
Figure BDA0003052981660000045
for formation obstacle avoidance, V m (. to) be particlesPotential energy of avoiding obstacles of c 11 ＞0，c 12 ＞0，c 21 ＞0，c 22 ＞0，c 31 ＞0，c 32 More than 0 is a design parameter;
assuming particle j is in the potential field generated by neighboring particles, the total potential energy function of the jth particle is defined as:
Figure BDA0003052981660000046
in the formula, the kth drone is a neighbor node of the ith drone, and Φ (·) is a potential energy function represented as follows:
Figure BDA0003052981660000047
k is a potential field intensity coefficient, a proper value is selected according to the inertia of the unmanned aerial vehicle and the control output of an actuating mechanism, and R is a potential field action range;
defining the obstacle avoidance potential energy function of the mass point as:
Figure BDA0003052981660000051
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000052
the coordinates of the projection point of the mass point j on the obstacle avoidance area (O) xm ,O ym ,O zm ) Position surrounding the centre of the circle for the m-th obstacle, R k The radius of a circle is enclosed, M is an obstacle number, M is 1, …, M is the number of obstacles;
the desired heading angle of the virtual particle is defined as:
ψ j，d ＝ψ j,rd +ψ j，t (12)
in the formula, # j,t Is an equal azimuth heading angle, which can be expressed as:
Figure BDA0003052981660000053
wherein, Delta e 0 is the designed forward-looking distance;
and 4, step 4: defining an altitude tracking error e for the altitude subsystem (3) j,1 ＝x j,1 -z j,d (ii) a Designing virtual control quantities
Figure BDA0003052981660000054
Comprises the following steps:
Figure BDA0003052981660000055
in the formula, k j,1 The more than 0 is the design parameter,
Figure BDA0003052981660000056
is the derivative of the highly desired instruction;
the first order filter is designed as follows:
Figure BDA0003052981660000057
in the formula, τ j,1 The parameters > 0 of the filter are the parameters of the filter,
Figure BDA0003052981660000058
design of the compensation signal z j,1 Comprises the following steps:
Figure BDA0003052981660000059
in the formula, z j,2 Given in subsequent designs;
tracking error after compensation is defined as:
v j,1 ＝e j,1 -z j,1 (17)
defining a tracking error as
Figure BDA0003052981660000061
Designing the actual control input τ j,1 Comprises the following steps:
Figure BDA0003052981660000062
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000063
for the optimal weight estimation value of the neural network,
Figure BDA0003052981660000064
is a vector of basis functions of the neural network, k j,2 More than 0 is a design parameter;
design of the compensation signal z j,2 Comprises the following steps:
Figure BDA0003052981660000065
tracking error after compensation is defined as:
v j,2 ＝e j,2 -z j,2 (20)
the prediction error is defined as:
Figure BDA0003052981660000066
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000067
for parallel estimation of states, it is obtained by the following serial-parallel model:
Figure BDA0003052981660000068
wherein, beta j,1 More than 0 is a design parameter;
designing a neural network adaptive updating law as follows:
Figure BDA0003052981660000069
in the formula of lambda j,1 ＞0，k j ,ω 1 > 0 and delta j,f1 More than 0 is a design parameter;
and 5: for horizontal motion (4), the design PD controller calculates the expected acceleration as:
Figure BDA00030529816600000610
in the formula, k j,3 ＞0，k j,4 ＞0，k j,5 ＞0，k j,6 The more than 0 is the design parameter,
Figure BDA00030529816600000611
the derivative of the desired command for horizontal position;
obtaining the desired roll and pitch angles as:
Figure BDA0003052981660000071
step 6: for the attitude sub-system (5), defining an attitude angle tracking error as e j,X1 ＝X j,1 -X j,d Wherein
Figure BDA0003052981660000072
An attitude angle expectation command; designing virtual control quantities
Figure BDA0003052981660000073
Comprises the following steps:
Figure BDA0003052981660000074
in the formula, k j,7 The more than 0 is the design parameter,
Figure BDA0003052981660000075
a derivative of the desired command for attitude angle;
the first order filter is designed as follows:
Figure BDA0003052981660000076
in the formula, τ j,2 The parameters > 0 of the filter are the parameters of the filter,
Figure BDA0003052981660000077
design of the compensation signal z j,3 Comprises the following steps:
Figure BDA0003052981660000078
in the formula, z j,4 Given in subsequent designs;
tracking error after compensation is defined as:
ν j,3 ＝e j,X1 -z j,3 (29)
defining a tracking error as
Figure BDA0003052981660000079
Designing the actual control input τ j,2 Comprises the following steps:
Figure BDA00030529816600000710
in the formula (I), the compound is shown in the specification,
Figure BDA00030529816600000711
is an estimation value of the optimal weight of the neural network,
Figure BDA00030529816600000712
is a vector of basis functions of the neural network, k j,8 More than 0 is a design parameter;
design of the compensation signal z j,4 Comprises the following steps:
Figure BDA00030529816600000713
tracking error after compensation is defined as:
v j,4 ＝e j,X2 -z j,4 (32)
the prediction error is defined as:
Figure BDA0003052981660000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000082
for parallel estimation of states, it is obtained by the following serial-parallel model:
Figure BDA0003052981660000083
wherein, beta j,2 More than 0 is a design parameter;
designing a neural network adaptive updating law as follows:
Figure BDA0003052981660000084
in the formula, λ j,2 ＞0，k j,ω2 > 0 and delta j,f2 More than 0 is a design parameter;
and 7: the obtained control input U of the vertical, rolling, pitching and yawing motion j,1 ,U j,2 ,U j,3 ,U j,4 Returning to the dynamics model of the unmanned aerial vehicle system, and realizing the expected instruction x under formation maintenance and obstacle avoidance d ,y d ，z d And performing tracking control.
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for performing the above-described method when executed.
A computer program comprising computer executable instructions which when executed perform the method described above.
Advantageous effects
The invention provides a flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field. The dynamics uncertainty of the unmanned aerial vehicle model is estimated by adopting a neural network algorithm, a serial-parallel model is established to obtain a parallel estimation state and construct prediction error evaluation estimation capability, and the tracking error is applied to a self-adaptive updating law, so that the uncertainty learning capability of the unmanned aerial vehicle is improved, and the system control performance is improved. The beneficial effects are as follows:
(1) the invention adopts a coordination strategy of a virtual formation structure and combines a formation reference point to form an expected organization formation; acquiring a particle track signal of a virtual structure as an expected instruction of a closed-loop system by the action of attractive force and repulsive force between unmanned aerial vehicles based on an artificial potential field strategy;
(2) the dynamics uncertainty of the under-actuated unmanned aerial vehicle is considered, the unknown nonlinearity is estimated by adopting a neural network algorithm, the control input is designed based on a backstepping method and fed forward to an unmanned aerial vehicle model, and the target tracking under formation accurate maintenance and obstacle avoidance is realized;
(3) the method deeply analyzes system dynamics, establishes a serial-parallel model to obtain a parallel estimation state so as to construct a prediction error mining estimation evaluation index, designs a self-adaptive updating law by combining tracking error design, and improves uncertain learning precision.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
Fig. 1 is a flow chart of a flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1, the invention relates to a flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field, which is realized by the following steps:
(a) adopting a dynamic model of the unmanned aerial vehicle:
Figure BDA0003052981660000101
wherein x, y, z are positions,
Figure BDA0003052981660000102
roll angle, theta pitch angle, psi yaw angle, m 2.3kg mass, g 9.81m/s 2 As acceleration of gravity, I x ＝1.676×10 -2 kg·m 2 ，I y ＝1.676×10 -2 kg·m 2 ，I z ＝2.314×10 - 2 kg·m 2 Is an inertia matrix, l is the distance from the center of mass of the unmanned aerial vehicle to the center of the rotor wing, J is 0.1725m r ＝3.36×10 -5 kg·m 2 Is the moment of inertia of the motor, omega r ＝ω 2 +ω 4 -ω 1 -ω 3 ，ω i The rotation speed of the ith motor is 1,2,3 and 4. U shape 1 ,U 2 ,U 3 ,U 4 The control inputs for vertical, roll, pitch, and yaw motions, respectively, are:
Figure BDA0003052981660000103
wherein, b is 2.92 multiplied by 10 -6 kg · m is the lift coefficient, d 1.12 × 10 -7 kg·m 2 Is a moment coefficient.
(b) And decoupling the unmanned aerial vehicle dynamic model to obtain a position subsystem and an attitude subsystem. Definition of x j,1 ＝z j ，
Figure BDA0003052981660000104
The jth drone altitude subsystem dynamics may be written as:
Figure BDA0003052981660000105
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000106
τ j,1 ＝U j,1 in order to control the input of the electronic device,
Figure BDA0003052981660000107
j is the number of the drones in the formation, and j is 1, … N, and N is 5.
Definition of x j,3 ＝x j ，x j,4 ＝y j ，
Figure BDA0003052981660000111
Figure BDA0003052981660000112
The attitude angle around the equilibrium position is assumed to be small. The jth horizontal motion dynamics of the unmanned aerial vehicle can be simplified as follows:
Figure BDA0003052981660000113
the jth drone attitude subsystem dynamics may be written as:
Figure BDA0003052981660000114
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000115
τ j,2 ＝[U j，2 ，U j,3 ，U j,4 ]in order to control the input of the electronic device,
Figure BDA0003052981660000116
(c) the positions and the yaw angles of the unmanned aerial vehicle formation particles are designed as follows:
Figure BDA0003052981660000117
in the formula, x j,rd ,y j,rd ,z j,rd Position signal of formation particle for jth drone, psi j,rd Yaw angle signal, x, for the jth drone formation particle d ＝y d ＝z d 100m is the position expectation command for the formation reference point, # d Pi/16 rad is the yaw angle expectation command in formation,
Figure BDA0003052981660000118
for the relative position of the jth drone formation particle and the reference point,
Figure BDA0003052981660000119
Figure BDA00030529816600001110
Figure BDA0003052981660000121
forming a team particle sum for the jth droneThe relative yaw angle of the reference point,
Figure BDA0003052981660000122
Figure BDA0003052981660000123
the virtual structure particle model is described as:
Figure BDA0003052981660000124
in the formula, x j,d ,y j，d ,z j,d Is the position signal of the jth virtual dot, μ j,1 ,μ j,2 ,μ j,3 The control input signal of the jth virtual dot.
The virtual particle control inputs are designed as:
Figure BDA0003052981660000125
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000126
is a negative gradient term of the artificial potential field, V (-) is a total potential energy function of the particle,
Figure BDA0003052981660000127
Figure BDA0003052981660000128
for formation obstacle avoidance, V m (. is obstacle avoidance potential energy of mass point, c 11 ＝5，c 12 ＝1，c 21 ＝5，c 22 ＝1，c 31 ＝5，c 32 ＝1。
Assuming particle j is in the potential field generated by neighboring particles, the total potential energy function of the jth particle is defined as:
Figure BDA0003052981660000129
in the formula, the kth drone is a neighbor node of the ith drone, and Φ (·) is a potential energy function represented as follows:
Figure BDA00030529816600001210
wherein, k-4 is the potential field intensity coefficient, and R-10 m is the potential field action range.
Defining the obstacle avoidance potential energy function of the mass point as:
Figure BDA0003052981660000131
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000132
the coordinates of the projection point of the mass point j on the obstacle avoidance area (O) xm ,O ym ,O zm ) For the position of the m-th obstacle surrounding the centre of the circle, O x1 ＝800m,O y1 ＝50m,O z1 ＝300m，O x1 ＝800m,O y1 ＝250m,O z1 ＝750m，R k 60m is the radius of the surrounding circle, m is the obstacle number, and m is 1, 2.
The desired heading angle of the virtual particle is defined as:
ψ j,d ＝ψ j,rd +ψ j,t (47)
in the formula, # j,t Is an equal azimuth heading angle, which can be expressed as:
Figure BDA0003052981660000133
wherein, Delta e 10 is the designed look-ahead distance.
(d) For the height subsystem (3), a height tracking error is defined as. Designing virtual control quantities
Figure BDA0003052981660000134
Comprises the following steps:
Figure BDA0003052981660000135
in the formula, k j,1 ＝3，
Figure BDA0003052981660000136
The derivative of the highly desirable instruction.
The first order filter is designed as follows:
Figure BDA0003052981660000137
in the formula, τ j,1 0.05 is the filter parameter,
Figure BDA0003052981660000138
designing a compensation signal z j,1 Comprises the following steps:
Figure BDA0003052981660000139
in the formula, z j,2 Given in the subsequent design, z j,1 (0)＝0。
Tracking error after compensation is defined as:
ν j,1 ＝e j,1 -z j,1 (52)
defining a tracking error as
Figure BDA0003052981660000141
Designing the actual control input τ j,1 Comprises the following steps:
Figure BDA0003052981660000142
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000143
is an estimate of the optimal weights of the neural network,
Figure BDA0003052981660000144
is a vector of basis functions of the neural network,
Figure BDA0003052981660000145
k j,2 ＝3。
design of the compensation signal z j,2 Comprises the following steps:
Figure BDA0003052981660000146
in the formula, z j,2 (0)＝0。
Tracking error after compensation is defined as:
ν j,2 ＝e j,2 -z j,2 (55)
the prediction error is defined as:
Figure BDA0003052981660000147
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000148
for parallel estimation of states, it is obtained by the following serial-parallel model:
Figure BDA0003052981660000149
wherein, beta j,1 ＝0.1。
The self-adaptive updating law of the neural network is designed as follows:
Figure BDA00030529816600001410
in the formula, λ j,1 ＝0.1，k j,ω1 100 and δ j,f1 ＝0.1。
(e) For horizontal motion (4), the design PD controller calculates the expected acceleration as:
Figure BDA0003052981660000151
in the formula, k j,3 ＝1，k j,4 ＝1，k j,5 ＝1，k j,6 ＝1，
Figure BDA0003052981660000152
The derivative of the command is expected for horizontal position.
Obtaining the desired roll and pitch angles as:
Figure BDA0003052981660000153
(f) for the attitude sub-system (5), defining an attitude angle tracking error as e j，X1 ＝X j，1 -X j，d Wherein
Figure BDA0003052981660000154
The command is expected for the attitude angle. Designing virtual control quantity
Figure BDA0003052981660000155
Comprises the following steps:
Figure BDA0003052981660000156
in the formula, k j,7 The number 5 is a design parameter,
Figure BDA0003052981660000157
the derivative of the desired command is the attitude angle.
The first order filter is designed as follows:
Figure BDA0003052981660000158
in the formula, τ j,2 0.05 is the filter parameter,
Figure BDA0003052981660000159
design of the compensation signal z j,3 Comprises the following steps:
Figure BDA00030529816600001510
in the formula, z j,4 Given in the subsequent design, z j,3 (0)＝0。
Tracking error after compensation is defined as:
v j,3 ＝e j,X1 -z j,3 (64)
defining a tracking error as
Figure BDA00030529816600001511
Designing the actual control input τ j,2 Comprises the following steps:
Figure BDA00030529816600001512
in the formula (I), the compound is shown in the specification,
Figure BDA00030529816600001513
is an estimation value of the optimal weight of the neural network,
Figure BDA00030529816600001514
is a vector of basis functions of the neural network,
Figure BDA00030529816600001515
k j,8 ＝5。
design of the compensation signal z j,4 Comprises the following steps:
Figure BDA0003052981660000161
in the formula, z j,4 (0)＝0。
Tracking error after compensation is defined as:
v j,4 ＝e j,X2 -z j,4 (67)
the prediction error is defined as:
Figure BDA0003052981660000162
in the formula (I), the compound is shown in the specification,
Figure BDA0003052981660000163
for parallel estimation of states, it is obtained by the following serial-parallel model:
Figure BDA0003052981660000164
wherein, beta j,2 ＝0.1。
Designing a neural network adaptive updating law as follows:
Figure BDA0003052981660000165
in the formula, λ j,2 ＝0.1，k j,ω2 100 and δ j,f2 ＝0.1。
(g) According to the obtained control input U of vertical, rolling, pitching and yawing motion j,1 ,U j,2 ,U j,3 ,U j,4 Returning to the dynamics model of the unmanned aerial vehicle system, and realizing the expected instruction x under formation maintenance and obstacle avoidance d ,y d ,z d And performing tracking control.
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.

Claims (3)

1. A flight formation cooperative obstacle avoidance self-adaptive control method based on a virtual structure and an artificial potential field is characterized by comprising the following steps:
step 1: adopting a dynamic model of the unmanned aerial vehicle:
Figure FDA0003692518630000011
wherein x, y, z are positions,
Figure FDA0003692518630000012
roll angle, theta pitch angle, psi yaw angle, m mass, g gravitational acceleration, I x ,I y ,I z For the inertial matrix, l is the distance from the center of mass of the unmanned aerial vehicle to the center of the rotor, J r Is the moment of inertia of the motor, omega r ＝ω 2 +ω 4 -ω 1 -ω 3 ，ω i The rotation speed of the ith motor is 1,2,3, 4; u shape 1 、U 2 、U 3 、U 4 Control inputs for vertical, roll, pitch and yaw motions respectively;
Figure FDA0003692518630000013
wherein b is a lift coefficient, and d is a moment coefficient;
step 2: decoupling the unmanned aerial vehicle dynamic model to obtain a position subsystem and an attitude subsystem; definition of x j,1 ＝z j ，
Figure FDA0003692518630000014
The jth drone altitude subsystem dynamics may be written as:
Figure FDA0003692518630000015
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000016
τ j,1 ＝U j,1 in order to control the input of the electronic device,
Figure FDA0003692518630000017
for the unknown smooth function obtained from equation (1),
Figure FDA0003692518630000021
a known function obtained by the formula (1), wherein j is the number of the unmanned aerial vehicles in the formation, j is 1, … N, and N is the number of the unmanned aerial vehicles in the flying formation;
definition of x j,3 ＝x j ，x j,4 ＝y j ，
Figure FDA0003692518630000022
Figure FDA0003692518630000023
Assuming that the attitude angle near the equilibrium position is small; the jth horizontal motion dynamics of the unmanned aerial vehicle can be simplified as follows:
Figure FDA0003692518630000024
the jth drone attitude subsystem dynamics may be written as:
Figure FDA0003692518630000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000026
τ j,2 ＝[U j,2 ,U j,3 ,U j,4 ]in order to control the input of the electronic device,
Figure FDA0003692518630000027
is obtained by the formula (1)The unknown smooth function of the received signal is obtained,
Figure FDA0003692518630000028
a known function derived from formula (1);
and step 3: the positions and the yaw angles of the unmanned aerial vehicle formation particles are designed as follows:
Figure FDA0003692518630000029
in the formula, x j,rd ,y j,rd ,z j,rd Position signal of formation particle for jth drone, psi j,rd Yaw angle signal, x, for the jth drone formation particle d ,y d ,z d For position expectation command of formation reference point, # d An instruction is expected for the yaw angle of the formation,
Figure FDA00036925186300000212
for the relative position of the jth drone formation particle and the reference point,
Figure FDA00036925186300000211
forming a relative yaw angle of a particle and a reference point for the jth unmanned aerial vehicle;
the virtual structure particle model is described as:
Figure FDA00036925186300000210
in the formula, x j,d ,y j,d ,z j,d Is the position signal of the jth virtual dot, μ j,1 ,μ j,2 ,μ j,3 A control input signal of the jth virtual dot;
the virtual particle control inputs are designed as:
Figure FDA0003692518630000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000032
is a negative gradient term of the artificial potential field, V (-) is a total potential energy function of the particle,
Figure FDA0003692518630000033
Figure FDA0003692518630000034
for formation obstacle avoidance, V m (. is obstacle avoidance potential energy of mass point, c 11 ＞0，c 12 ＞0，c 21 ＞0，c 22 ＞0，c 31 ＞0，c 32 More than 0 is a design parameter;
assuming particle j is in the potential field generated by neighboring particles, the total potential energy function of the jth particle is defined as:
Figure FDA0003692518630000035
in the formula, the kth drone is a neighbor node of the ith drone, and Φ (·) is a potential energy function represented as follows:
Figure FDA0003692518630000036
wherein, kappa is a potential field intensity coefficient, a proper value is selected according to the inertia of the unmanned aerial vehicle and the control output of an actuating mechanism, and R is a potential field action range;
defining the obstacle avoidance potential energy function of the mass point as:
Figure FDA0003692518630000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000042
the coordinates of the projection point of the mass point j on the obstacle avoidance area (O) xm ,O ym ,O zm ) Position surrounding the centre of the circle for the m-th obstacle, R k The radius of a circle is enclosed, M is an obstacle number, M is 1, …, M is the number of obstacles;
the desired heading angle of the virtual particle is defined as:
ψ j,d ＝ψ j,rd +ψ j,t (12)
in the formula, # j,t Is an equal azimuth heading angle, which can be expressed as:
Figure FDA0003692518630000043
wherein, Delta e 0 is the designed forward-looking distance;
and 4, step 4: defining an altitude tracking error e for the altitude subsystem (3) j,1 ＝x j,1 -z j,d (ii) a Designing virtual control quantities
Figure FDA0003692518630000044
Comprises the following steps:
Figure FDA0003692518630000045
in the formula, k j,1 The more than 0 is the design parameter,
Figure FDA0003692518630000046
is the derivative of the highly expected command;
the first order filter is designed as follows:
Figure FDA0003692518630000047
in the formula, τ j,1 The parameters > 0 of the filter are the parameters of the filter,
Figure FDA0003692518630000048
design of the compensation signal z j,1 Comprises the following steps:
Figure FDA0003692518630000049
in the formula, z j,2 Given in subsequent designs;
tracking error after compensation is defined as:
ν j,1 ＝e j,1 -z j,1 (17)
defining a tracking error as
Figure FDA0003692518630000051
Designing the actual control input τ j,1 Comprises the following steps:
Figure FDA0003692518630000052
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000053
for the optimal weight estimation value of the neural network,
Figure FDA0003692518630000054
is a vector of basis functions of the neural network, k j,2 More than 0 is a design parameter;
design of the compensation signal z j,2 Comprises the following steps:
Figure FDA0003692518630000055
tracking error after compensation is defined as:
ν j,2 ＝e j,2 -z j,2 (20)
the prediction error is defined as:
Figure FDA0003692518630000056
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000057
for parallel estimation of states, it is obtained by the following serial-parallel model:
Figure FDA0003692518630000058
wherein, beta j,1 More than 0 is a design parameter;
the self-adaptive updating law of the neural network is designed as follows:
Figure FDA0003692518630000059
in the formula, λ j,1 ＞0，k j,ω1 > 0 and delta j,f1 More than 0 is a design parameter;
and 5: for horizontal motion (4), the design PD controller calculates the expected acceleration as:
Figure FDA00036925186300000510
in the formula, k j,3 ＞0，k j,4 ＞0，k j,5 ＞0，k j,6 The more than 0 is the design parameter,
Figure FDA00036925186300000511
expecting a derivative of the command for horizontal position;
obtaining the desired roll and pitch angles as:
Figure FDA0003692518630000061
step 6: for the attitude sub-system (5), defining an attitude angle tracking error as e j,X1 ＝X j,1 -X j,d Wherein
Figure FDA0003692518630000062
An attitude angle expectation command; designing virtual control quantities
Figure FDA0003692518630000063
Comprises the following steps:
Figure FDA0003692518630000064
in the formula, k j,7 The more than 0 is the design parameter,
Figure FDA0003692518630000065
a derivative of the desired command for attitude angle;
the first order filter is designed as follows:
Figure FDA0003692518630000066
in the formula, τ j,2 The parameters > 0 of the filter are the parameters of the filter,
Figure FDA0003692518630000067
design of the compensation signal z j,3 Comprises the following steps:
Figure FDA0003692518630000068
in the formula, z j,4 Given in subsequent designs;
tracking error after compensation is defined as:
ν j,3 ＝e j,X1 -z j,3 (29)
defining a tracking error as
Figure FDA0003692518630000069
Designing the actual control input τ j,2 Comprises the following steps:
Figure FDA00036925186300000610
in the formula (I), the compound is shown in the specification,
Figure FDA00036925186300000611
is an estimation value of the optimal weight of the neural network,
Figure FDA00036925186300000612
is a vector of basis functions of the neural network, k j,8 More than 0 is a design parameter;
design of the compensation signal z j,4 Comprises the following steps:
Figure FDA00036925186300000613
tracking error after compensation is defined as:
ν j,4 ＝e j,X2 -z j,4 (32)
the prediction error is defined as:
Figure FDA0003692518630000071
in the formula (I), the compound is shown in the specification,
Figure FDA0003692518630000072
for parallel estimation of states, it is obtained by the following serial-parallel model:
Figure FDA0003692518630000073
wherein, beta j,2 More than 0 is a design parameter;
designing a neural network adaptive updating law as follows:
Figure FDA0003692518630000074
in the formula, λ j,2 ＞0，k j,ω2 > 0 and delta j,f2 More than 0 is a design parameter;
and 7: the obtained control input U of the vertical, rolling, pitching and yawing motion j,1 ,U j,2 ,U j,3 ,U j,4 Returning to the dynamics model of the unmanned aerial vehicle system, and realizing the expected instruction x under formation maintenance and obstacle avoidance d ,y d ,z d And performing tracking control.
2. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
3. A computer-readable storage medium having stored thereon computer-executable instructions for, when executed, implementing the method of claim 1.
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