CN109062252B - Four-rotor unmanned aerial vehicle cluster control method and device based on artificial potential field method - Google Patents

Four-rotor unmanned aerial vehicle cluster control method and device based on artificial potential field method Download PDF

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CN109062252B
CN109062252B CN201810980595.XA CN201810980595A CN109062252B CN 109062252 B CN109062252 B CN 109062252B CN 201810980595 A CN201810980595 A CN 201810980595A CN 109062252 B CN109062252 B CN 109062252B
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杨雪榕
吕永申
姚静波
辛朝军
陈超
单上求
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Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Abstract

The invention discloses a quad-rotor unmanned aerial vehicle cluster control method and a quad-rotor unmanned aerial vehicle cluster control device based on an artificial potential field method, wherein the method comprises the following steps of: step S100: adopting M quadrotor unmanned aerial vehicles to form a quadrotor unmanned aerial vehicle cluster, setting expected positions and speed vectors of all internal members of the cluster according to formation configuration of the quadrotor unmanned aerial vehicle cluster, and establishing a kinematic equation of the ith internal member; step S200: constructing a speed control function of the ith inner member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, and S300: and controlling each internal member to move according to the movement type by adopting each speed control function. The control method has the advantages of being easy to implement, good in real-time performance and good in formation control effect, is suitable for large-scale quad-rotor unmanned aerial vehicle cluster control, and can achieve cluster formation, target movement and obstacle avoidance. The invention also provides a device for the method.

Description

Four-rotor unmanned aerial vehicle cluster control method and device based on artificial potential field method
Technical Field
The invention relates to a quad-rotor unmanned aerial vehicle cluster control method and device based on an artificial potential field method, and belongs to the field of control.
Background
With the continuous expansion of the application field of the unmanned aerial vehicle, the task types are more and more extensive, and the application style of the unmanned aerial vehicle gradually develops from a single platform to a multi-platform cluster direction. The unmanned aerial vehicle cluster can form a coordinated and ordered collective motion mode, can quickly and consistently respond to external stimulation, has the characteristics of wide distribution, strong self-organization, high coordination, strong stability and the like, and has strong adaptability to the environment.
Quad-rotor unmanned aerial vehicles are special unmanned rotorcraft with four rotor shafts, which rotate through each on-axis motor, driving the rotor, thereby producing lift. The collective pitch of rotor is fixed, through the relative speed who changes between the different rotors, can change the size of unipolar propulsive force to control the orbit of aircraft, it is strong to have the nature controlled, characteristics such as but VTOL and hover.
With the increasingly complex task environment of the unmanned aerial vehicle and the increasing scale and density of unmanned aerial vehicles in the task area, flight control and safety of the unmanned aerial vehicle cluster can face a series of challenges, so that the seeking of an unmanned aerial vehicle cluster control method with strong robustness, good consistency and remarkable control effect is a problem to be solved urgently.
An artificial potential field method in the existing common unmanned aerial vehicle cluster control method guides individual clusters to move towards the direction of potential energy reduction by constructing a global potential field function, has the characteristics of simplicity, practicability, good robustness and the like, and can be avoided by optimizing the potential field function although the method has the problems of local extremum and the like.
The existing control methods are mainly used for controlling fixed-wing clusters, and for the quad-rotor unmanned aerial vehicle which is high in flexibility and can be suspended and stopped, the control method is low in control precision and difficult to realize cluster control of the quad-rotor unmanned aerial vehicle.
Disclosure of Invention
According to one aspect of the application, the method for controlling the quad-rotor unmanned aerial vehicle cluster based on the artificial potential field method is provided, and the method considers that the quad-rotor unmanned aerial vehicle has the characteristics of high flexibility, hovering capability, simplicity in control, high reliability and the like, is less in constraint compared with a fixed wing cluster, is simpler and more convenient to control, and can flexibly deal with various tasks.
The four-rotor unmanned aerial vehicle cluster control method based on the artificial potential field method comprises the following steps:
step S100: adopting M sets of four-rotor unmanned aerial vehicles to form the four-rotor unmanned aerial vehicle cluster, setting expected positions and speed vectors of all internal members of the cluster according to the formation configuration of the four-rotor unmanned aerial vehicle cluster, and establishing a kinematic equation of the ith internal member;
step S200: constructing a speed control function of the ith internal member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, taking i as i +1, and repeating the steps S100-S200 until i is M to obtain the speed control functions of all the internal members;
step S300: controlling each of the internal members to perform the motion of the motion type by using each of the speed control functions;
the motion type includes at least one of a formation motion, a movement toward a target, and an obstacle avoidance motion.
Preferably, the velocity control function v of the ith said inner memberiIs represented as follows:
Figure BDA0001778404700000031
wherein, χiA position vector representing the ith said inner member, gij(. represents an interaction function between each of said internal members, pERepresenting the ambient source location vector, gE(. represents the function of the effect of the environmental source vector on each of said internal members, paRepresenting the target point position vector, ga(. -) represents the function of the target point location vector's contribution to each of the internal members.
Preferably, when the motion type is formation motion, the speed control function of the ith inner member is:
Figure BDA0001778404700000032
wherein, χjA position vector, v, representing a jth of said internal memberiRepresenting the velocity vector, p, of the ith said inner memberaiIndicating the expected position of the ith said inner member, ga(. represents the i-th internal memberIs given as an attraction function of said desired position to said inner member of ith, expressed as:
ga(χi-χj)＝-ka·exp(ea·||χi-χj||)·(χi-χj) (5)
wherein k isa、eaA constant for adjusting the attraction force in an attraction function for the ith said inner member and the desired position;
gij(. said) represents an attraction/repulsion function between said inner member of ith and said inner member of jth, expressed as follows:
Figure BDA0001778404700000033
wherein, aijIs a constant greater than 0 for adjusting the magnitude of the attraction/repulsion function between the ith and jth said inner members, bij、cij、dijAre each set to a constant greater than 0 to determine an equilibrium distance, a, between the ith and jth said internal membersijSet to a constant greater than 0.
Preferably, when the motion type is towards the target, the speed control function of the ith inner member is:
Figure BDA0001778404700000041
wherein, χLPosition vector representing a virtual leader, gi(. h) represents the attraction/repulsion function between the ith internal member and the virtual lead, as follows:
Figure BDA0001778404700000042
wherein, ai＞0，δiIs the equilibrium distance between the ith inner member and the virtual lead.
Preferably, when said type of motion is towards a target, a virtual lead is established in said cluster of quad-rotor drones, each of said inner members following the virtual lead in a formation configuration towards the target.
Preferably, when the motion type is obstacle avoidance motion, the speed control function of the ith internal member is as follows:
Figure BDA0001778404700000043
wherein N is the number of obstacles or unfavorable environment sources encountered by the cluster moving area,
Figure BDA0001778404700000044
representing the repulsive source potential field function between the kth repulsive ambient source and the ith inner member,
Figure BDA0001778404700000045
to reject the ambient source position vector,%jA position vector representing said inner member of jth.
Preferably, the repulsive source potential field function
Figure BDA0001778404700000046
gE(||y||)＝-y[J5(||y||)+J6(||y||)+J7(||y||)+J8(||y||)] (10)
Wherein, J5(| y |) is a linear rejection function, expressed as follows:
Figure BDA0001778404700000051
wherein m is3And m4To satisfy m3＞0，m4A constant of < 0, then
Figure BDA0001778404700000052
When the linear repulsion source is at the ith stationSaid internal member producing a repulsive interaction;
J6(| y |) is an exponential rejection function, expressed as follows:
Figure BDA0001778404700000053
wherein k is>0，n3And n4To satisfy n3＜0，n4A constant of < 0 when
Figure BDA0001778404700000054
Said exponential repulsion source exerts a repulsive effect on said internal member of the ith;
J7(| y |) is a logarithmic exclusion function, expressed as follows:
Figure BDA0001778404700000055
wherein q is3、q4To satisfy p3＞0，p4A constant < 0, where 0 < | y | < p3, the logarithmic exclusion source produces a repulsive effect on the ith said inner member;
J8(| y |) is the reciprocal rejection function, expressed as follows:
Figure BDA0001778404700000056
wherein q is3、q4To satisfy q3＜0、q4A constant > 0.
Preferably, the velocity v of the ith said inner memberiThe following constraints are satisfied:
Figure BDA0001778404700000061
wherein, VmaxIndicating the speed limit that the inner member can reach.
Preferably, the kinematic equation of the i-th inner member is:
Figure BDA0001778404700000062
wherein v isiRepresenting the velocity vector of the ith said inner member.
A further aspect of the present invention provides an apparatus used in the control method as described above, including:
the system comprises a kinematics equation module, a four-rotor unmanned aerial vehicle cluster and a four-rotor unmanned aerial vehicle cluster, wherein the kinematics equation module is used for forming the four-rotor unmanned aerial vehicle cluster by adopting M four-rotor unmanned aerial vehicles, setting expected positions and speed vectors of all internal members of the cluster according to formation configuration of the four-rotor unmanned aerial vehicle cluster, and establishing a kinematics equation of the ith internal member;
the function module is used for constructing a speed control function of the ith internal member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, and returning to the kinematic equation module and the function module after i +1 is taken until i M is obtained, so that the speed control functions of all the internal members are obtained;
the motion control module is used for controlling each internal member by adopting each speed control function to carry out motion of the motion type;
the motion type includes at least one of a formation motion, a movement toward a target, and an obstacle avoidance motion.
The beneficial effects of the invention include but are not limited to:
(1) according to the cluster control method and device for the four-rotor unmanned aerial vehicles based on the artificial potential field method, the unmanned aerial vehicle cluster dynamic model is established firstly, and then the four-rotor unmanned aerial vehicle cluster control algorithm based on the artificial potential field method is designed.
(2) The method comprises formation control, target-oriented motion control and obstacle avoidance control algorithm design of the quad-rotor unmanned aerial vehicle cluster, is suitable for formation control, target-oriented motion control and obstacle avoidance control of the unmanned aerial vehicles, and is simple and practical.
(3) According to the artificial potential field method-based quad-rotor unmanned aerial vehicle cluster control method and device, simulation experiments show that the method has good control effects in the aspects of formation control, target-oriented motion control and obstacle avoidance control of unmanned aerial vehicles, is strong in anti-interference capability and good in robustness, can effectively enable the cluster to avoid adverse environments, can quickly achieve a control stable state under the action of a potential field function, is high in control efficiency, can quickly and efficiently complete experiment tasks, and is remarkable in control effect.
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Fig. 1 is a schematic block diagram of a flow of a quad-rotor unmanned aerial vehicle cluster control method based on an artificial potential field method, provided by the invention;
fig. 2 is a schematic diagram of a quad-rotor drone cluster formation used in the method of the present invention;
fig. 3 is a schematic diagram of a cluster configuration of unmanned aerial vehicles for setting a virtual lead in the method of the present invention;
fig. 4 is a schematic diagram of a quad-rotor drone pre-formation in accordance with a preferred embodiment 1 of the present invention;
fig. 5 is a schematic diagram of a simulation result of formation control of an unmanned aerial vehicle cluster in preferred embodiment 1 of the present invention, wherein a) is a diagram of a three-dimensional spatial motion trajectory of the unmanned aerial vehicle cluster; b) the method comprises the steps that a y-z plane trajectory projection graph of an unmanned aerial vehicle cluster is obtained, four curves represent motion trajectories of internal members 1-4 of the unmanned aerial vehicle cluster in the preferred embodiment respectively, and symbols are expected positions of the internal members 1-4 in formation;
fig. 6 is a schematic diagram of a quad unmanned helicopter configuration according to a preferred embodiment 2 of the present invention;
fig. 7 is a schematic diagram of a simulation result of formation control of an unmanned aerial vehicle cluster in preferred embodiment 2 of the present invention, where the simulation result includes a three-dimensional space movement track diagram of the unmanned aerial vehicle cluster, a square represents a virtual leader position, and other curves drawn by asterisks represent movement tracks of the unmanned aerial vehicles;
fig. 8 is a schematic diagram of a quad drone pre-formation in accordance with a preferred embodiment 3 of the present invention;
fig. 9 is a schematic diagram of target positions of the drone cluster in the preferred embodiment 3 of the present invention, where diamonds represent the central positions of the drone cluster formation, and symbols represent expected positions of internal members of each drone;
fig. 10 is a schematic diagram of a simulation result of formation control of a cluster of unmanned aerial vehicles in preferred embodiment 3 of the present invention, wherein a) is a diagram of a flight path of a cluster without obstacles; b) the unmanned aerial vehicle is a cluster flight path diagram when an obstacle exists, two circles with different sizes represent the positions of the two obstacles, and symbols and traction line segments thereof represent the motion tracks of members in the unmanned aerial vehicle;
illustration of the drawings:
in fig. 2 and 4, the UAV is an english abbreviation of drone, UAVi stands for the ith drone, i is 1, 2, 3, 4; deltaijDenotes the equilibrium distance between the ith and jth internals, i 1, 2, 3, 4, j 1, 2, 3, 4;
delta. in FIG. 3iThe balance distance between the ith internal member and the virtual leader is represented, and 1, 2, 3 and 4 respectively represent an internal member 1, an internal member 2, an internal member 3 and an internal member 4 of the unmanned aerial vehicle cluster.
Detailed Description
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments.
The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the application, its application, or uses. 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.
Referring to fig. 1, the method for cluster control of quad-rotor unmanned aerial vehicles based on an artificial potential field method provided by the invention comprises the following steps:
step S100: adopting M sets of four-rotor unmanned aerial vehicles to form the four-rotor unmanned aerial vehicle cluster, setting expected positions and speed vectors of all internal members of the cluster according to the formation configuration of the four-rotor unmanned aerial vehicle cluster, and establishing a kinematic equation of the ith internal member;
step S200: constructing a speed control function of the ith internal member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, taking i as i +1, and repeating the steps S100-S200 until i is M to obtain the speed control functions of all the internal members;
step S300: controlling each of the internal members to perform the motion of the motion type by using each of the speed control functions;
the motion type comprises at least one of formation motion, target facing motion and obstacle avoidance motion, and the velocity control function v of the ith inner memberiIs represented as follows:
Figure BDA0001778404700000091
wherein, gij(. represents an interaction function between each of said internal members, pERepresenting an ambient source position vector, gE(. represents the function of the effect of the environmental source vector on each of said internal members, paRepresenting the target point position vector, ga(. cndot.) represents the contribution of the target point location vector to each of said interior members.
Under the action of the potential field function, the members in the unmanned aerial vehicle cluster can finally reach an equilibrium position under the action of attraction/repulsion between each other and the attraction of the expected position points of all the unmanned aerial vehicles in the cluster. At the moment, the resultant force of the potential field force borne by each unmanned aerial vehicle is 0, and the relative positions of cluster members are not changed any more, so that a preset formation is formed.
The method controls the unmanned aerial vehicle cluster, and achieves control over formation, target movement and obstacle avoidance movement of the unmanned aerial vehicle cluster through the established speed potential field function of members in the unmanned aerial vehicle cluster. And the method only carries out constraint control on the speed of the unmanned aerial vehicle, reduces the control quantity and simultaneously obtains better control precision and stability. Compared with the existing control method, the cluster control robustness of the method is enhanced, the control method is simpler and more convenient, and the method is suitable for large-scale unmanned aerial vehicle cluster control.
Preferably, when the motion type is formation motion, the speed control function of the ith inner member is:
Figure BDA0001778404700000101
wherein, χi、χjPosition vectors, v, representing the ith and jth said inner members, respectivelyiRepresenting the velocity vector of the ith inner member, paiIndicates the expected position of the ith inner member, ga(. h) represents the attraction function that the desired position of the ith inner member produces for the ith inner member as follows:
ga(χi-χj)＝-ka·exp(ea·||χi-χj||)·(χi-χj) (5)
wherein k isa、eaA constant for adjusting the attraction force in the attraction function for the ith inner member and the desired position;
when the unmanned aerial vehicle cluster moves, the expected position of the ith inner member generates an exponential attraction potential field force to the ith inner member;
gij(. cndot.) represents the attraction/repulsion function between the ith and jth internal members, expressed as follows:
Figure BDA0001778404700000111
wherein, aijIs a constant greater than 0 for adjusting the magnitude of the attraction/repulsion function between the ith and jth inner members, bij、cij、dijAre respectively set to be a constant greater than 0 according to needs, so as to determine the balance distance between the ith inner member and other unmanned aerial vehicles. a isijAnd setting a constant larger than 0 according to needs, wherein M is the number of members of the unmanned aerial vehicle cluster.
Preferably, when the motion type is towards the target, the speed control function of the ith inner member is:
Figure BDA0001778404700000112
wherein, χLA position vector representing a virtual lead;
gi(. cndot.) represents the attraction/repulsion function between the ith internal member and the virtual lead, expressed as follows:
Figure BDA0001778404700000113
wherein, ai＞0，δiIs the equilibrium distance between the ith inner member and the virtual lead.
The movement towards the target means that at least one virtual lead is established in the quad-rotor drone cluster, and members in the cluster follow the virtual lead in a formation configuration to move towards the target.
And when the unmanned aerial vehicle cluster is controlled to move towards the target point, setting the virtual leading position as the target position. In the flight process of the unmanned aerial vehicle cluster, the members in the unmanned aerial vehicle cluster can be attracted/repelled by other members and attracted by the virtual leading team. Under the action of the two potential field forces, all the unmanned members move towards the virtual point and finally form a preset cluster configuration with the virtual leading team.
The obstacle that meets in the unmanned aerial vehicle cluster flight process and the unfavorable environment that probably exists are collectively called as repelling the environmental source, and when the inside member of cluster exists interact, there is the interact equally between inside member and the repelling environmental source simultaneously, according to this condition, controls, makes the inside member of unmanned aerial vehicle cluster keep away the obstacle motion. Preferably, when the motion type is obstacle avoidance motion, the speed control function of the ith internal member is as follows:
Figure BDA0001778404700000121
wherein N is the number of obstacles or unfavorable environment sources encountered by the unmanned aerial vehicle cluster moving area,
Figure BDA0001778404700000122
representing the potential field function between the kth repulsive environmental source and the ith drone internal member,
Figure BDA0001778404700000123
the ambient source location vector is rejected.
The repulsive effects of the repulsive sources mainly include linear repulsive effects, exponential repulsive effects, logarithmic repulsive effects, and reciprocal attractive effects.
Repulsive source potential field function:
gE(||y||)＝-y[J5(||y||)+J6(||y||)+J7(||y||)+J8(||y||)] (10)
wherein, J5(| y |) is a linear rejection function, which can be expressed as follows:
Figure BDA0001778404700000124
wherein m is3＞0，m4If < 0, then
Figure BDA0001778404700000125
Then, the linear repulsion source produces a repulsive effect on the ith inner member;
J6(| y |) is an exponential rejection function, expressed as follows:
Figure BDA0001778404700000131
wherein k is>0,n3＜0，n4Is less than 0 when
Figure BDA0001778404700000132
The exponential repulsion source exerts a repulsive effect on the ith said internal member. k is a constant for adjusting the range of repulsive force field. That is, when the distance between the unmanned plane and the repulsion source is less than the value, the two generate repulsion action.
J7(| y |) is a logarithmic exclusion function, expressed as follows:
Figure BDA0001778404700000133
wherein p is3＞0，p4Less than 0, when 0 < y < p3A logarithmic exclusion source produces an exclusion effect on the ith said internal member.
J8(| y |) is the reciprocal rejection function, expressed as follows:
Figure BDA0001778404700000134
wherein q is3＜0、q4＞0。
According to the different types of the repulsion environmental sources, the repulsion effect on the unmanned aerial vehicle is different. According to the potential function expression, the action range of the repelling environmental source is limited, and after the unmanned aerial vehicle cluster enters the potential field range of the repelling environmental source, the repelling force borne by the unmanned aerial vehicle cluster is in inverse proportion to the distance between the unmanned aerial vehicle cluster and the repelling source. By adopting the method provided by the invention to control the cluster, under the interaction between members in the unmanned aerial vehicle cluster and the repulsion action of the environmental repulsion source, the unmanned aerial vehicle cluster can effectively avoid various obstacles or adverse environments with a certain formation configuration. By adopting the method provided by the invention, the accuracy of the cluster obstacle movement is higher.
Preferably, the speed constraint of the ith fourth rotary-wing drone is:
Figure BDA0001778404700000141
wherein, VmaxIndicating the speed limit that can be reached by the inner member.
Preferably, the kinematic equation of the i-th said inner member:
Figure BDA0001778404700000142
wherein, χiA position vector, χ, representing the ith said internal memberiThe upper point represents the differential of the position vector with respect to time, viRepresenting the velocity vector of the ith said inner member.
According to the method provided by the invention, a virtual potential field is constructed in the unmanned aerial vehicle cluster motion space by designing the potential field function used in the control method, so that members in the unmanned aerial vehicle cluster move from a high potential energy position to a low potential energy position under the action of the virtual potential field force, and finally reach an equilibrium position. At this time, the resultant force of the virtual potential field force borne by each unmanned aerial vehicle is 0, and the relative positions of the cluster members are not changed any more, so that a preset formation is formed.
Preferably, when said type of motion is towards a target, a virtual lead is established in said cluster of quad-rotor drones, each of said inner members following the virtual lead in a formation configuration towards the target.
The cluster can adopt the distance delta between all unmanned planes in the unmanned plane clusterijThe configuration of the preset formation is determined, and the distance between the member and the virtual leading is further restricted.
Still another aspect of the present invention provides an apparatus for the above control method, including:
the system comprises a kinematics equation module, a four-rotor unmanned aerial vehicle cluster and a four-rotor unmanned aerial vehicle cluster, wherein the kinematics equation module is used for forming the four-rotor unmanned aerial vehicle cluster by adopting M four-rotor unmanned aerial vehicles, setting expected positions and speed vectors of all internal members of the cluster according to formation configuration of the four-rotor unmanned aerial vehicle cluster, and establishing a kinematics equation of the ith internal member;
the function module is used for constructing a speed control function of the ith internal member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, and returning to the kinematic equation module and the function module after i +1 is taken until i M is obtained, so that the speed control functions of all the internal members are obtained;
the motion control module is used for controlling each internal member by adopting each speed control function to carry out motion of the motion type;
the motion type includes at least one of a formation motion, a movement toward a target, and an obstacle avoidance motion.
The method provided by the present invention is described in detail below with reference to specific examples:
step S100: and establishing a kinematic equation of the internal members of the quad-rotor unmanned aerial vehicle cluster.
Consider a cluster of M-frame quad-rotor drones, and x ═ x (χ)1,χ2,...,χi,...,χM) Position vector representing M drones, V ═ V1,v2,...,vi,...,vM) Representing velocity vectors of members of respective unmanned aerial vehicles, known
Figure BDA0001778404700000151
Is the velocity vector of the ith inner member,
Figure BDA0001778404700000152
is the velocity vector of the ith inner member,
Figure BDA0001778404700000153
for the Euclidean space set, the kinematic equation of the ith inner member is established as follows:
Figure BDA0001778404700000154
and v isiThe following speed constraints are satisfied:
Figure BDA0001778404700000155
wherein, VmaxRepresenting the speed limit that can be reached by the individual drone.
The factors influencing the individual speed of the unmanned aerial vehicle are considered in the method provided by the invention and comprise the following steps: the interaction and environment between the members in the unmanned aerial vehicle cluster act on the unmanned aerial vehicle individuals, and the target point acts on the unmanned aerial vehicle individuals. By gij(. represents the interaction function between any two individual drones, pERepresenting the ambient source location vector, gE(. represents the function of the source of the environment on the members of the unmanned aerial vehicle cluster, paVector representing target point position, ga(. represents the function of action on members of a drone cluster, viCan be expressed as follows:
Figure BDA0001778404700000161
formula (3) is viThe potential field function equation of (1).
The four-rotor unmanned aerial vehicle cluster control algorithm is designed as follows:
(1) control algorithm design for cluster formation of quad-rotor unmanned aerial vehicle
Firstly, a formation configuration of a cluster of unmanned aerial vehicles is designed, in the embodiment, a formation control scheme of the cluster of the four-rotor unmanned aerial vehicles is shown in fig. 2, four-rotor unmanned aerial vehicles (numbered: UAV1, UAV2, UAV3 and UAV4) form a quadrilateral formation, and delta in the figure14Represents the link distance of UAV1 to UAV 4; delta41Represents the link distance from UAV4 to UAV1, and so on, δ12Represents the link distance of UAV1 to UAV 2; delta21The distance of the connecting line from the UAV2 to the UAV1 is shown, and the other letters are similar and will not be repeated here.
After the relative positions of the unmanned aerial vehicles are determined, the formation configuration of the unmanned aerial vehicle cluster is determined. And when the unmanned aerial vehicle clusters form a formation, the distance between each other is the equilibrium distance under the interaction.
Second, the expected position in space of each drone in the formation configuration is determined.
When the artificial potential field method is adopted to carry out formation control on the unmanned aerial vehicle cluster, each unmanned aerial vehicle in the cluster can be influenced by two virtual potential field forces, firstly, attraction acting force generated by the individual expected position of the unmanned aerial vehicle on the unmanned aerial vehicle, secondly, attraction/repulsion acting force between the unmanned aerial vehicle individuals, and the two potential field forces jointly determine the motion conditions of members of the unmanned aerial vehicle cluster. Neglecting the influence of environmental effects, establishing a kinematic equation containing the ith internal member and the unmanned plane j after the cluster formation as follows:
Figure BDA0001778404700000171
wherein, χi、χjRespectively representing the position vectors, p, of the ith and jth inner membersaiIndicating the target position, g, of the ith inner membera(·) represents the attraction function that the target location generates to the drone individual, expressed as:
ga(χi-χj)＝-ka·exp(ea·||χi-χj||)·(χi-χj) (5)
wherein k isa、eaThe larger the value of the parameter for adjusting the attraction in the ith internal member and target point attraction function is, the larger the attraction of the target position to the unmanned aerial vehicle individual is, so the values of the two parameters are set under the condition of meeting the speed constraint of the unmanned aerial vehicle. Under the action of the potential field function, when the unmanned aerial vehicle cluster moves, the expected position of the target generates exponential attraction potential field force to the unmanned aerial vehicle cluster.
gij(. h) represents an interaction function between the ith and jth internal members, includingAttraction and repulsion functions, expressed as follows:
Figure BDA0001778404700000172
aijis a parameter greater than 0 for adjusting the magnitude of the attraction/repulsion function between the ith and jth inner members, and further bij、cij、dijAlso a parameter greater than 0, to determine the equilibrium distance between the ith inner member and the other drones. The parameters can be given an initial value during the experiment and further adjusted during the control experiment.
(2) Motion control of unmanned aerial vehicle cluster towards target
In order to realize the motion control of the unmanned aerial vehicle cluster towards the target, a virtual leading team is established in the cluster, and the cluster members can follow the virtual leading team to move towards the target in the set formation configuration. At the moment, each member in the unmanned aerial vehicle cluster can be subjected to two potential forces which are respectively from the virtual leader and other members of the cluster. And the magnitude and direction of the potential field force depends on the distance and relative position between the ith inner member and the virtual lead, other members of the cluster. When the unmanned aerial vehicle cluster moves towards the target, the cluster configuration diagram is shown in fig. 3. In FIG. 3, δ1Is the connecting line distance between the virtual leading team and the No. 1 unmanned aerial vehicle, and is delta2The connection distance between the virtual leader and the No. 2 unmanned aerial vehicle is defined, and so on, and the description is not repeated. Delta12The meaning of (a) is the same as that described above.
Distance delta between unmanned aerial vehicles in unmanned aerial vehicle clusterijThe configuration of the preset formation is determined, and the distance between the member and the virtual leading further restricts the configuration of the formation and enables the formation to have directivity.
The kinematic equation of the ith inner member in the unmanned plane cluster containing the virtual lead is as follows:
Figure BDA0001778404700000181
wherein: chi shapeLPosition vector representing a virtual leader, gi(. cndot.) represents the attraction/repulsion function between the ith internal member and the virtual lead, expressed as follows:
Figure BDA0001778404700000182
wherein, ai＞0，δiIs the equilibrium distance between the ith inner member and the virtual lead. And when the unmanned aerial vehicle cluster is controlled to move towards the target point, setting the virtual leading position as the target position. Then the members inside the drone cluster will be attracted/repelled by other members and the attraction of the virtual lead during the flight of the drone cluster. Under the action of the two virtual potential field forces, all members of the unmanned aerial vehicle move towards a virtual point and finally form a preset cluster configuration with the virtual leading team.
(3) Obstacle avoidance motion control of unmanned aerial vehicle cluster
In the flying process of the unmanned aerial vehicle cluster, the unmanned aerial vehicle can meet the threats of obstacles such as birds, enemy aircrafts and the like, and the environment is interfered by a strong magnetic field. In order to ensure the flight safety of the unmanned aerial vehicle cluster, obstacles or adverse environments need to be avoided, and the obstacles and the adverse environments are collectively referred to as repulsive environment sources. When only the interaction between the individuals of the unmanned aerial vehicle and the interaction between the unmanned aerial vehicle and the repulsive environment source are considered, an unmanned aerial vehicle cluster obstacle avoidance motion equation can be established as follows:
Figure BDA0001778404700000191
wherein N is the number of obstacles or unfavorable environment sources encountered by the unmanned aerial vehicle cluster moving area,
Figure BDA0001778404700000192
representing the potential field function between the kth repulsive environmental source and the drone individual,
Figure BDA0001778404700000193
the ambient source location vector is rejected. The repulsion of the repulsive source mainly includes linear repulsion, exponential repulsion, logarithmic repulsion and reciprocal attraction, so the repulsive source potential field function can be expressed as follows:
gE(||y||)＝-y[J5(||y||)+J6(||y||)+J7(||y||)+J8(||y||)] (10)
wherein y is the Euclidean distance between the unmanned aerial vehicle and the obstacle, J5(| y |) is a linear rejection function, which can be expressed as follows:
Figure BDA0001778404700000194
wherein m is3＞0，m4If < 0, then
Figure BDA0001778404700000195
Linear repulsive sources produce repulsive effects on clustered individuals.
J6(| y |) is an exponential rejection function, which can be expressed as follows:
Figure BDA0001778404700000196
wherein k is>0,n3＜0,n4Is less than 0 when
Figure BDA0001778404700000197
The exponential repulsion source can generate repulsion effect on the clustered individuals.
J7(| y |) is a logarithmic exclusion function, which can be expressed as follows:
Figure BDA0001778404700000201
wherein p is3＞0，p4Less than 0, when 0 < y < p3The time-logarithmic repulsion source can generate repulsion action on the clustered individuals.
J8(| y |) is a reciprocal rejection function, which can be expressed as follows:
Figure BDA0001778404700000202
wherein q is3＜0、q4＞0。
According to the different types of the repulsion environmental sources, the repulsion effect on the unmanned aerial vehicle is different. As can be known from formulas (11) to (14), after the unmanned aerial vehicle cluster enters the range of the repulsive environment source potential field, the smaller the value of | y is, the larger the amplitude of the repulsive source potential field function is, that is, the larger the virtual repulsive force of the repulsive source borne by the unmanned aerial vehicle is.
The method provided by the invention is explained in detail below by combining with a specific simulation example:
in order to illustrate the effectiveness of the quad-rotor unmanned aerial vehicle cluster control method, stability verification is firstly carried out on an unmanned aerial vehicle cluster control algorithm. According to the formula (3), under the control of the artificial potential field function, the members in the unmanned aerial vehicle cluster are influenced by three potential field forces, namely the attraction/repulsion acting force from other unmanned aerial vehicle members, the attraction potential field force from a target point and the repulsion potential field force from an environmental repulsion source, and then the speed control function of the ith member can be written as follows:
Figure BDA0001778404700000203
wherein g isa(χi-pai) G is shown in equation (5)ij(χi-χj) G is shown in the formula (6)E(χi-pE) Is represented as follows:
gE(χi-pE)＝-kr·exp(er·||χi-pE||)·(χi-pE) (16)
wherein k isr、erIs a constant less than 0.
Order to
Figure BDA0001778404700000211
Wherein
Figure BDA0001778404700000212
Is the cluster center. Then there is
Figure BDA0001778404700000213
Establishing Lyapunov functions
Figure BDA0001778404700000214
And (3) carrying out derivation on the obtained product to obtain:
Figure BDA0001778404700000215
let u (y) yeayDerived from it
Figure BDA0001778404700000216
When a > 0, u (y) is
Figure BDA0001778404700000217
There is a minimum value
Figure BDA0001778404700000218
When a < 0, u (y) is
Figure BDA0001778404700000219
There is a maximum value
Figure BDA00017784047000002110
Then there are:
Figure BDA00017784047000002111
thus when
Figure BDA00017784047000002112
At a time there is
Figure BDA00017784047000002113
That is, when the distance between the members of the unmanned aerial vehicle cluster and the cluster center exceeds a certain distance, the members converge towards the cluster center, that is, the cluster system finally reaches a stable state.
To the cluster that 4 four rotor unmanned aerial vehicles constitute, all follow above-mentioned method in embodiment 1 ~ 3 and advance, control different motion types, carry out simulation analysis to the control result.
Embodiment 1 simulation test for controlling cluster formation of unmanned aerial vehicles
The number of unmanned aerial vehicles is 4, and the parameter value of formula (6) is: a is 5, b is 0.5, c is 0.1, and the preset formation structure is shown in fig. 4.
The target point locations are taken as: a (30,50,10), b (30,50,40), c (30,10,40) and d (30,10,10) with the unit of m, the unmanned planes are preset to form a rectangle, and the speed of each unmanned plane meets the speed constraint of the formula (2). Suppose maximum velocity V of the dronemaxAnd obtaining the unmanned aerial vehicle cluster formation control simulation result as shown in fig. 5, wherein the unmanned aerial vehicle cluster formation control simulation result is 30 m/s.
The formation used in this embodiment 1 includes 4 quadrotor drones, the initial positions of the 4 quadrotor drones are randomly distributed, as can be seen from fig. 5, a preset rectangular formation is formed after the quadrotor drones move to the final position (at this time, the speed of each drone is 0), the relative distance can be kept unchanged, and the simulation result verifies the effectiveness of the formation control algorithm.
Embodiment 2 simulation experiment for controlling unmanned aerial vehicle cluster to move towards target
In the simulation experiment, in this embodiment 2, adopt 6 four rotor unmanned aerial vehicles and 1 virtual lead team to carry out the cluster formation, the preset formation of unmanned aerial vehicle cluster is shown as figure 6, and wherein 6 light color blocks represent the unmanned aerial vehicle node, and dark square represents the virtual lead team, and 6 four rotor unmanned aerial vehicles use the virtual lead team as the apex angle, have formed a regular triangle formation configuration in one side of virtual lead team.
In the simulation test of example 2, first, the speed parameter a is set to 5, the virtual point position is set to (35,35,30), and the unit: m, are also target pointsLocation. In the unmanned aerial vehicle cluster configuration, 6 unmanned aerial vehicles are in the same plane, and the plane normal amount of the final position of the unmanned aerial vehicle is measured as
Figure BDA0001778404700000221
The motion trajectory diagram of the unmanned aerial vehicle cluster in the three-dimensional space is shown in fig. 7, which is the expected position of each unmanned aerial vehicle when the unmanned aerial vehicle cluster reaches the target point, and the dots represent the virtual lead position and are also the target positions of the unmanned aerial vehicle cluster. The 6 curves represent the motion trajectories of 7 drones respectively. As can be seen from fig. 7, the initial movement of 6 drones is irregular, and flies to the virtual pilot orderly at the middle section, and the movement direction is consistent, and finally forms a preset formation with the virtual point. The trajectory diagram of the unmanned aerial vehicle cluster shows that under the control of the proposed cluster motion control algorithm, the unmanned aerial vehicle cluster can rapidly adjust the self state, fly to the target point in order and consistently, and finally form a preset formation at the target point.
Embodiment 3 simulation experiment for controlling unmanned aerial vehicle cluster to avoid obstacles
In this embodiment, the obstacle avoidance algorithm is adopted to perform obstacle avoidance simulation of the unmanned aerial vehicle cluster, in the simulation experiment, the number of members of the unmanned aerial vehicle is 8, the formation configuration is as shown in fig. 8, the square represents the unmanned aerial vehicle, and the circle represents the central position of the unmanned aerial vehicle cluster.
For the convenience of observation, the unmanned aerial vehicle cluster position is projected to the x-y plane for analysis, the cluster target position is shown in fig. 9, when the unmanned aerial vehicle cluster moves to the target position, the unmanned aerial vehicle cluster is formed into a square configuration, and the central point target position is (60, 60, 60) (unit: m).
And then establish the position of the obstacle. Here two spherical obstacles are placed, with radii of 3 and 4 respectively, whose projections in the x-y plane are shown as two circles in fig. 10 (b). In fig. 10, fig. 10(a) is a diagram of a flight path of a cluster of unmanned aerial vehicles when no obstacle exists, and fig. 10(b) is a diagram of a flight path of a cluster of unmanned aerial vehicles when an obstacle exists, and it can be seen from the diagrams that when a cluster composed of 8 unmanned aerial vehicles moves toward a target position, two obstacles can be effectively avoided. Simulation results prove that the unmanned aerial vehicle cluster obstacle avoidance control method provided by the design has a good effect.
The above description is only for the purpose of illustrating the present invention and is not intended to limit the present invention in any way, and the present invention is not limited to the above description, but rather should be construed as being limited to the scope of the present invention.

Claims (9)

1. A quad-rotor unmanned aerial vehicle cluster control method based on an artificial potential field method is characterized by comprising the following steps:
step S100: adopting M quadrotor unmanned aerial vehicles to form the quadrotor unmanned aerial vehicle cluster, setting expected positions and speed vectors of all internal members of the cluster according to formation configuration of the quadrotor unmanned aerial vehicle cluster, and establishing a kinematic equation of the ith internal member;
step S200: constructing a speed control function of the ith internal member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, taking i +1, and repeating the steps S100-S200 until i is M to obtain the speed control functions of all the internal members;
step S300: controlling each internal member to move according to the movement type by adopting each speed control function;
the motion type comprises at least one of formation motion, target-oriented motion and obstacle avoidance motion, and the speed control function v of the ith inner memberiIs represented as follows:
Figure FDA0002942576610000011
wherein, χiA position vector, g, representing the ith said inner memberij(. h) represents an attraction/repulsion function between the ith and jth said internal members，pERepresenting the ambient source location vector, gE(. represents the function of the effect of the environmental source vector on each of said internal members, paRepresenting the target point position vector, ga() represents an attraction function of the expected location of the ith said internal member to the ith said internal member;
when the motion type is formation motion, the speed control function of the ith internal member is as follows:
Figure FDA0002942576610000021
wherein, χjA position vector, v, representing the jth of said inner membersiRepresenting the velocity vector, p, of the ith said inner memberaiRepresenting the expected position, g, of the ith said internal membera(. h) represents an attraction function of the expected position of the ith said internal member to the ith said internal member, expressed as:
ga(χi-χj)＝-ka·exp(ea·||χi-χj||)·(χi-χj) (5)
wherein k isa、eaA constant greater than 0 for adjusting the attraction force in the attraction function for the ith said inner member and desired position;
gij(. h) represents an attraction/repulsion function between the ith and jth said internal members, as follows:
Figure FDA0002942576610000022
wherein, aijSet to a constant greater than 0 for adjusting the magnitude of the attraction/repulsion function between the ith and jth said internal members, bij、cij、dijAre all set to be greater than 0, for determining the ith and jth of said internal membersThe equilibrium distance therebetween.
2. A method for cluster control of quad-rotor unmanned aerial vehicles based on artificial potential field method according to claim 1, wherein when the type of motion is towards a target, the speed control function of the ith inner member is:
Figure FDA0002942576610000023
wherein, χLPosition vector representing a virtual leader, gi(. cndot.) represents the attraction/repulsion function between the ith internal member and the virtual lead.
3. Method for quad-rotor unmanned aerial vehicle cluster control based on artificial potential field method according to claim 2, wherein the attraction/repulsion function gi(. cndot.) represents the following:
Figure FDA0002942576610000031
wherein, ai＞0，δiIs the equilibrium distance between the ith inner member and the virtual lead.
4. The artificial potential field method based quad-rotor drone cluster control method of claim 2, wherein when the type of motion is toward target motion, a virtual lead is established in the quad-rotor drone cluster, each of the inner members following the virtual lead in a formation configuration toward target motion.
5. The artificial potential field method-based quad-rotor unmanned aerial vehicle cluster control method of claim 1, wherein when the motion type is obstacle avoidance motion, the speed control function of the ith inner member is as follows:
Figure FDA0002942576610000032
wherein N is the number of obstacles or unfavorable environment sources encountered by the cluster moving area,
Figure FDA0002942576610000033
representing the repulsive source potential field function between the kth repulsive ambient source and the ith inner member,
Figure FDA0002942576610000034
to exclude the ambient source position vector,%jA position vector representing the jth of said inner members.
6. The artificial potential field method based quad-rotor unmanned aerial vehicle cluster control method of claim 5, wherein the repulsive source potential field function
Figure FDA0002942576610000035
gE(||y||)＝-y[J5(||y||)+J6(||y||)+J7(||y||)+J8(||y||)] (10)
Wherein, J5(| y |) is a linear rejection function, expressed as follows:
Figure FDA0002942576610000041
wherein m is3And m4To satisfy m3＞0，m4A constant of < 0, then
Figure FDA0002942576610000042
Then, a linear repulsive source produces a repulsive effect on the ith said inner member;
J6(| y |) is an exponential rejection function, expressed as follows:
Figure FDA0002942576610000043
wherein k is>0，n3And n4To satisfy n3＜0，n4A constant of < 0 when
Figure FDA0002942576610000044
Said exponential repulsion source exerts an repulsive effect on the ith said internal member;
J7(| y |) is a logarithmic exclusion function, expressed as follows:
Figure FDA0002942576610000045
wherein q is3、q4To satisfy p3＞0，p4A constant < 0, when 0 < | | y | < p3Then, a logarithmic-exclusion source produces an exclusion effect on the ith said internal member;
J8(| y |) is the reciprocal rejection function, expressed as follows:
Figure FDA0002942576610000046
wherein q is3、q4To satisfy q3＜0、q4A constant > 0.
7. Method for quad-rotor unmanned aerial vehicle cluster control based on artificial potential field method according to claim 1, wherein the velocity v of the ith inner memberiThe following constraints are satisfied:
Figure FDA0002942576610000051
wherein, VmaxIndicating the speed that the inner member can reachAnd (4) limiting.
8. The artificial potential field method based quad-rotor unmanned aerial vehicle cluster control method of claim 1, wherein the kinematic equation of the ith inner member is:
Figure FDA0002942576610000052
wherein v isiRepresenting the velocity vector of the ith said inner member.
9. An apparatus for controlling a method according to any one of claims 1 to 8, comprising:
the system comprises a kinematics equation module, a four-rotor unmanned aerial vehicle cluster and a four-rotor unmanned aerial vehicle control module, wherein the kinematics equation module is used for forming the four-rotor unmanned aerial vehicle cluster by adopting M four-rotor unmanned aerial vehicles, setting expected positions and speed vectors of all internal members of the cluster according to formation configuration of the four-rotor unmanned aerial vehicle cluster, and establishing a kinematics equation of the ith internal member;
the function module is used for constructing a speed control function of the ith internal member based on an artificial potential field method according to the expected position, the speed vector, the kinematic equation and the motion type, and returning to the kinematic equation module and the function module after i +1 is taken until i M is obtained, so that the speed control functions of all the internal members are obtained;
the motion control module is used for controlling each internal member by adopting each speed control function to carry out motion of the motion type;
the motion type includes at least one of a formation motion, a movement toward a target, and an obstacle avoidance motion.
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