CN109557936B - Anti-collision control method between erectable unmanned aerial vehicles based on artificial potential field method - Google Patents

Anti-collision control method between erectable unmanned aerial vehicles based on artificial potential field method Download PDF

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CN109557936B
CN109557936B CN201811465370.7A CN201811465370A CN109557936B CN 109557936 B CN109557936 B CN 109557936B CN 201811465370 A CN201811465370 A CN 201811465370A CN 109557936 B CN109557936 B CN 109557936B
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speed
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全权
郭正龙
李梦芯
杨坤
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Beihang University
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Abstract

The invention relates to an anti-collision control method between erectable unmanned aerial vehicles based on an artificial potential field method, which comprises the following steps: 1: and establishing a basic control model of the unmanned aerial vehicle. 2: and establishing a safety control model of the unmanned aerial vehicle. 3: and obtaining a speed control instruction of the unmanned aerial vehicle in the current state based on the point-to-point controller given in the step according to the current position and speed of the unmanned aerial vehicle and the position of the target point of the unmanned aerial vehicle. And a plurality of unmanned aerial vehicles flight anti-collision control parts. 4: based on the current position and speed of the unmanned aerial vehicle and the positions and speeds of other unmanned aerial vehicles around the unmanned aerial vehicle, the relative filtering distance between the unmanned aerial vehicle and the unmanned aerial vehicle is calculated, the potential field repulsive force of the current unmanned aerial vehicle from other unmanned aerial vehicles around the unmanned aerial vehicle is calculated according to the artificial potential field generated by each unmanned aerial vehicle around the unmanned aerial vehicle, namely, a speed control instruction, the total speed control instruction of the unmanned aerial vehicle in the current state is calculated according to the designed controller, and each unmanned aerial vehicle is controlled to reach a target point under the condition that the unmanned aerial vehicle does not collide with other unmanned aerial vehicles.

Description

Anti-collision control method between erectable unmanned aerial vehicles based on artificial potential field method
Technical Field
The invention relates to an anti-collision control method capable of hanging up an unmanned aerial vehicle room based on an artificial potential field method, and belongs to the field of flight control.
Background
With the development of the micro unmanned aerial vehicle, the great use of the unmanned aerial vehicle also raises the worry of people about safety, and the phenomena of 'black flight' such as affecting the aviation order and breaking into sensitive areas occur at all times, and the unmanned aerial vehicle capable of being hung is a typical representative of the micro unmanned aerial vehicle in recent years. After the number of unmanned aerial vehicles in the small-size region is increased, when a plurality of unmanned aerial vehicles finish tasks together, in order to ensure the safety of the unmanned aerial vehicles in flight and work, planning decisions in the flight process cannot be avoided. Because the unmanned aerial vehicles all fly at the ultra-low altitude, the air flight environment is very complex, and the unmanned aerial vehicles must be prevented from colliding with the unmanned aerial vehicles except for avoiding collision between the unmanned aerial vehicles and some static obstacles such as surrounding buildings and the like. Therefore, anti-collision flight control between multiple machines is necessary.
In order to solve the problems, the invention provides an anti-collision control method between the drooping unmanned aerial vehicles based on an artificial potential field method, and anti-collision flight control among multiple unmanned aerial vehicles is realized.
Disclosure of Invention
The invention provides an anti-collision control method capable of hanging up an unmanned aerial vehicle based on an artificial potential field method. The method is based on a traditional artificial potential field method. Firstly, establish the unmanned aerial vehicle basic control model that can hang down and can hang down unmanned aerial vehicle safety control model, then, establish other unmanned aerial vehicle's that can hang down artificial potential field around the unmanned aerial vehicle that can hang down, finally, according to the current position speed of unmanned aerial vehicle, control unmanned aerial vehicle flies to the target point under the condition that does not bump with unmanned aerial vehicle on every side.
The invention provides an anti-collision control method between erectable unmanned aerial vehicles based on an artificial potential field method. The following variables are defined here:
Figure BDA0001889611710000021
the filter positions of the ith unmanned aerial vehicle and the ith unmanned aerial vehicle are respectively,
Figure BDA0001889611710000022
the current positions of the ith unmanned aerial vehicle and the ith unmanned aerial vehicle are respectively,
Figure BDA0001889611710000023
is the current speed of the ith drone,
Figure BDA0001889611710000024
is the speed control instruction of the ith unmanned aerial vehicle output by the controller,
Figure BDA0001889611710000025
are each pi、vi、ξiThe first derivative.
Figure BDA0001889611710000026
Is the maximum value of the flight speed of the drone;
Figure BDA0001889611710000027
is a safe distance to the user,
Figure BDA0001889611710000028
is based on the safe distance of the filtering,
Figure BDA0001889611710000029
is the maneuvering distance, r, of obstacle avoidancevIs the noise error of the distance measurement;
Figure BDA00018896117100000210
is the target point position of the ith unmanned aerial vehicle;
Figure BDA00018896117100000211
is the position difference between the ith unmanned aerial vehicle and the target point,
Figure BDA00018896117100000212
is the filtering position difference between the ith unmanned aerial vehicle and the target point;
Figure BDA00018896117100000213
is the position difference between the ith unmanned aerial vehicle and the ith unmanned aerial vehicle,
Figure BDA00018896117100000214
is the filter position difference between the ith unmanned aerial vehicle and the ith unmanned aerial vehicle.
The control method comprises the following steps: please refer to fig. 6;
step 1: establishing a basic control model of a liftable unmanned aerial vehicle
First a basic control model of the drone needs to be defined. Considering the drone here as a particle model, then the ith drone satisfies the following model relationship:
Figure BDA00018896117100000215
here, |cIs a parameter of the control performance of the drone, determined by the drone itself. Due to the limited maneuverability of the drone, the speed command resolved by the controller cannot be infinite. Here the following saturation function is designed:
Figure BDA0001889611710000031
therefore, the speed control instruction of the ith unmanned aerial vehicle output by the final controller is as follows:
vc,i＝sat(vc,i,vm) (3)
a concept is defined herein, called filtering position. The filtering position is used for describing the current position and the speed of the unmanned aerial vehicle by a meter. This has the advantage that we can represent the second order control model of the drone in a first order form. The definition is shown as formula (4):
Figure BDA0001889611710000032
this is followed by:
Figure BDA0001889611710000033
here, it is defined that:
Figure BDA0001889611710000034
for convenience of description, the following positional differences are defined:
Figure BDA0001889611710000035
Figure BDA0001889611710000036
the position difference of the corresponding filtering distance is:
Figure BDA0001889611710000037
Figure BDA0001889611710000038
according to the definition of the filtering distance, we have:
Figure BDA0001889611710000041
where i, l is 1,2,3, i ≠ l. In order to ensure safety, a certain distance must be kept between any unmanned aerial vehicles. Let this distance be r, for the ith unmanned aerial vehicle and the l unmanned aerial vehicle, then have:
||pi-pl||≥r,i≠l (7)
step 2: establishing a safety control model of the unmanned aerial vehicle according to the current position and speed of the unmanned aerial vehicle capable of being hoisted and the safety distance of the unmanned aerial vehicle capable of being hoisted;
in a multi-airplane flying area, the unmanned planes can report the positions and postures of the unmanned planes mutually in a wireless network mode and the like. Due to the fact that communication is delayed, noise exists in the acquired navigation data, and therefore uncertainty exists in the position information of the unmanned aerial vehicle. To avoid collision of the drone with surrounding objects, we define a safe distance rmThe safe distance must be greater than the physical radius of the drone, as shown in figure 1. For any two drones, their filtering distance should satisfy:
||ξi-ξl||≥2rM(8)
equation (7) can be satisfied by equation (8). Where r isM＝rm+rv，rMIs a safety distance defined based on the filtering distance. In order to ensure that the drones can have sufficient time and space to maneuver to avoid obstacles when discovering surrounding drones, as shown in fig. 1. r isaOnly with respect to the power performance and response time of the drone itself. Maneuvering distance r for avoiding obstacleaIt must be as large as practical, where:
ra＞2rM(9)
and step 3: point-to-point flight control of a drapable unmanned aerial vehicle
The filtering distance between the current position of the unmanned aerial vehicle and the target point is
Figure BDA0001889611710000042
The conditions for the unmanned aerial vehicle to reach the target point are as follows:
Figure BDA0001889611710000051
in order to ensure that the ith unmanned aerial vehicle can reach a target point, the output volume v of the controller can be designedc,iThe speed control instruction of the ith unmanned aerial vehicle output by the controller is as follows:
Figure BDA0001889611710000052
wherein k is1A gain factor output by the controller.
And 4, step 4: calculating a control instruction of collision prevention received by the drooping unmanned aerial vehicle based on the relative position and speed of the drooping unmanned aerial vehicle and other surrounding drooping unmanned aerial vehicles
The current positions of the ith frame and the first unmanned aerial vehicle are respectively
Figure BDA0001889611710000053
And
Figure BDA0001889611710000054
the current speeds are respectively
Figure BDA0001889611710000055
And
Figure BDA0001889611710000056
the flying target points of the two unmanned planes are respectively
Figure BDA0001889611710000057
And
Figure BDA0001889611710000058
the speed control command input accepted is respectively
Figure BDA0001889611710000059
And
Figure BDA00018896117100000510
according to the safety control model of the unmanned aerial vehicle, the current filtering positions are
Figure BDA00018896117100000511
And
Figure BDA00018896117100000512
the filtering distance between the current position of the unmanned aerial vehicle and the target point is
Figure BDA00018896117100000513
And
Figure BDA00018896117100000514
the relative filtering distance between the two unmanned planes is
Figure BDA00018896117100000515
According to the safety control model of the unmanned aerial vehicle, the distances between the target points of all unmanned aerial vehicles must be greater than the safety distance.
The conditions under which the drones cannot collide while flying to their respective target points are:
Figure BDA00018896117100000516
wherein t is time.
Consider the scenario shown in fig. 3, which is a schematic top view of three drones and their target points in an area. Including three unmanned aerial vehicles UAV1, UAV2, and UAV3, and their respective three target points
Figure BDA00018896117100000517
For the unmanned aerial vehicles flying in the area, it is necessary to ensure that no collision occurs between the unmanned aerial vehicles and the unmanned aerial vehicles reach respective target points. Namely:
Figure BDA0001889611710000061
remember of Nm,iAnd (4) a set of other unmanned planes except the ith unmanned plane in the unmanned plane cluster in the area. Taking the flight scenario in fig. 3 as an example, there are three unmanned planes. N (in)m,1＝{2,3}，Νm,2＝{1,3}， Ν m,31, 2. Based on the above properties, the speed control instruction of the ith unmanned aerial vehicle output by the controller can be given, and the expression form is as follows:
Figure BDA0001889611710000062
wherein the content of the first and second substances,
Figure BDA0001889611710000063
the potential energy function for the artificial potential field is defined as follows:
Figure BDA0001889611710000064
for convenience of description, let us note
Figure BDA0001889611710000065
d1＝2rM,d2＝raMemory for recording
Figure BDA0001889611710000066
rsIs a minimum value.
Figure BDA0001889611710000067
Is a smooth cut-off function that is,
Figure BDA0001889611710000068
is a smooth saturation function. These two second-order smoothed basis functions are shown in fig. 2(a) and 2 (b). The introduced function is to simplify the operation relationship between formulas, so the parameters in the following formulas are all intermediate variables, and have no meaning per se, and are only for convenience of description.
Figure BDA0001889611710000069
Wherein A is-2/(d)1-d2)3，B＝3(d1+d2)/(d1-d2)3，C＝-6d1d2/(d1-d2)3，D＝d2 2(3d1-d2)/(d1-d2)3. Function σ (x, d)1,d2) The partial derivatives with respect to x are:
Figure BDA00018896117100000610
saturation function s (y, r)s) Comprises the following steps:
Figure BDA0001889611710000071
wherein the content of the first and second substances,
Figure BDA0001889611710000072
y1＝y2-sin45°rs
for any rs∈[0,tan67.5°/(tan67.5°sin45°-1)]The number of the carbon atoms is equal to that of the carbon atoms,
Figure BDA0001889611710000073
where min (y,1) represents the smaller of the variable y and 1. Function s (y, r)s) The partial derivative with respect to y is given by equation (19), which is obvious
Figure BDA0001889611710000074
Figure BDA0001889611710000075
k2A gain factor output by the controller. There is a very small amount of epsilon, such that,
Figure BDA0001889611710000076
besides collision avoidance, we need to control the drone to reach the target point, so the controller outputs the speed control command of the ith drone:
Figure BDA0001889611710000077
the constraint that the drone reach the target point steadily is that there is a minimum amount epsilon such that equation (22) holds.
Figure BDA0001889611710000081
Therefore, the method for preventing collision between the unmanned aerial vehicles comprises the following steps:
inputting: real-time position and speed information of all unmanned aerial vehicles in the area and corresponding target points.
And (3) outputting: speed control command v for each dronec,i。
4.1: acquiring real-time position and speed information and target point positions of all unmanned aerial vehicles in an area;
4.2: calculating anti-collision instructions between the unmanned aerial vehicle and surrounding unmanned aerial vehicles according to the formula (14) and the formula (15);
4.3: calculating a control instruction generated by a target point according to a formula (11) and the position of the target point of the unmanned aerial vehicle;
4.4: superposing the instructions generated in the step 4.2 and the step 4.3 according to a formula (21) and carrying out saturation treatment on the direction;
4.5: if the constraint condition formula (22) is met, the unmanned aerial vehicle is shown to reach the target point; otherwise, step 4.2 is continued.
The advantages and the effects are as follows: the invention provides an anti-collision control method between erectable unmanned aerial vehicles based on an artificial potential field method. The method has the advantages that: the problem of collision that probably takes place between them when having solved unmanned aerial vehicle multimachine flight, the advantage is as follows:
(1) the multi-rotor unmanned aerial vehicle model used is a double-integral model with speed command input, and is suitable for most unmanned aerial vehicles. The model is simple and easy to implement, and more importantly, the model is a link connecting the bottom-layer control and the top-layer application algorithm. The design development can be correspondingly completed for various tasks based on the commercial semi-autonomous self-driving instrument.
(2) The speed control command has saturation protection. There is a limit to the maximum speed command in a designed controller. When unmanned aerial vehicle and barrier are close, the speed command that anticollision produced can be far greater than the speed control command that unmanned aerial vehicle reachd the target point, uses the saturation control back of guaranteeing the direction, can improve unmanned aerial vehicle anticollision control's priority, guarantees unmanned aerial vehicle's safety.
(3) According to the controller, the unmanned aerial vehicle finally converges to the target point whether encountering an obstacle or not. That is to say, this controller can not only make unmanned aerial vehicle accomplish the flight task, can also guarantee to accomplish the security of task in-process.
(4) When the distance between the two unmanned aerial vehicles is smaller than the safe distance, the whole control algorithm can still quickly separate the two unmanned aerial vehicles.
Drawings
FIG. 1: and (4) a safe distance two-dimensional projection model.
Fig. 2 (a): is a smooth truncation function.
Fig. 2 (b): is a smooth saturation function.
FIG. 3: flight schematic diagram in many unmanned aerial vehicle regions.
FIG. 4: the three unmanned aerial vehicle anticollision experiments set up the schematic diagram.
Fig. 5 (a): is the three-dimensional track of three and four rotors.
Fig. 5 (b): is the horizontal projection of the track of three four rotors.
FIG. 6: is a flow chart of the present invention.
Description of the symbols in the drawings
FIG. 1: safety distance rmDistance r to avoid obstaclea。
Fig. 2 (b): r iss∈[0,tan67.5°/(tan67.5°sin45°-1)]It is a minimum value.
FIG. 3: three unmanned aerial vehicles UAV1, UAV2, and UAV3 and their respective three target points
Figure BDA0001889611710000091
FIG. 4: three unmanned planes, respectively marked as U1,U2,U3Their target points are respectively pd,1,pd,2,pd,3
Detailed Description
The invention provides an anti-collision control method between erectable unmanned aerial vehicles based on an artificial potential field method, and a specific implementation mode of the invention is further explained by taking a plurality of unmanned aerial vehicles flying in an area as an example. The following describes the inter-drone anti-collision flight control of drones according to the method mentioned in the present invention. Please refer to fig. 1-6.
(1) The method comprises the following concrete implementation steps:
the method comprises the following steps: establishing a basic control model of a liftable unmanned aerial vehicle
The establishment of a basic control model requires two parameters: l 10, vm2.0 m/s. Our filtering positions are:
Figure BDA0001889611710000101
the speed control instruction of the ith unmanned aerial vehicle with the saturated controller output is as follows:
Figure BDA0001889611710000102
step two: establishing safety control model capable of erecting unmanned aerial vehicle
The core parameters of the safe distance model are as follows: r ism＝0.6m,ra＝1.8m，rM＝0.8m。
Step three: point-to-point flight control of a drapable unmanned aerial vehicle
This step needs to be given the parameter k10.5, the speed control instruction of the ith unmanned aerial vehicle with the saturated controller output is:
Figure BDA0001889611710000103
step four: based on the relative position and speed of the drapable unmanned aerial vehicle and other surrounding drapable unmanned aerial vehicles, the anti-collision control instruction received by the drapable unmanned aerial vehicle is calculated.
In this experiment, three unmanned aerial vehicles are used together and are respectively recorded as U1,U2,U3See fig. 4. Their respective starting positions are:
pu1＝[-2.0 -0.5 1.2]T
pu2＝[0.0 0.0 1.2]T(26)
pu3＝[2.0 1.0 1.2]T
their target points are corresponding pd,1,pd,2,pd,3As shown in fig. 4, their coordinates are:
pd,1＝[2.2 0.5 1.2]T
pd,2＝[-0.1 0.6 1.2]T(27)
pd,3＝[-1.8 -0.6 1.2]T
the straight lines connecting the starting points of the drones with their respective target points are shown by the dotted lines in fig. 4, and it can be seen that these straight lines intersect.
The parameters of the unmanned aerial vehicle multi-machine flight anti-collision experiment are as follows:
1) anti-collision speed command gain coefficient: k is a radical of2＝0.5
2) Convergence minimum: ε ═ 0.01
3) Saturation basis function parameters: r iss＝0.01
The speed control instruction of the ith unmanned aerial vehicle output by the anti-collision flight controller of the unmanned aerial vehicle is as follows:
Figure BDA0001889611710000111
wherein the content of the first and second substances,
Figure BDA0001889611710000112
if there is not the safeguard measure of anticollision between the unmanned aerial vehicle, the unmanned aerial vehicle will collide at the in-process of flying to the target point. But the collision of the unmanned aerial vehicle in the air can be avoided by adding the anti-collision protection algorithm.
Since each drone is subjected to the repulsive force generated by the other two drones, the repulsive force generated by the area boundary, and the attractive force of the target point to the drone, it is impossible for the drone to advance toward the target point completely in a straight line, and the position and speed of the drone are changing every moment, as shown by the trajectories of the three drones in fig. 5(a), 5 (b).

Claims (2)

1. The utility model provides a but unmanned aerial vehicle machine room anticollision control method that hangs down based on artifical potential field method which characterized in that: the method comprises the following steps: wherein the parameters are defined as follows:
Figure FDA00024061140900000116
the filter positions of the ith unmanned aerial vehicle and the ith unmanned aerial vehicle are respectively,
Figure FDA0002406114090000012
the current positions of the ith unmanned aerial vehicle and the ith unmanned aerial vehicle are respectively,
Figure FDA0002406114090000013
is the current speed of the ith drone,
Figure FDA00024061140900000117
is the speed control instruction of the ith unmanned aerial vehicle output by the controller,
Figure FDA0002406114090000015
are each pi、vi、ξiFirst-order derivation;
Figure FDA0002406114090000016
is the maximum value of the flight speed of the drone;
Figure FDA0002406114090000017
is a safe distance to the user,
Figure FDA0002406114090000018
is based on the safe distance of the filtering,
Figure FDA0002406114090000019
is the maneuvering distance, r, of obstacle avoidancevIs the noise error of the distance measurement;
Figure FDA00024061140900000118
is the target point position of the ith unmanned aerial vehicle;
Figure FDA00024061140900000111
is the position difference between the ith unmanned aerial vehicle and the target point,
Figure FDA00024061140900000119
is the filtering position difference between the ith unmanned aerial vehicle and the target point;
Figure FDA00024061140900000113
is the position difference between the ith unmanned aerial vehicle and the ith unmanned aerial vehicle,
Figure FDA00024061140900000114
the filter position difference between the ith unmanned aerial vehicle and the ith unmanned aerial vehicle is obtained;
step 1: establishing a basic control model of a liftable unmanned aerial vehicle
Firstly, defining a basic control model of the unmanned aerial vehicle; considering a drone as a particle model, then the ith drone satisfies the following model relationship:
Figure FDA00024061140900000115
here, |cIs a parameter of the control performance of the unmanned aerial vehicle, and is determined by the unmanned aerial vehicle; because the maneuvering performance of the unmanned aerial vehicle is limited, the speed instruction calculated by the controller cannot be infinite; here the following saturation function is designed:
Figure FDA0002406114090000021
therefore, the speed control instruction of the ith unmanned aerial vehicle output by the final controller is as follows:
vc,i＝sat(vc,i,vm) (3)
a concept is defined herein, called filtering position; the filtering position is used for expressing the current position and the speed of the unmanned aerial vehicle by using one meter; representing a second-order control model of the unmanned aerial vehicle by using a first-order form; the definition is shown as formula (4):
Figure FDA0002406114090000022
the following results are obtained:
Figure FDA0002406114090000023
here, it is defined that:
Figure FDA0002406114090000024
for convenience of description, the following positional differences are defined:
Figure FDA0002406114090000025
Figure FDA0002406114090000026
the position difference of the corresponding filtering distance is:
Figure FDA0002406114090000027
Figure FDA0002406114090000028
the definition according to the filtering distance is:
Figure FDA0002406114090000031
where i, l is 1,2,3., i ≠ l; in order to ensure safety, a certain distance must be kept between any unmanned aerial vehicles; let this distance be r, for the ith unmanned aerial vehicle and the l unmanned aerial vehicle, then have:
||pi-pl||≥r,i≠l (7)
step 2: establishing a safety control model of the unmanned aerial vehicle according to the current position and speed of the unmanned aerial vehicle capable of being hoisted and the safety distance of the unmanned aerial vehicle capable of being hoisted;
in order to avoid the unmanned aerial vehicle and surrounding objects from happeningCollision, defining a safety distance rmSafe distance must be greater than unmanned aerial vehicle's physical radius, to two arbitrary unmanned aerial vehicles, their filtering distance should satisfy:
||ξi-ξl||≥2rM(8)
the formula (7) is satisfied by the formula (8); where r isM＝rm+rv，rMIs a safety distance defined based on the filtering distance; in order to ensure that the unmanned aerial vehicle has sufficient time and space to maneuver and avoid the obstacle when finding surrounding unmanned aerial vehicles, raOnly with respect to the power performance and response time of the drone itself; maneuvering distance r for avoiding obstacleaIt must be as large as practical, where:
ra＞2rM(9)
and step 3: point-to-point flight control of a drapable unmanned aerial vehicle
The filtering distance between the current position of the unmanned aerial vehicle and the target point is
Figure FDA0002406114090000033
The conditions for the unmanned aerial vehicle to reach the target point are as follows:
Figure FDA0002406114090000032
in order to ensure that the ith unmanned aerial vehicle reaches a target point, the output quantity v of the controller is designedc,iThe speed control instruction of the ith unmanned aerial vehicle output by the controller is as follows:
Figure FDA0002406114090000041
wherein k is1A gain factor for the controller output;
and 4, step 4: calculating a control instruction of collision prevention received by the drooping unmanned aerial vehicle based on the relative position and speed of the drooping unmanned aerial vehicle and other surrounding drooping unmanned aerial vehicles
The current positions of the ith frame and the first unmanned aerial vehicle are respectively
Figure FDA0002406114090000042
And
Figure FDA0002406114090000043
the current speeds are respectively
Figure FDA00024061140900000418
And
Figure FDA0002406114090000045
the flying target points of the two unmanned planes are respectively
Figure FDA0002406114090000046
And
Figure FDA0002406114090000047
the speed control command input accepted is respectively
Figure FDA0002406114090000048
And
Figure FDA0002406114090000049
according to the safety control model of the unmanned aerial vehicle, the current filtering positions are
Figure FDA00024061140900000410
And
Figure FDA00024061140900000411
the filtering distance between the current position of the unmanned aerial vehicle and the target point is
Figure FDA00024061140900000412
And
Figure FDA00024061140900000413
the relative filtering distance between the two unmanned planes is
Figure FDA00024061140900000414
According to the safety control model of the unmanned aerial vehicle, the distances between target points of all the unmanned aerial vehicles must be greater than the safety distance;
the conditions under which the drones cannot collide while flying to their respective target points are:
Figure FDA00024061140900000415
wherein t is time;
three unmanned aerial vehicles and their target points in the area, including three unmanned aerial vehicles UAV1, UAV2, and UAV3, and their respective three corresponding target points
Figure FDA00024061140900000416
For unmanned aerial vehicles flying in the area, the unmanned aerial vehicles need to be ensured not to collide and reach respective target points; namely:
Figure FDA00024061140900000417
note Nm,iA set of other unmanned aerial vehicles except the ith unmanned aerial vehicle in the unmanned aerial vehicle cluster in the area is obtained; there are three unmanned planes; n is a radical ofm,1＝{2,3}，Nm,2＝{1,3}，Nm,31, 2; giving a speed control instruction of the ith unmanned aerial vehicle output by the controller, wherein the speed control instruction is represented by the following form:
Figure FDA0002406114090000051
wherein the content of the first and second substances,
Figure FDA0002406114090000052
the potential energy function for the artificial potential field is defined as follows:
Figure FDA0002406114090000053
for convenience of description, note
Figure FDA0002406114090000054
d1＝2rM,d2＝raMemory for recording
Figure FDA0002406114090000055
rsIs a minimum value;
Figure FDA0002406114090000056
is a smooth cut-off function that is,
Figure FDA0002406114090000057
is a smooth saturation function; the introduced functions are used for simplifying the operational relationship between formulas, so that the parameters in the following formulas are intermediate variables, have no meaning and are only used for convenience of description;
Figure FDA0002406114090000058
wherein A is-2/(d)1-d2)3，B＝3(d1+d2)/(d1-d2)3，C＝-6d1d2/(d1-d2)3，
D＝d2 2(3d1-d2)/(d1-d2)3(ii) a Function σ (x, d)1,d2) The partial derivatives with respect to x are:
Figure FDA0002406114090000059
saturation function s (y, r)s) Comprises the following steps:
Figure FDA00024061140900000510
wherein the content of the first and second substances,
Figure FDA00024061140900000511
y1＝y2-sin45°rs
for any rs∈[0,tan67.5°/(tan67.5°sin45°-1)]The number of the carbon atoms is equal to that of the carbon atoms,
Figure FDA0002406114090000061
wherein min (y,1) represents the smaller of the variable y and 1; function s (y, r)s) The partial derivative with respect to y is given by equation (19), which is obvious
Figure FDA0002406114090000062
Figure FDA0002406114090000063
k2A gain factor for the controller output; there is a very small amount of epsilon, such that,
Figure FDA0002406114090000064
besides collision avoidance, the unmanned aerial vehicle needs to be controlled to reach a target point, so the speed control instruction of the ith unmanned aerial vehicle output by the controller is as follows:
Figure FDA0002406114090000065
the constraint condition that the unmanned aerial vehicle stably reaches the target point is that a minimum quantity epsilon exists, so that a formula (22) is established;
Figure FDA0002406114090000066
2. the unmanned aerial vehicle inter-airplane anti-collision control method based on the artificial potential field method, according to claim 1, is characterized in that: also comprises the following steps:
inputting: real-time position and speed information of all unmanned aerial vehicles in the area and corresponding target points;
and (3) outputting: speed control command v for each dronec,i；
4.1: acquiring real-time position and speed information and target point positions of all unmanned aerial vehicles in an area;
4.2: calculating anti-collision instructions between the unmanned aerial vehicle and surrounding unmanned aerial vehicles according to the formula (14) and the formula (15);
4.3: calculating a control instruction generated by a target point according to a formula (11) and the position of the target point of the unmanned aerial vehicle;
4.4: superposing the instructions generated in the step 4.2 and the step 4.3 according to a formula (21) and carrying out saturation treatment on the direction;
4.5: if the constraint condition formula (22) is met, the unmanned aerial vehicle is shown to reach the target point; otherwise, step 4.2 is continued.
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