CN104503457A - Turning anti-collision control method for UAV formation flight - Google Patents

Abstract

The invention provides a turning anti-collision control method for UAV formation flight. Aimed at an isomorphic lead aircraft and wining plane type rhombus formation, a method based on airway restriction is used. According to maneuvering characteristic limitation of an UAV, the turning airway of the lead aircraft is corrected, and wining planes change respective airways according to the relation positions with the lead aircraft. Thus, a practical formation turning airway is generated. Using the anti-collision method, formation tacking error is reduced, and the method prevents the formation structure from being damaged. On airway planning, the method solves a problem of anticollision when the formation turns.

Description

Unmanned aerial vehicle formation flight turning collision prevention control method

Technical Field

The invention relates to an unmanned aerial vehicle formation flight turning collision prevention control method, in particular to an unmanned aerial vehicle formation turning air route limiting method, and belongs to the field of air route planning.

Background

In addition to maneuverability and agility, the modern unmanned aerial vehicle also requires the unmanned aerial vehicle to have the capability of multi-machine cooperative flight and battle. Unmanned aerial vehicle formation flight carries out three-dimensional space arrangement with many unmanned aerial vehicles that have autonomic function according to certain structural style, guarantees the stability of its flight in-process formation, but can carry out dynamic adjustment according to the change of external condition and task demand. The success rate of the unmanned aerial vehicle formation task execution and the capability of resisting emergency are much higher than that of single-machine flight, and close-range formation can effectively increase the lift/drag ratio pneumatic performance of the unmanned aerial vehicle at the following position, and fuel is saved.

The formation of unmanned aerial vehicle formation flight when turning keeps especially important, and most of route planning algorithm do not fully consider unmanned aerial vehicle's maneuverability restriction, especially the restriction of speed at present, and when formation turn like this, inboard unmanned aerial vehicle flying speed if can not reduce to the theoretical design value of route regulation when, will collide with the unmanned aerial vehicle in the outside easily, and when formation from straight line flight to turn flight transition, because the switching of control law, lead to the unstability of system easily, and then the emergence probability of collision accident when having increased the turn.

Aiming at the problem of collision prevention during formation flight turning of unmanned aerial vehicles, the invention designs a turning collision prevention control method based on air route limitation. According to the maneuvering performance limit of the unmanned aerial vehicle, the air route is corrected and limited, and the formation turning air route is strictly realized, so that the collision phenomenon caused by improper air route planning is avoided.

Disclosure of Invention

The technical problem to be solved is as follows:

the invention aims to provide an unmanned aerial vehicle formation flight turning collision prevention control method, which corrects and limits an air route according to the maneuvering performance limit of an unmanned aerial vehicle, so that the collision phenomenon caused by improper air route planning is avoided.

The technical scheme is as follows:

in order to realize the functions, the invention provides an unmanned aerial vehicle formation flight turning collision prevention control method, which is characterized by comprising the following steps: the method is realized by the following steps:

step 1, calculating the maneuvering performance limits of the unmanned aerial vehicle, namely the relative maximum speed and the relative minimum speed; an overshoot sigma is set to obtain the following formula,

<math> <mrow> <mfrac> <mrow> <msub> <mi>v</mi> <mi>min</mi> </msub> <mo>-</mo> <mmultiscripts> <mi>v</mi> <mi>min</mi> <mo>*</mo> </mmultiscripts> </mrow> <mrow> <msub> <mi>V</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>min</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mi>&sigma;</mi> <mo>,</mo> <mfrac> <mrow> <mmultiscripts> <mi>v</mi> <mi>max</mi> <mo>*</mo> </mmultiscripts> <mo>-</mo> <msub> <mi>v</mi> <mi>max</mi> </msub> </mrow> <mrow> <msub> <mi>v</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mi>&sigma;</mi> <mo>;</mo> </mrow> </math>

in the formula,^*v_min、^*v_maxis the actual minimum and maximum velocity, v_min、v_maxIs the relative minimum and maximum speed, V₀Is the flight speed of the formation before entering a turn;

step 2, combining the formation, calculating the maximum and minimum wing plane turning radius when turning, and adjusting the turning radius of the long plane according to the relative maximum and minimum speed limits;

and 3, generating the turning radius of each wing plane through the change of the formation configuration position relationship according to the adjusted turning radius of the long plane to obtain the final formation turning fairway.

Further, the formation in the step 2 is set to four isomorphic unmanned planes, a is a franchisee, B, C, D is a franchisee, and a franchisee rhomboid formation is formed.

Further, the formation of the pedestrial-wing-type rhombus formation is according to each unmanned aerial vehicleThe distance relationship between A and B is divided into three configurations, and the distance between B and D is set as l, and the distance between B and D is set as 2l₁And the distance between A and C is 2l₂The three configurations are:

rhomboid configuration I is l-2 l₂The diamond configuration II is I>2l₂A rhombus configuration III is<2l₂。

Furthermore, in step 1, the actual speed control system is designed to be in an underdamping mode, and the overshoot is tracked, so that the overshoot with the σ of 20% is introduced into the calculation of the actual maximum and minimum speeds to obtain the relative maximum and minimum speeds:

$\frac{v_{\min }-v_{\min }^{*}}{V_0-v_{\min }}=20\%,\frac{v_{\max }^{*}-v_{\max }}{v_{\max }-V_0}=20\%---\left(4\right).$

further, the specific method for adjusting the turning radius of the long crane in the step 2 is as follows:

let R_L、V_LIs the turning radius and speed, r, of the longator L_B、V_BRadius of turning and speed, r, of a wing plane B_C、V_CRadius of turning and speed, r, of a wing plane C_D、V_DThe turning radius and the speed of the wing machines D, in order to guarantee the configuration of the formation unchanged, the following holds:

V_L/R_L＝V_B/r_B＝V_C/r_C＝V_D/r_D (1)

let the minimum turning radius in each wing plane be r_SCorresponding to a velocity V_S(ii) a Maximum turning radius r_MCorresponding to a velocity V_M(ii) a Then V_SMinimum velocity v to satisfy unmanned aerial vehicle_minLimitation, V_MMaximum speed v to satisfy unmanned aerial vehicle_maxThe number of the limits, that is,

V_S＝(V_L/R_L)r_S≥v_min (2)

V_M＝(V_L/R_L)r_M≤v_max (3)

according to the concrete three diamond configurations, firstly determining the corresponding minimum turning radius as r_SAnd a maximum turning radius of r_MThen substituting the obtained values into the expressions (2) and (3) to obtain the value of R_LSolving the inequality to obtain R satisfying the constraint condition_LAnd the minimum value of (3) is set as the turning radius of the tractor a after correction.

Further, the turning radius of each bureaucratic is determined according to the adjusted turning radius of the long plane to obtain the final formation turning route, and the turning radius of each bureaucratic is as follows:

<math> <mrow> <msubsup> <mi>r</mi> <mi>B</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mi>&alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>C</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>D</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

in the formula, r_B、r_C、r_DThe turning radius of the wing-planes B, C, D, respectively, the angle between the wing-planes B, D and the long-plane a is 2 phi and alpha pi/2-phi.

Has the advantages that:

the invention relates to a method for controlling collision prevention of flying turns of formation of unmanned aerial vehicles, which aims at isomorphic Tao wing type rhombus formation and adopts a method based on airway restriction, and corrects the turn airways of the Tao wing according to the maneuverability restriction of the unmanned aerial vehicles, and the respective airways of the Tao wing are changed according to the relative position of the Tao wing and the Tao wing to generate the actual flying turn airways of the formation. The motor performance and parameters of the equal chanters and the bureaucratic planes in the isomorphic chanter plane type rhombic formation are the same, and the special plane type drilling formation is a common formation in the unmanned plane formation. The maneuvering performance limit of the unmanned aerial vehicle refers to the relative maximum and minimum speed limit of the unmanned aerial vehicle, and the relative maximum and minimum speed limit is obtained by considering the oscillation of the actual speed control according to the actual maximum and minimum speed. The formation tracking error is reduced, the damage of the formation structure is avoided, and the collision prevention problem when the formation turns is solved on the aeronautical route planning.

Drawings

The invention is further illustrated with reference to the following figures and examples:

fig. 1 is a schematic diagram of relative minimum and maximum speeds of an unmanned aerial vehicle according to the present invention;

fig. 2 shows a formation of isomorphic bureaucratic-type diamond formations according to the present invention;

fig. 3 is a schematic left-turn diagram of a formation long machine of unmanned aerial vehicles in a diamond configuration;

fig. 4 is a schematic left-turn diagram of a formation long machine of unmanned aerial vehicles in a diamond configuration II;

fig. 5 is a schematic left-turn diagram of a formation long machine of unmanned aerial vehicles in a diamond-shaped configuration III;

FIG. 6 is a diagram of a formation turn route for UAVs not using the route restriction method of the present invention;

FIG. 7 is a graph of a tracking error curve when unmanned aerial vehicles form a turn without using the route limiting method of the present invention;

FIG. 8 is a diagram of a formation turn route for UAVs using the route restriction method of the present invention;

fig. 9 is a graph of a tracking error curve when unmanned aerial vehicles form a turn by using the route limiting method of the present invention.

Detailed Description

The invention provides an unmanned aerial vehicle formation flight turning collision prevention control method, which aims to enable the purpose, technical scheme and effect of the invention to be clearer and more clear and definite, and further detailed description is given for the invention by referring to the attached drawings and taking examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The method for controlling the unmanned aerial vehicle formation flying turning collision prevention specifically comprises the following steps.

Step 1, calculating the maneuvering performance limit of the unmanned aerial vehicle, namely the relative maximum speed and the relative minimum speed. Considering that actual speed control systems are generally designed in an underdamped form, tracking situations where overshoot exists, adding an overshoot of 20% to the actual maximum and minimum speed limits yields the relative maximum and minimum speeds. As shown in fig. 1, the following formula is obtained,

$\frac{v_{\min }-v_{\min }^{*}}{V_0-v_{\min }}=20\%,\frac{v_{\max }^{*}-v_{\max }}{v_{\max }-V_0}=20\%$

in the formula,^*v_min、^*v_maxis the actual minimum and maximum velocity, v_min、v_maxIs the relative minimum and maximum speed, V₀Is the flight speed of the formation before entering the turn.

And 2, combining the formation, calculating the maximum and minimum wing plane turning radius when turning, and adjusting the turning radius of the long plane according to the relative maximum and minimum speed limits.

In the plane rhombus formation formed by four drones shown in fig. 2, drone a is a leader and B, C, D is a bureaucratic. The distance between A and B is denoted as l, and the distance between B and D is denoted as 2l₁And the distance between A and C is 2l₂B, D is at an angle of 2 phi to the bench. When the longeron makes a turning manoeuvre, taking the example of the left turn of the longeron (as shown in fig. 3), the wing plane speed inside the turning radius is less than the speed of the longeron and the wing plane speed outside the turning radius is greater than the speed of the longeron in order to keep the formation configuration unchanged. For unmanned aerial vehicleThe minimum maximum speed limit, so the turning radius of the long machine is limited. Setting the flying speed of the long machine to be V_LThe turning radius is R_L，r_B、V_BRadius of turning and speed, r, of a wing plane B_C、V_CRadius of turning and speed, r, of a wing plane C_D、V_DIs the turning radius and speed of the wing plane D. To ensure that the formation configuration is unchanged, the following holds,

V_L/R_L＝V_B/r_B＝V_C/r_C＝V_D/r_D (1)

let the minimum turning radius in each wing plane be r_SCorresponding to a velocity V_S(ii) a Maximum turning radius r_MCorresponding to a velocity V_M. Then V_SMinimum velocity v to satisfy unmanned aerial vehicle_minLimitation, V_MMaximum speed v to satisfy unmanned aerial vehicle_maxThe number of the limits, that is,

V_S＝(V_L/R_L)r_S≥v_min (2)

V_M＝(V_L/R_L)r_M≤v_max (3)

according to l, l₁、l₂Consider the three diamond formations shown in fig. 3-5: the rhomboid configuration shown in fig. 3 corresponds to 2l₂The diamond configuration II shown in FIG. 4 corresponds to l>2l₂The diamond configuration III shown in FIG. 5 corresponds to l<2l₂。

(1)l＝2l₂Formation

In the formation of FIG. 3, there is r_B<r_C<r_DI.e. r_S＝r_B，r_M＝r_D。

<math> <mrow> <msubsup> <mi>r</mi> <mi>S</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mi>B</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mi>&alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>M</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mi>D</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mi></mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

α＝π/2-φ (6)

Substituting the formula (4) into the formula (2) to obtain

<math> <mrow> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

Similarly, by substituting the formula (5) into the formula (3), the compound

<math> <mrow> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>&le;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

Order to

<math> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>&alpha;</mi> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> </math>

In order to satisfy equations (7) and (8), the minimum turning radius of the long machine is:

if sin α>v_min/V_LThen R is_min＝R₂；

Otherwise R_min＝max(R₁,R₂)。

(2)l>2l₂Formation

In the formation of fig. 4, the straight line EF is the perpendicular bisector of the diamond-shaped edge BC. The length of the score line AE is

<math> <mrow> <mover> <mi>AE</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>1</mn> </msub> <mo>-</mo> <mfrac> <mrow> <mn>3</mn> <mi>l</mi> </mrow> <mrow> <mn>2</mn> <mi>sin</mi> <mi>&phi;</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

When in useWhen, there is r_C<r_B<r_D。

<math> <mrow> <msubsup> <mi>r</mi> <mi>S</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mi>C</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>M</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mi>D</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mi></mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> </math>

α＝π/2-φ (12)

By substituting the formula (10) into the formula (2), the compound

<math> <mrow> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mrow> <mn>4</mn> <mi>R</mi> </mrow> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>1</mn> </msub> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mrow> <mn>4</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mrow> <mn>4</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

Similarly, by substituting formula (11) into formula (3), the compound

<math> <mrow> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>&le;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

Since it can be seen that equation (13) is always satisfied, equation (14) is only required to be satisfied.

Order to <math> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mi></mi> <mo>-</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mi></mi> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> </mrow> </math> The minimum turning radius of the long machine is: r_min＝R₂。

When in useWhen, there is r_B<r_C<r_DWhen the solving step and the sum of the results l is 2l₂The situation is the same, namely the minimum turning radius of the long machine is as follows:

if sin α>v_min/V_LThen R is_min＝R₂；

Otherwise R_min＝max(R₁,R₂)。

Wherein, <math> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>&alpha;</mi> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>

it should be noted thatIn the case of (1), the adjusted R_LMay appearThe current R is needed_LThe value is carried out againAdjustment of the case to obtain the final corrected R_LThe value is obtained.

(3)l<2l₂Formation

In the formation of fig. 5, the straight line EF is the perpendicular bisector of the diamond-shaped edge CD. The length of the score line AE is

<math> <mrow> <mover> <mi>AE</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mi>l</mi> </mrow> <mrow> <mn>2</mn> <mi>sin</mi> <mi>&phi;</mi> </mrow> </mfrac> <mo>-</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>1</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

When in use(center of turning is shown as O in FIG. 5)₁Shown) is at r_B<r_D<r_C。

<math> <mrow> <msubsup> <mi>r</mi> <mi>S</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mi>B</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mi>&alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>M</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>r</mi> <mi>D</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mi></mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow> </math>

α＝π/2-φ (18)

By substituting the formula (16) into the formula (2), the compound

<math> <mrow> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>&GreaterEqual;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow> </math>

Similarly, by substituting the formula (17) into the formula (3), the compound

<math> <mrow> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mrow> <mn>4</mn> <mi>R</mi> </mrow> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>1</mn> </msub> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mrow> <mn>4</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mrow> <mn>4</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mn>2</mn> </msup> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>&le;</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow> </math>

Order to <math> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>&alpha;</mi> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <msub> <mi>V</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>

In order to satisfy equations (19) and (20), the minimum turning radius of the long machine is:

if sin α>v_min/V_LThen R is_min＝R₂；

Otherwise R_min＝max(R₁,R₂)。

When in use(center of turning is shown as O in FIG. 5)₂Shown) is at r_B<r_C<r_DWhen the solving step and the sum of the results l is 2l₂The situation is the same, namely the minimum turning radius of the long machine is as follows:

if sin α>v_min/V_LThen R is_min＝R₂；

Otherwise R_min＝max(R₁,R₂)。

Wherein, <math> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mi>&alpha;</mi> <mo>+</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mi>&alpha;</mi> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>min</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>lV</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>lV</mi> <mi>L</mi> </msub> <msqrt> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <msup> <mi>sin</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> </msqrt> </mrow> <mrow> <msubsup> <mi>V</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>v</mi> <mi>max</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>

it should be noted thatIn the case of (1), the adjusted R_LMay appearThe current R is needed_LThe value is carried out againAdjustment of the case to obtain the final corrected R_LThe value is obtained.

And 3, determining the turning radius of each wing plane according to the adjusted turning radius of the long plane to generate a formation turning fairway. The turning radius of each wing plane is as follows:

<math> <mrow> <msubsup> <mi>r</mi> <mi>B</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mi>&alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>C</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>D</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow> </math>

in order to verify the effectiveness of the method in preventing collision during formation flight turning of the unmanned aerial vehicles, the following simulation experiment is carried out. The simulation tool adopts MATLAB/Simulink software. The formation adopts a diamond configuration shown in fig. 4, and all parameters take values: phi 75 deg., l 400m, l₁＝386m，l₂＝103m，^*v_max＝400m/s，^*v_min130 m/s. The long machine is arranged to turn at the coordinates (0m,0m), and the turning speed is kept V_L＝V₀＝200m/s²Centripetal acceleration a_L＝40m/s²Turning radius R_L1000 m. The relative maximum and minimum speeds v can be calculated_max＝367m/s、v_min＝142m/s。

From formula (1) the theoretical velocity V of a wing plane B can be calculated_BTheoretical speed V of 124m/s, wing plane C_CTheory of wing aircraft D at 204m/sTheoretical velocity V_D278 m/s. It can be seen that V_BThe speed limit is added into the formation control structure when the minimum speed limit is not met, then a simulation experiment is carried out, the experimental result is shown in fig. 6 and 7, and it can be seen from fig. 7 that the formation distance between the bureaucratic plane B and the long plane can not be maintained, and the formation structure is damaged.

By adopting the route limiting method of the invention, the calculation can be carried outThus correspond toThe situation of (2) is corrected.

Correcting the turning radius of the tractor to be R_min＝R₁1312m, the theoretical speed V of a wing B is calculated again_BTheoretical speed V of a wing plane C, 142m/s_CTheoretical speed V of 202m/s wing plane D_D259 m/s. The simulation experiment is carried out, the experimental result is shown in fig. 8 and fig. 9, and the comparison of fig. 7 and fig. 9 shows that the formation tracking error is reduced after the turning radius of the long crane is limited, the damage of the formation structure is avoided, and the collision prevention problem during the formation turning is solved on the aeronautical route planning.

It should be understood that equivalents and modifications of the technical solution and inventive concept thereof may occur to those skilled in the art, and all such modifications and alterations should fall within the scope of the appended claims.

Claims (6)

1. The unmanned aerial vehicle formation flight turning collision prevention control method is characterized by comprising the following steps: the method is realized by the following steps:

step 1, calculating the maneuvering performance limits of the unmanned aerial vehicle, namely the relative maximum speed and the relative minimum speed; an overshoot sigma is set to obtain the following formula,

<math> <mrow> <mfrac> <mrow> <msub> <mi>v</mi> <mi>min</mi> </msub> <mo>-</mo> <msub> <mo>*</mo> <msub> <mi>v</mi> <mi>min</mi> </msub> </msub> </mrow> <mrow> <msub> <mi>V</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>V</mi> <mi>min</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mi>&sigma;</mi> <mo>,</mo> <mfrac> <mrow> <msub> <mo>*</mo> <msub> <mi>v</mi> <mi>max</mi> </msub> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>max</mi> </msub> </mrow> <mrow> <msub> <mi>v</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>V</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mi>&sigma;</mi> <mo>;</mo> </mrow> </math>

in the formula,is the actual minimum and maximum velocity, v_min、v_maxIs the relative minimum and maximum speed, V₀Is the flight speed of the formation before entering a turn;

step 2, combining the formation, calculating the maximum and minimum wing plane turning radius when turning, and adjusting the turning radius of the long plane according to the relative maximum and minimum speed limits;

and 3, generating the turning radius of each wing plane through the change of the formation configuration position relationship according to the adjusted turning radius of the long plane to obtain the final formation turning fairway.

2. The unmanned aerial vehicle formation flight turning collision prevention control method according to claim 1, characterized in that: the formation in step 2 is set to four isomorphic unmanned planes, a is a captain, B, C, D is a bureaucratic, forming a bureaucratic-type diamond formation.

3. The unmanned aerial vehicle formation flight turning collision prevention control method according to claim 2, characterized in that: the formation of the rhombus formation of the bureaucratic plane type is divided into three configurations according to the distance relationship between the unmanned aerial vehicles, the distance between A and B is set as l, and the distance between B and D is set as 2l₁And the distance between A and C is 2l₂The three configurations are: rhomboid configuration I is l-2 l₂The diamond configuration II is I>2l₂A rhombus configuration III is<2l₂。

4. The unmanned aerial vehicle formation flight turning collision prevention control method according to any one of claims 1 to 3, characterized in that: in step 1, the actual speed control system is designed into an underdamping mode, and the overshoot is tracked, so that the overshoot with the sigma of 20% is introduced into the calculation of the actual maximum speed and the actual minimum speed to obtain the relative maximum speed and the relative minimum speed:

$\frac{v_{\min }-{*}_{v_{\min }}}{V_0-V_{\min }}=20\%,\frac{{*}_{v_{\max }}-v_{\max }}{v_{\max }-V_0}=20\%---\left(4\right).$

5. the unmanned aerial vehicle formation flight turning collision prevention control method according to claim 4, characterized in that: the specific method for adjusting the turning radius of the long crane in the step 2 comprises the following steps:

let R_L、V_LIs the turning radius and speed, r, of the longator L_B、V_BRadius of turning and speed, r, of a wing plane B_C、V_CRadius of turning and speed, r, of a wing plane C_D、V_DThe turning radius and the speed of the wing machines D, in order to guarantee the configuration of the formation unchanged, the following holds:

V_L/R_L＝V_B/r_B＝V_C/r_C＝V_D/r_D (1)

let the minimum turning radius in each wing plane be r_SCorresponding to a velocity V_S(ii) a Maximum turning radius r_MCorresponding to a velocity V_M(ii) a Then V_SMinimum velocity v to satisfy unmanned aerial vehicle_minLimitation, V_MMaximum speed v to satisfy unmanned aerial vehicle_maxThe number of the limits, that is,

V_S＝(V_L/R_L)r_S≥v_min (2)

V_M＝(V_L/R_L)r_M≤v_max (3)

according to the concrete three diamond configurations, firstly determining the corresponding minimum turning radius as r_SAnd a maximum turning radius of r_MThen substituting the obtained values into the expressions (2) and (3) to obtain the value of R_LSolving the inequality to obtain R satisfying the constraint condition_LAnd the minimum value of (3) is set as the turning radius of the tractor a after correction.

6. The unmanned aerial vehicle formation flight turning collision prevention control method according to claim 5, characterized in that: determining the turning radius of each wing plane according to the adjusted turning radius of the lead plane to obtain a final formation turning route, wherein the turning radius of each wing plane is as follows:

<math> <mrow> <msubsup> <mi>r</mi> <mi>B</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mi>&alpha;</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>C</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mrow> <mn>2</mn> <mi>l</mi> </mrow> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>4</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <msub> <mi>l</mi> <mn>2</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <msubsup> <mi>r</mi> <mi>D</mi> <mn>2</mn> </msubsup> <mo>=</mo> <msubsup> <mi>R</mi> <mi>L</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msup> <mi>l</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>L</mi> </msub> <mi>l</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mn>2</mn> <mi>&phi;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> </math>

in the formula, r_B、r_C、r_DThe turning radius of the wing-planes B, C, D, respectively, the angle between the wing-planes B, D and the long-plane a is 2 phi, alpha pi-2-phi.