CN115268474A - Underwater vehicle formation method based on improved Dubins curve - Google Patents
Underwater vehicle formation method based on improved Dubins curve Download PDFInfo
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Abstract
The invention relates to an underwater vehicle formation method based on an improved Dubins curve, which is characterized in that an underwater vehicle group enters water at the same time, then the cruising speed is achieved at the same acceleration and is kept until the underwater vehicle dives to a target horizontal plane, and the improved Dubins curve method is used for path planning, so that the purpose of cluster formation generation is finally achieved. By using the path planning method, all aircrafts can simultaneously reach the designated destination under the condition of not changing the speed, and the aim of formation generation is fulfilled. The method greatly reduces the requirement of monitoring and adjusting the speed of each underwater vehicle in the formation generation process of the underwater vehicle cluster, thereby greatly improving the formation generation efficiency of the underwater vehicles, and being widely applied to solving the actual problem of formation generation in engineering.
Description
Technical Field
The invention belongs to the field of formation generation of underwater vehicles, and relates to an underwater vehicle formation method based on an improved Dubins curve.
Background
The underwater autonomous vehicle has the advantages of high maneuverability, high stability and high endurance, and is widely applied to executing ocean tasks. With the increase of the demand of underwater exploration, single vehicles cannot meet the requirements of people in recent years, and therefore, the formation of underwater vehicles becomes a popular research direction.
With the development of science and technology, when autonomous underwater vehicles are generated in a team, the speed of the autonomous underwater vehicles needs to be adjusted at any time according to different destinations, so that the autonomous underwater vehicles can reach positions needing to be reached at the same time. However, in the case of an underwater vehicle, the speed adjustment range is limited, and the effect of ideal formation cannot be achieved by only considering the speed adjustment.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides the underwater vehicle formation method based on the improved Dubins curve, the speed is not required to be adjusted at any time, all vehicles can directly reach the cruising speed at the same time, and the path planning is carried out by improving the Dubins curve, so that the formation can achieve a more ideal effect.
Technical scheme
An underwater vehicle formation method based on an improved Dubins curve is characterized by comprising the following steps:
step 1: all underwater vehicles participating in formation enter water at the same time, and are accelerated to cruise speed v at the same speed direction and the same acceleration, so that the submerged tracks of all the underwater vehicles are equal in length and are positioned on the same plane;
and 2, step: the underwater vehicle is spirally descended at cruising speed v to a horizontal plane with the same height as a destination to be reached, and the length x of a flight path of the vehicle spirally descended along a cylinder is calculated 1 ；
And 3, step 3: the path planning of the aircraft is converted into the path planning on a two-dimensional plane so as to improve the Dubins curve for path planning, and the shortest track length X at the moment is calculated m And the longest track length X M ，
Step 3-1: taking an aircraft as a particle, transforming the particle to a two-dimensional plane, wherein the position of the particle is O (0, 0), and the target position is O e (x e ，y e ) The boundary position is x = -b, and the center of the minimum turning circle is recorded as O r (x r ，y e -r)；
Step 3-2: the absolute value of the difference between the center of the minimum turning circle and the abscissa of the position of the destination is as follows:
x＝x e -x r ，x≥0
step 3-3:
shortest track X m : when x is e When X is more than or equal to 0, the aircraft directly starts towards the destination and then drives in a straight line, and the shortest track X is obtained at the moment m Comprises the following steps:
longest track X M : when x is e +b≥x＞x e In time, the aircraft starts to move away from the destination first and then moves straight towards the destination, and the longest flight path X M Comprises the following steps:
and 4, step 4: calculating the coordinate of the center of the minimum turning circle, wherein the given track length is between the shortest track and the longest track, namely X m ≤X≤X M ：
Step 4-1: order to
With (x) r ，y r ) As the circle center, r is the minimum turning radius, and the track length X at the moment is calculated 2 ；
Step 4-2: and taking the difference between the given track length and the calculated track length as a judgment whether the requirement that the aircraft reaches the destination is met:
|X-X 2 |≤ε
wherein: epsilon is a given precision;
(x) when the requirement of step 4-2 is satisfied r ，y r ) Is the center coordinate of the minimum turning circle;
and 5: with a given initial position (x) 0 ，y 0 ，z 0 ) Position reached (x) e ，y e ，z e ) And the center coordinates (x) of the minimum turning circle r ，y r ，z r ) And obtaining a motion trail diagram of each underwater vehicle.
Step 2, calculating the flight path length x of the aircraft along the spiral descending of the cylinder 1 The method comprises the following steps:
wherein pitch angle of the vehicle
Number of turns of aircraft descending
r is the radius of the bottom surface of the cylinder, namely the minimum turning radius of the aircraft, and L is the screw pitch of the cylindrical spiral; the starting position of the aircraft is (x) 0 ，y 0 ，z 0 ) The destination position is (x) e ，y e ，z e )。
Advantageous effects
The invention provides an underwater vehicle formation method based on an improved Dubins curve, which enables underwater vehicles to enter water simultaneously, when the cruising speed is reached at the same speed, the underwater vehicles continue to dive to a target horizontal plane at the cruising speed, and then the improved Dubins curve is used for path planning, so that the purpose of formation generation is achieved. According to the invention, the speed is not required to be adjusted at any time, all aircrafts can directly reach the cruising speed at the same time, and by using the path planning method, all aircrafts can simultaneously reach corresponding positions under the condition of not changing the speed, so that formation is completed. Meanwhile, the method greatly improves the formation generation efficiency of the underwater vehicles, so that the method can be widely applied to solving the actual problem of formation generation in engineering.
Drawings
FIG. 1: flow chart
FIG. 2: three-dimensional track planning map
FIG. 3: shortest track map based on Dubins curve
FIG. 4: longest track map of improved Dubins curve
FIG. 5: fixed-length track chart for improving Dubins curve
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the technical scheme of the scheme is as follows: the underwater vehicles enter water simultaneously, when the cruising speed is reached at the same speed, the underwater vehicles continue to dive to a target horizontal plane at the cruising speed, and then the improved Dubins curve is used for path planning, so that the formation generation purpose is achieved, and the scheme mainly comprises five steps:
the method for forming and generating the underwater vehicle on the basis of the improved Dubins curve is characterized by comprising the following steps of:
step 1: accelerating all the underwater vehicles to a cruising speed v from the water entry point in the same speed direction and the same acceleration, wherein the lengths of the submerged tracks of all the underwater vehicles are equal and the submerged tracks are positioned on the same plane;
step 2: the underwater vehicle spirally descends to a horizontal plane with the same height as a destination to be reached, the underwater vehicle spirally descends at a cruising speed v, and the flight path length x of the vehicle spirally descending along the cylinder is calculated 1 ；
Step 2-1: calculating the pitch angle θ of the aircraft:
r is the radius of the bottom surface of the cylinder, i.e. the minimum turning radius of the aircraft;
step 2-2: calculating the number of descending turns of the aircraft:
l is the thread pitch of the cylindrical spiral; the starting position of the aircraft is (x) 0 ，y 0 ，z 0 ) The destination position is (x) e ，y e ，z e )。
Step 2-3: calculating the flight path length X of the aircraft for extending the spiral descending of the cylinder 1 ：
And step 3: when the aircraft reaches the same horizontal plane with the destination, the path planning of the aircraft is converted into the path planning on the two-dimensional plane, the path planning is carried out based on the Dubins curve at the moment, and the shortest track length X at the moment is calculated m And the longest track length X M ；
Step 3-1: assuming that the aircraft is a particle at this time, the particle is transformed to a two-dimensional plane, and the position is set to be O (0, 0), and the destination position is set to be O e (x e ，y e ) The boundary position is x = -b, and the center of the minimum turning circle is recorded as O r (x r ，y e -r)；
Step 3-2: the absolute value of the difference between the center of the minimum circle and the abscissa of the position of the destination is recorded as
x＝x e -x r It can be seen that x is not less than 0;
step 3-3: when x is e When X is more than or equal to 0, the aircraft can directly start towards the destination and then drive in a straight line, and the shortest track X is obtained m Comprises the following steps:
step 3-4: when x is e +b≥x＞x e It can be obtained that the aircraft starts in a direction away from the destination and then travels straight towards the destination, at which time the longest flight path X M Comprises the following steps:
and 4, step 4: solving the circle center coordinate of the minimum turning circle;
step 4-1: judging whether the length of the given track is between the shortest track and the longest track, namely X m ≤X≤X M If not, the problem is not solved;
step 4-2: order to
With (x) r ，y r ) As the circle center, r is the minimum turning radius, and the track length X at the moment is calculated 2 ；
Step 4-3: and (3) making a difference between the given track length and the calculated track length so as to judge whether the requirement of the aircraft for reaching the destination is met or not, namely:
|X-X 2 | ≦ ε (given precision)
Step 4-4: repeating the steps until the requirements are met;
and 4-5: solved for at this time (x) r ，y r ) Is the center coordinate of the minimum turning circle;
and 5: all the underwater vehicles in the underwater vehicle cluster can reach the designated position at the same time, and formation and generation of the underwater vehicles are finished.
The present embodiment utilizes python for simulation and all underwater vehicles are spiraled down from the point of entry into the water. Since the same cruising speed is initially reached with the same acceleration, the same level can be reached at the same time. By the method, all aircrafts can simultaneously reach cruising speed and the same horizontal plane without adjusting the speed at any time. And then planning the paths of the underwater vehicles on the same horizontal plane, thereby achieving the purpose of reaching the corresponding positions at the same time. The formation of underwater vehicle formation is completed, and fig. 1 is a schematic diagram of the whole path planning. Table 1 shows the initial position information and the destination position information of any aircraft in the formation.
TABLE 1
| AUV initial position coordinates | AUV destination location coordinates | Cruising speed |
| (0，0，0) | (105，94，40) | 20 |
Step 1: accelerating each underwater vehicle to cruise speed v =20 from the water entry point at the same speed direction and the same acceleration, wherein the submerged tracks of each underwater vehicle are equal in length and are located on the same plane z =40;
step 2: the underwater vehicle spirally descends to a horizontal plane with the same height as a destination to be reached, the underwater vehicle spirally descends at the cruising speed v =20, and the flight path length x of the vehicle spirally descending along the cylinder is calculated 1 ；
Step 2-1: calculating the pitch angle theta of the aircraft:
r is the radius of the bottom surface of the cylinder, namely the minimum turning radius of the aircraft; l is the thread pitch of the cylindrical spiral; the starting position of the aircraft is (x) 0 ，y 0 ，z 0 ) The destination position is (x) e ，y e ，z e )。
Step 2-2: calculating the number of descending turns of the aircraft:
step 2-3: calculating the flight path length X of the aircraft for extending the spiral descending of the cylinder 1 ：
The position information and the given track length of the known aircraft are shown in a table 2;
TABLE 2
| Initial position coordinates | Destination location coordinates | Given track | At the horizontal plane |
| (10，13，40) | (105，94，40) | 215.9 | Z＝40 |
And 3, step 3: the aircraft reaches the same horizontal plane with the destination, the path planning of the aircraft is converted into the path planning on the two-dimensional plane, and the two-dimensional plane is used for planning the path based on the Dubins curvePlanning the path, and calculating the shortest track length X at the moment m And the longest track length X M ；
Step 3-1: assuming that the aircraft at the moment is a particle, the particle is transformed to a two-dimensional plane, the position at the moment is recorded as O (10, 13), and the destination position is recorded as O e (105, 94), wherein the lower water boundary position is x = -80;
step 3-2: center O of minimum turning circle cut-in circle when calculating shortest path r1 (13.01, 12.59) and cutting out the center O of the circle r2 (103.67，93.49)；
Step 3-3: the absolute value of the difference between the center of the circle of the minimum circle and the abscissa of the position of the destination is x = x e -x r =1.33, it can be seen that x ≧ 0;
step 3-4: when X is more than or equal to 105 and more than or equal to 0, the aircraft can obtain the shortest track X, and the aircraft directly starts towards the destination and then drives linearly m As shown in fig. 2:
X m ＝126.42
step 3-5: calculating the center O of the minimum turning circle when calculating the longest path r1 ' (13.03, 15.58) and cutting out the center O of the circle r2 ’(-76.65，97.48)；
Step 3-6: in this case, the absolute value of the difference between the center of the circle of the minimum circle and the abscissa of the position of the destination is x = x e -x r =181.65, it can be seen that x ≧ 105;
step 3-6:185 is more than or equal to X and more than 105, the aircraft can start towards the direction far away from the destination and then drive towards the destination in a straight line, and the longest flight path X is obtained at the moment M As shown in fig. 3:
X M ＝319.03
and 4, step 4: solving the circle center coordinate of the minimum turning circle;
step 4-1: judging whether the length of the given track is between the shortest track and the longest track, namely X m ≤X≤X M If not, the problem is not solved;
step 4-2: order to
With (x) r ，y r ) As the circle center, r is the minimum turning radius, and the track length X at the moment is calculated 2 ；
Step 4-3: and (3) making a difference between the given track length and the calculated track length so as to judge whether the requirement of the aircraft for reaching the destination is met or not, namely:
|X-X 2 | ≦ ε =0.01 (given precision)
Step 4-4: repeating the steps until the requirements are met;
and 4-5: solved for at this time (x) r ，y r ) Cutting a circle center coordinate of the minimum turning circle;
and 5: path planning is performed according to the center of the solved minimum turning circle as shown in fig. 4;
and 6: all the underwater vehicles in the underwater vehicle cluster can reach the designated position at the same time, and formation of the underwater vehicles is finished;
according to the embodiment results, all aircrafts can simultaneously reach corresponding positions to complete formation generation under the condition of not changing the speed by using the path planning method. Meanwhile, the method greatly improves the formation generation efficiency of the underwater vehicles, so that the method can be widely applied to solving the actual problem of formation generation in engineering.
Claims (2)
1. An underwater vehicle formation method based on an improved Dubins curve is characterized by comprising the following steps:
step 1: all underwater vehicles participating in formation enter water at the same time, and are accelerated to cruise speed v at the same speed direction and the same acceleration, so that the submerged tracks of all the underwater vehicles are equal in length and are positioned on the same plane;
step 2: the underwater vehicle is spirally descended at cruising speed v to a horizontal plane with the same height as a destination to be reached, and the length x of a flight path of the vehicle spirally descended along a cylinder is calculated 1 ；
Step (ii) of3: converting the path planning of the aircraft into the path planning on a two-dimensional plane to improve the Dubins curve for path planning, and calculating the shortest track length X at the moment m And the longest track length X M ，
Step 3-1: taking an aircraft as a particle, transforming the particle to a two-dimensional plane, wherein the position of the particle is O (0, 0), and the target position is O e (x e ,y e ) The boundary position is x = -b, and the center of the minimum turning circle is recorded as O r (x r ,y e -r)；
Step 3-2: the absolute value of the difference between the center of the minimum turning circle and the abscissa of the position of the destination is as follows:
x＝x e -x r ，x≥0
step 3-3:
shortest track X m : when x is e When X is more than or equal to 0, the aircraft directly starts towards the destination and then drives in a straight line, and the shortest track X is obtained at the moment m Comprises the following steps:
longest track X M : when x is e +b≥x>x e In time, the aircraft starts to move away from the destination first and then moves straight towards the destination, and the longest flight path X M Comprises the following steps:
and 4, step 4: calculating the coordinate of the center of the minimum turning circle, wherein the given track length is between the shortest track and the longest track, namely X m ≤X≤X M ：
Step 4-1: order to
With (x) r ,y r ) As the circle center, r is the minimum turning radius, and the track length X at the moment is calculated 2 ；
Step 4-2: and taking the difference between the given track length and the calculated track length as a judgment whether the requirement of the aircraft for reaching the destination is met:
|X-X 2 |≤ε
wherein: epsilon is a given precision;
(x) when the requirement of step 4-2 is satisfied r ,y r ) Is the center coordinate of the minimum turning circle;
and 5: with a given initial position (x) 0 ,y 0 ,z 0 ) Position of arrival (x) e ,y e ,z e ) And the center coordinates (x) of the minimum turning circle r ,y r ,z r ) And obtaining a motion trail diagram of each underwater vehicle.
2. The improved Dubins curve based underwater vehicle formation method of claim 1, wherein: step 2, calculating the flight path length x of the aircraft along the spiral descending of the cylinder 1 Comprises the following steps:
wherein pitch angle of the vehicle
Number of turns of aircraft descending
r is the radius of the bottom surface of the cylinder, namely the minimum turning radius of the aircraft, and L is the screw pitch of the cylindrical spiral; the starting position of the aircraft is (x) 0 ,y 0 ,z 0 ) The destination position is (x) e ,y e ,z e )。
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117289722A (en) * | 2023-11-24 | 2023-12-26 | 西安现代控制技术研究所 | Directional hitting route planning method considering initial heading |
| CN117289722B (en) * | 2023-11-24 | 2024-05-14 | 西安现代控制技术研究所 | Directional hitting route planning method considering initial heading |
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- 2022-08-04 CN CN202210933642.1A patent/CN115268474A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117289722A (en) * | 2023-11-24 | 2023-12-26 | 西安现代控制技术研究所 | Directional hitting route planning method considering initial heading |
| CN117289722B (en) * | 2023-11-24 | 2024-05-14 | 西安现代控制技术研究所 | Directional hitting route planning method considering initial heading |
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