^{1}

^{2}

^{1}

^{1}

^{2}

^{1}

^{1}

^{1}

^{2}

In order to make multirotor unmanned aerial vehicles (UAV) compose a desired dense formation and improve the practicality of UAV formation, a distributed algorithm based on fuzzy logic was proposed. The airflow created by multirotor UAVs was analyzed according to the structure of the multirotor UAV and the characteristic equation of the fluid. This paper presented a dynamic model for the process of formation of and path search algorithm based on this model. The membership function in this model combines the factors of position, flow field, and movement. Integrating the dynamic model and its desired position in formations, each UAV evaluates the surrounding points and then selects the direction for step motion. Through simulation, this algorithm was improved by a by-step formation approach, and the effectiveness of this method in dense formation of multirotor UAVs was proved.

The improvement of communication abilities and the distributed systems have led researchers to pay increasing attention to multiagent systems [

However, research on distributed control drones is often used in fixed-wing drones to study how to make the formation well maintained in high-speed movement and achieve rapid convergence after avoiding obstacles [

Unlike fixed-wing drones and other intelligent robots, multirotor drones rely on the rotation of rotors to generate power, which will generate powerful airflow. Especially for drones those weights are not so light; strong airflow will be generated, affecting the flight safety of other drones. In applications, the space between drones is maintained at a sufficiently large safe distance. And if we want to reduce the spacing as much as possible, it is necessary to consider the effect of flow field according to the characteristics of the UAV. In addition, the improvement of control technology provides technical support for further narrowing the safety distance, while reducing the distance between drones can enhance the performance of UAV formations. Therefore, the impact of airflow determines the minimum distance when carrying out dense formation.

Although the centralized control of the UAV can easily achieve the collaborative flight, however, in practice, there are many limitations in this way. Without the control of the base station, UAVs will lose control. The route must be planned in advance and cannot be controlled in real time. And, with the increase in the number of drones, as well as the increase in algorithm speed and computational complexity, control bottlenecks will be encountered.

Distributed control can get rid of these restrictions in application and make multirotor UAVs into true intelligent agents. In recent years, the intelligent agent system based on distributed control has been rapidly developed. Various types of robot formation technology had gradually improved [

The multirotor UAV has the characteristic of simple and flexible control and high degree of freedom of movement, making it similar to the intelligent robot [

Regarding problems mentioned above, this paper analyzed the characteristics of flow field of multi-rotor UAVs. According to the characteristics of multirotor UAV, designed membership functions in fuzzy logic, and a distributed formation algorithm were proposed. The remainder of this paper is organized as follows: the influence of multirotor UAV flow field is introduced in Section

CFD (Computational Fluid Dynamics) simulation is a common method of analyzing flow fields. Using finite element analysis method; the continuous fluids is discretized. This method first uses the fluid conservation equation to describe the discrete fluids mathematically, forming a large algebraic equation group, and then choose the transport equation to close the system of equations and calculate it on a computer [

where

This paper selects the S-A model; the transport equation is a function of the turbulent kinetic energy

where

Take the model in Figure

Model of multirotor UAV selected for analysis.

where R is the radius of the rotor and

By pressure equivalent replacement method, we can get the flow field when hovering, as shown in Figure

Flow field of multirotor UAV when hovering.

When flying, multirotor UAV pitch angle changes coupling. The component of lift in the horizontal direction is equal to the air resistance. The air resistance received is the integral of air pressure on the surface of the drone. Through the simulation, we can get pitch angles at different flight speeds.

where

In this way, we can get the flow field of UAV when moving, as shown in Figure

Flow field of multirotor UAV when moving.

It can be seen from the simulation results that, in the horizontal direction, the disturbed area is approximately circular due to the symmetrical shape of the multirotor UAV structure. The radius of the disturbed area is slightly larger than the drone radius. In the vertical direction, the disturbed area of the flow field is mainly located below the UAV. Overall, the area is approximately cylindrical. The intensity of interference decreases with the distance to the UAV increase. The tilt of the cylindrical air flow is opposite to that of the drone’s movement, approximately perpendicular to the plane of the fuselage. Due to the speed limitation when carrying out dense formation, the tilt angle is generally not greater than 10 degrees. In addition, the drone itself has a certain degree of ability to resist wind, and it can resist the interference of airflow with a certain intensity. Therefore, the airflow generated by a multirotor UAV primarily affects the area below it; the direction is slightly inclined according to the direction of flight. And the horizontal spacing can be significantly less than the vertical spacing.

According to the needs of distributed formations, this paper adopts a behavior-based control approach. Each drone performs calculations based on the information it receives and chooses behaviors.

This article uses a point-based formation method, that means, all drones have the same set of global coordinates. And in a dynamic environment, the three-dimensional coordinates of the drone can be provided with high-precision GPS. Taking into account multiple drones, point-to-point communication expense is too large. So we can use the blackboard to achieve communication. Drones broadcast their own coordinates and speeds, providing reference for other drones. With its own coordinates, these can be set as input to the formation control system.

The multirotor UAV can move to all directions because of its control features. The output can be set to the step motion in one of the directions to neighbor point.

In a dynamic environment, the drones have different motion states. Therefore, it is necessary to introduce fuzzy concepts to express this uncertainty [

where

Membership function of two-dimensional stationary object.

For moving objects, the membership function should include the speed of motion. The membership function can be set to the following form:

This formula introducing function

where a is

Membership function of two-dimensional moving object.

Refer to the two-dimensional membership function; the membership function in three-dimensional space is a function of the points in space. According to the above analysis, the membership function when the multi-rotor drone hovering should have the following characteristics:

So the membership function can be set to

where

Membership function of multirotor UAV when hovering in three-dimensions.

The graph represents the value of the function by color and evenly selects the slice for observation. As can be seen in the figure, the value of the membership function can express the degree of threat posed by the drone and the flow field approximately.

For a moving drone, the area affected by the flow field will be skewed. According to geometric relations, the membership function can be set to

where

Membership function of multirotor UAV when moving in three-dimensions.

With reference to the two-dimensional membership function, the attenuation of the function in the direction of motion can be reduced, and this can optimize the dynamic characteristics of the model. We can also introduce the function

The function image is shown in Figure

Membership function of multirotor UAV when moving in three-dimensions after adding speed effect.

Through improvement, the value of the region where the membership function takes a large value shifts toward the direction of speed, reflecting the prediction of the next moment.

In addition, in order to let the drone move to its own position in the formation, target location needs to attract its drone. The closer the distance to the target is, the more favorable it will be to form a formation. Set function

In the formula, (

The local search method is used in this paper. Each drone selects the direction of movement only by analyzing the conditions in its surrounding area. The analysis of the surrounding environment has mainly two aspects: the likelihood of a collision and whether it is conducive to achieving desired formation. After considering these two factors find the point with the highest evaluation around and move to this point. In this article, the evaluation function is set to:

where A and B are a constant and the value is positive;

The method in this article belongs to distributed control and program flow chart is shown in Figure

Algorithm flowchart.

In this paper, we set the triangular formation as the desired formation. Set the initial position of the UAV randomly and then carry out the formation. We repeat 50 tests and statistical simulation results. Table

Simulation result statistics.

| | |
---|---|---|

| 82% | 114 |

| 80% | 137 |

| 56% | 139 |

From the simulation results and process, it is found that when the number of drones is small, the success rate is high. But when the number of drones increases, success rate is not high and often falls into a local minimum due to the limitation of local information. Since the range of membership functions is larger than the real size of the drone, when the formation is dense, each drone is limited by local information, and sometimes it is difficult to bypass the area affected by other drones, resulting in a local minimum point.

For ease of analysis, we define the cost function

Figures

The cost function graph when falling into a local minimum.

Simulation results when falling into a local minimum.

In order to solve the problem of low success rate caused by local minimum, the by-step formation can be used, first to form the formation with the same structure, but a larger spacing between each other. As the membership function area remains the same, relatively sparse formations make formation easier. But at the same time, too large spacing will increase the range of the entire drone group, which will cause difficulties for communication, and it will also increase the time for the formation to complete. Based on the above factors, when the distance is set to 2 to 3 times the minimum distance, the formation is well achieved. After that, reduce spacing to complete the desired dense formation.

One of the simulation results is shown in Figures

Simulation result statistics using by-step formation.

| | |
---|---|---|

| 92% | 133 |

| 90% | 135 |

| 86% | 156 |

The cost function graph using by-step formation.

Simulation results using by-step formation.

This article designed a position-based formation method in dynamic environment and added the factor of speed. This method uses distributed control, using local search to reduce the computational complexity and taking into account the movement in three-dimensional space, collision avoidance, and the influence of the flow field. Through the above methods, dense formations of multirotor UAVs can be achieved with a high success rate. And the process of the formation meets the common sense.

At the same time, the parameters in this algorithm are difficult to set, especially when the number of drones changes; the optimal parameter settings in the algorithm will also change. In addition, further increasing the success rate of the formation requires the addition of more advanced sensing equipment and faster computing equipment. Therefore, the future work can find the optimal parameters autonomously through related methods such as machine learning and enhanced learning and try to sense more information to improve the performance of the formation.

No data were used to support this study.

The author declares that there are no conflicts of interest regarding the publication of this paper.

This work is supported by the National Natural Science Foundation of China (Grants nos. 41775039, 41775165, and 91544230).