# Starling-Behavior-Inspired Flocking Control of Fixed-Wing Unmanned Aerial Vehicle Swarm in Complex Environments with Dynamic Obstacles

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model of Starling Behavior

#### 2.1. The Behavioral Mechanism of Starlings

#### 2.2. Bevioral Patterns Based on Bevioral Mechanisms of Starlings

#### 2.2.1. Collective Pattern

#### 2.2.2. Evasion Pattern

#### 2.2.3. Local-Following Pattern

## 3. Starling-Behavior-Inspired Flocking Control for UAV Swarm

#### 3.1. Model of UAV

^{2}is the gravitational acceleration. Due to constrains of velocity, the fixed-wing UAV cannot hover or fly backwards.

#### 3.2. Collision Prediction Mechanism

#### 3.3. Mapping of the Intelligent Behavioral Patterns of Starlings

Algorithm 1. Starling-behavior-inspired flocking control algorithm for UAVs |

/*Initialization*/ Set initial parameters of the proposed algorithm and the model of fixed-wing UAV Generate the position ${x}_{i},{y}_{i},{h}_{i},\text{}\mathrm{heading}\text{}\mathrm{angle}\text{}{\psi}_{i}\text{}\mathrm{and}\text{}\mathrm{velocity}\text{}{V}_{i},\text{}{\dot{h}}_{i}$ of UAV i randomly /*Begin*/ for i = 1 to nfor j = 1 to nSelect neighbors according to Equation (1) if UAV j is the neighbor of UAV iUAV i interact with UAV j according to Equation (21) $\mathrm{Calculate}\text{}{C}_{ij}$ according to Equation (9) end if$\mathrm{Calculate}\text{}{\phi}_{i}$ according to Equation (12) $\mathrm{Find}\text{}\mathrm{the}\text{}\mathrm{local}\text{}\mathrm{leader}\text{}{l}_{i}$ according to Equations (10) and (11) end for$\mathrm{Calculate}\text{}{R}_{i}^{obs}$ to Equation (16) $\mathbf{if}\text{}{R}_{d}\le {R}_{i}^{obs}$ Execute collision prediction according to Equation (17) $\mathbf{if}\text{}\phi -\mathsf{\Delta}\phi \le {\theta}_{i}\le \phi +\mathsf{\Delta}\phi $ $\mathrm{Set}\text{}\mathrm{parameter}\text{}\gamma =1$ Calculate the control signal of evasion pattern of UAV i according to Equation (22) end ifif there exist a local leader l_{i}Set parameter β = 0 UAV i follows the local leader according to Equation (21) end ifend ifFollow the virtual leader according to Equation (23) /*Limitation*/ Set limitations according to Equation (15) Update the position ${\mathit{q}}_{i}$ and velocity ${\mathit{p}}_{i}$ according to Equations (24) and (25) end for |

#### 3.4. Conversion of Patterns

## 4. Simulation Results and Analysis

#### 4.1. Performance Metrics

- (1)
- Order parameter: it captures the coordination of the motion of the UAV swarm and represents the velocity alignment degree of all UAVs in the swarm.$$\mathsf{\Phi}=\frac{1}{n(n-1)}{\displaystyle \sum _{i,j\ne 1}\frac{{\mathit{v}}_{i}\cdot {\mathit{v}}_{j}}{\Vert {\mathit{v}}_{i}\Vert \Vert {\mathit{v}}_{j}\Vert}}$$
- (2)
- Safety metrics: it measures the risk of collision between the UAV swarm and obstacles and assesses the ability of the UAV swarm to avoid collisions with the obstacles.$${\mathsf{\Phi}}_{s}=1-\frac{{n}_{obs}}{n}$$
- (3)
- Tracking error: it evaluates the tracking performance of the UAV swarm. The tracking error of position is error between the position of UAV swarm and virtual leader, which can be described as follows:$$\begin{array}{l}{e}_{\mathit{q}}=\Vert \langle \mathit{q}\rangle -{\mathit{q}}_{L}\Vert \\ \langle \mathit{q}\rangle =\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{\mathit{q}}_{i}}\end{array}$$The tracking error of altitude is error between the altitude of UAV swarm and virtual leader, which can be described as follows:$$\begin{array}{l}{e}_{h}=\Vert \langle h\rangle -{h}_{L}\Vert \\ \langle h\rangle =\frac{1}{N}{\displaystyle \sum _{i=1}^{N}{h}_{i}}\end{array}$$

#### 4.2. Simulation in Obstacle-Dense Environment

#### 4.3. Simulation in Dynamic Threat Environment

#### 4.4. Simulation in Obstacle Environment with Static and Dynamic Obstacles

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**A flock of starlings in the sky [35] copyright: 5434760037420.

**Figure 2.**Schemes follow the same formatting [5] copyright: © 2015, The Author(s).

**Figure 4.**Schematic of the neighbor set, the red marker represents the individual i and pink markers represent neighbors of individual i.

**Figure 5.**Diagram of the threat. (

**a**) is in x-y plane, while (

**b**) is in the 3D space, the dark grey circled area represents the real obstacle while the radius of the light grey circle area is the expected distance from individual i to the center of obstacle. The red arrows in (

**b**) represent the motion direction of the individual i.

**Figure 6.**Schematic of the selection of local leader, the red marker represents the individual i and pink markers represent neighbors of individual i.

**Figure 7.**The collision prediction between the UAV and obstacle. (

**a**) is in the 3D space, while (

**b**) is in the x-y plane, the red marker represents the individual I, the virtual points A and B are the edge points of scope of the obstacle, $\overline{UA},\overline{US}$ and $\overline{SA}$ represent the length of line segment UA, US and SA, respectively.

**Figure 10.**Flight paths in obstacle-dense environment. (

**a**,

**c**) are trajectories using the proposed algorithm in 3D space and x-y plane. (

**b**,

**d**) are trajectories using the basic flocking algorithm in 3D space and x-y plane.

**Figure 11.**The time–response curves of velocity, heading angle, altitude for each UAV and virtual leader in obstacle-dense environment. (

**a**,

**c**,

**e**) are the results using the proposed algorithm; (

**b**,

**d**,

**f**) are the results using the basic flocking algorithm.

**Figure 12.**The order parameter curves of UAV swarm in obstacle-dense environment. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using the basic flocking algorithm.

**Figure 13.**Tracking errors of position and altitude curves in obstacle-dense environment. (

**a**,

**c**) are tracking error curves using the proposed algorithm while (

**b**,

**d**) are tracking error curves using the basic flocking algorithm.

**Figure 14.**The safety parameter curves of the UAV swarm in obstacle-dense environment. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using basic flocking algorithm.

**Figure 15.**Curves of minimum distances between obstacles and each UAV in obstacle-dense environment. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using the basic flocking algorithm.

**Figure 16.**Snapshots of the motion of the UAV swarm and dynamic threat at t = 0 s, t = 12 s, t = 15 s, t = 18 s. (

**a**,

**c**) are the results using the proposed algorithm, while (

**c**,

**d**) are the results using the basic algorithm. (

**a**,

**b**) are in the 3D space while (

**c**,

**d**) are in the horizontal plane.

**Figure 17.**The time–response curves of velocity, heading angle, altitude for each UAV and virtual leader in dynamic threat environment. (

**a**,

**c**,

**e**) are the results using the proposed algorithm; (

**b**,

**d**,

**f**) are the results using the basic flocking algorithm.

**Figure 18.**The order parameter curves of UAV swarm in dynamic threat environment. (

**a**) is the result using the proposed algorithm; (

**b**) is the result of using the basic flocking algorithm.

**Figure 19.**Tracking errors of position and altitude curves in dynamic threat environment. (

**a**,

**c**) are tracking error curves using the proposed algorithm, while (

**b**,

**d**) are tracking error curves using the basic flocking algorithm.

**Figure 20.**The safety parameter curves of the UAV swarm in dynamic threat environment. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using basic flocking algorithm.

**Figure 21.**Curves of minimum distances between dynamic threat and each UAV in the UAV swarm. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using basic flocking algorithm.

**Figure 22.**Flight paths in obstacle environment with static and dynamic obstacles. (

**a**,

**c**) are trajectories using the proposed algorithm in 3D space and x-y plane. (

**b**,

**d**) are trajectories using the basic flocking algorithm in 3D space and x-y plane.

**Figure 23.**The time–response curves of velocity, heading angle, altitude for each UAV and virtual leader in obstacle environment with static and dynamic obstacles. (

**a**,

**c**,

**e**) are the results using the proposed algorithm; (

**b,d**,

**f**) are the results using the basic flocking algorithm.

**Figure 24.**The order parameter curves of UAV swarm in obstacle environment with static and dynamic obstacles. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using the basic flocking algorithm.

**Figure 25.**Tracking errors of position and altitude curves in obstacle environment with static and dynamic obstacles. (

**a**,

**c**) are tracking error curves using the proposed algorithm, while (

**b**,

**d**) are tracking error curves using the basic flocking algorithm.

**Figure 26.**The safety parameter curves of the UAV swarm in obstacle environment with static and dynamic obstacles. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using basic flocking algorithm.

**Figure 27.**Curves of minimum distances between obstacles and each UAV in obstacle environment with static and dynamic obstacles. (

**a**) is the result using the proposed algorithm; (

**b**) is the result using the basic flocking algorithm.

Parameter | Value |
---|---|

Sensing range, R | 15 m |

Desired distance between neighboring UAVs, d | 5 m |

Desired distance between UAV and obstacle, ${R}_{d}$ | 15 m |

Coefficient for the selection of local leader, $\alpha $ | 2.5 |

Control gains of local-following pattern, ${c}_{1},{c}_{2}$ | 0.5, 2 |

Step-size, $\mathsf{\Delta}t$ | 0.025 s |

Control gains of collective pattern, ${c}_{3},{c}_{4}$ | 1, 4 |

Control gains of evasion pattern, ${c}_{5}$ | 1 |

Control gains of virtual leader-follower, ${c}_{6},{c}_{7}$ | 1, 2 |

Parameter | Value |
---|---|

Velocity time constant, ${\tau}_{v}$ | 5 |

Heading angle time constant, ${\tau}_{\psi}$ | 0.75 |

Altitude time constant, ${\tau}_{\dot{h}},{\tau}_{h}$ | 0.3, 1 |

Minimum and maximum velocity, ${v}_{\mathrm{min}},{v}_{\mathrm{max}}$ | 5 m/s, 15 m/s |

Maximum lateral overload, ${n}_{\mathrm{max}}$ | 5 g |

Maximum climbing and gliding velocity, ${\lambda}_{\mathrm{climb}},{\lambda}_{\mathrm{glide}}$ | −5 m/s, 5 m/s |

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**MDPI and ACS Style**

Wu, W.; Zhang, X.; Miao, Y.
Starling-Behavior-Inspired Flocking Control of Fixed-Wing Unmanned Aerial Vehicle Swarm in Complex Environments with Dynamic Obstacles. *Biomimetics* **2022**, *7*, 214.
https://doi.org/10.3390/biomimetics7040214

**AMA Style**

Wu W, Zhang X, Miao Y.
Starling-Behavior-Inspired Flocking Control of Fixed-Wing Unmanned Aerial Vehicle Swarm in Complex Environments with Dynamic Obstacles. *Biomimetics*. 2022; 7(4):214.
https://doi.org/10.3390/biomimetics7040214

**Chicago/Turabian Style**

Wu, Weihuan, Xiangyin Zhang, and Yang Miao.
2022. "Starling-Behavior-Inspired Flocking Control of Fixed-Wing Unmanned Aerial Vehicle Swarm in Complex Environments with Dynamic Obstacles" *Biomimetics* 7, no. 4: 214.
https://doi.org/10.3390/biomimetics7040214