# 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

## References

- Reynolds, A.; Mclvor, G. Stochastic modeling of bird flocks: Accounting for the cohesiveness of collective motion. J. R. Soc. Interface
**2022**, 19, 20210745. [Google Scholar] [CrossRef] - Papadopoulou, M.; Hildenbrandt, H. Emergence of splits and collective turns in pigeon flocs under predation. R. Soc. Open Sci.
**2022**, 9, 211898. [Google Scholar] [CrossRef] [PubMed] - Susumu, I.; Nariya, U. Emergence of a giant rotating cluster of fish in three dimensions by local interactions. J. Phys. Soc. Jpn.
**2022**, 91, 064806. [Google Scholar] - Costanzo, A.; Hildenbrandt, H. Causes of variation of darkness in flocks of starlings, a computational model. Swarm Intell.
**2022**, 16, 91–105. [Google Scholar] [CrossRef] - Hemelrijk, C.; Zuidam, L. What underlies waves of agitation in starling flocks. Behav. Ecol. Sociobiol.
**2015**, 69, 755–764. [Google Scholar] [CrossRef] [PubMed][Green Version] - Reynolds, C. Flocks, herds and schools: A distributed behavioral model. Comput. Graph.
**1987**, 21, 25–34. [Google Scholar] [CrossRef][Green Version] - Vicsek, T.; Czirok, A. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett.
**1995**, 75, 1226–1229. [Google Scholar] [CrossRef] [PubMed][Green Version] - Couzin, I.; Krause, J. Collective memory and spatial sorting in animal groups. J. Theor. Biol.
**2002**, 218, 1–11. [Google Scholar] [CrossRef][Green Version] - Olfati-Saber, R. Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Trans. Autom. Control.
**2006**, 51, 401–420. [Google Scholar] [CrossRef][Green Version] - Tanner, H.G.; Jadbabaie, F. Flocking in fixed and switch networks. IEEE Trans. Autom. Control.
**2007**, 52, 863–868. [Google Scholar] [CrossRef] - Duan, H.; Qiao, P. Pigeon-inspired optimization a new swarm intelligence optimizer for air robot path planning. Int. J. Intell. Comput. Cybern.
**2014**, 7, 24–37. [Google Scholar] [CrossRef] - Zhang, X.; Xia, S. Quantum behavior-based enhanced fruit fly optimization algorithm with application to UAV path planning. Int. J. Comput. Intell. Syst.
**2020**, 13, 1315–1331. [Google Scholar] [CrossRef] - Zhou, Z.; Duan, H. Unmanned aerial vehicle close formation control based on the behavior mechanism in wild geese. Sci. Sin. Technol.
**2017**, 47, 230–238. [Google Scholar] [CrossRef] - Xie, R.; Gu, C. A starling swarm coordination algorithm. Wuhan Univ. (Nat. Sci. Ed.)
**2019**, 65, 229–237. [Google Scholar] - Grammatikis, P.; Sarigianndis, P. A compilation of UAV applications for precision agriculture. Comput. Netw.
**2020**, 172, 107148. [Google Scholar] [CrossRef] - Liu, W.; Zhang, T. A hybrid optimization framework for UAV reconnaissance mission planning. Comput. Ind. Eng.
**2022**, 173, 108653. [Google Scholar] [CrossRef] - Pei, J.; Chen, H. UAV-assisted connectivity enhancement algorithms for multiple isolated sensor networks in agricultural Internet of things. Comput. Netw.
**2022**, 207, 108854. [Google Scholar] [CrossRef] - Shi, Y.; Liu, Y. Multi-UAV cooperative reconnaissance mission planning novel method under multi-radar detection. Sci. Prog.
**2022**, 105, 1–20. [Google Scholar] [CrossRef] [PubMed] - He, Z.; Liu, C. Dynamic anti-collision A-star algorithm for multi-ship encounter situations. Appl. Ocean. Res.
**2022**, 118, 102995. [Google Scholar] [CrossRef] - Wu, Y.; Gou, J. A new consensus theory-based method for formation and obstacle avoidance of UAVs. Aerosp. Sci. Technol.
**2020**, 107, 106332. [Google Scholar] [CrossRef] - Tian, S.; Li, Y. Multi-robot path planning in wireless sensor networks based on jump mechanism PSO and safety gap obstacle avoidance. Future Gener. Comput. Syst.
**2021**, 118, 37–47. [Google Scholar] [CrossRef] - Vargas, S.; Becerra, H. MPC-based distributed formation control of multiple quadcopters with obstacle avoidance and connectivity maintenance. Control. Eng. Pract.
**2022**, 121, 105054. [Google Scholar] [CrossRef] - Zhang, X.; Duan, H. Altitude consensus-based 3D flocking control for fixed-wing unmanned aerial vehicle swarm trajectory tracking. Proc. Inst. Mech.Eng. Part G J. Aerosp. Eng.
**2016**, 230, 2628–2638. [Google Scholar] [CrossRef] - Qi, J.; Guo, J. Formation tracking and obstacle avoidance for multi quadrotors with static and dynamic obstacles. IEEE Robot. Autom. Lett.
**2022**, 7, 1713–1722. [Google Scholar] [CrossRef] - Wu, J.; Wang, H. Learning-based fixed-wing UAV reactive maneuver control for obstacle avoidance. Aerosp. Sci. Technol.
**2022**, 316, 107623. [Google Scholar] [CrossRef] - Liu, X.; Yan, C. Towards flocking navigation and obstacle avoidance for multi-UAV systems through hierarchical weighting Vicsek model. Aerospace
**2021**, 8, 286. [Google Scholar] [CrossRef] - Fu, X.; Pan, J. A formation maintenance and reconstruction method of UAV swarm based on distributed control. Aerosp. Sci. Technol.
**2020**, 104, 105981. [Google Scholar] [CrossRef] - Lim, J.; Pyo, S.; Kim, N.; Lee, J.; Lee, J. Obstacle magnification for 2-D collision and occlusion avoidance autonomous multirotor aerial vehicles. IEEE/ASME Trans. Mechatron.
**2020**, 25, 2428–2436. [Google Scholar] [CrossRef] - Hemelrijk, C.; Hildenbrant, H. Diffusion and topological neighbors in flocks of starlings: Relating a model to empirical data. PLoS ONE
**2015**, 10, e0126913. [Google Scholar] [CrossRef] [PubMed] - Ballerini, M.; Cabibbo, N. Empirical investigation of starling flocks: A benchmark study in collective animal behavior. Anim. Behav.
**2008**, 76, 201–215. [Google Scholar] [CrossRef] - Carere, C.; Montanino, S. Aerial flocking patterns of wintering starlings, Sturnus vulgaris, under different predation risk. Anim. Behav.
**2009**, 77, 101–107. [Google Scholar] [CrossRef] - Procaccini, A.; Orlandi, A. Propagating waves in starling, Sturnus vulgaris, flocks under predation. Anim. Behav.
**2011**, 82, 759–765. [Google Scholar] [CrossRef] - Hogan, B.; Hidenbrandt, H. The confusion effect when attacking simulated three-dimensional starling flocks. R. Soc. Open Sci.
**2017**, 4, 160564. [Google Scholar] [CrossRef] [PubMed][Green Version] - Brown, J.; Bossomaier, T. Information transfer in finite flocks with topological interactions. J. Comput. Sci.
**2021**, 53, 101370. [Google Scholar] [CrossRef] - Zamani, H.; Nadimi-Sharaki, M. Starling murmuration optimizer: A novel bio-inspired algorithm for global and engineering. Computer Methods in Applied Mechanics and Engineering.
**2022**, 392, 114616. [Google Scholar] [CrossRef] - Storms, R.; Carere, C. Complex patterns of collective escape in starling flocks under predation. Behav. Ecol. Sociobiol.
**2019**, 73, 10. [Google Scholar] [CrossRef][Green Version] - Olcay, E.; Schuhmann, F. Collective navigation of a multi-robot system in an unknown environment. Robot. Auton. Syst.
**2020**, 132, 103604. [Google Scholar] [CrossRef] - Yu, Y.; Duan, H. Turning control multiple UAVs imitating the super-maneuver behavior in massive starling. Robot
**2020**, 42, 385–393. [Google Scholar] - Lei, X.; Liu, M. Fission control algorithm for swarm based on local following interaction. Control. Decis.
**2013**, 28, 741–746. [Google Scholar] - Nagy, M.; Ákos, Z.; Biro, D.; Vicsek, T. Hierarchical group dynamic in pigeon flocks. Nature
**2010**, 464, 890–893. [Google Scholar] [CrossRef][Green Version] - Vásárhelyi, G.; Virágh, C. Optimized flocking of autonomous drone in confined environments. Sci. Robot.
**2018**, 3, 3536–3550. [Google Scholar] [CrossRef] [PubMed]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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