# A Self-Organized Reciprocal Decision Approach for Sensing Coverage with Multi-UAV Swarms

^{*}

## Abstract

**:**

^{3}-size UAVs, the proposed method has excellent scalability and collision-avoiding ability.

## 1. Introduction

^{3}-size UAVs, the proposed method is found to have excellent scalability and collision-avoiding ability. And a Robotic Operation System (ROS) Simulation is conducted to validate the proposed method.

## 2. Basic Idea

## 3. Reciprocal Decision Approach

#### 3.1. Two-UAV Cooperative Coverage

**Definition**

**1.**

#### 3.2. Multi-UAV Swarm Coverage

#### 3.3. Collision-Free Constrains

#### 3.3.1. Collision Avoidance between UAVs

**Corollary**

**1.**

**Proof.**

#### 3.3.2. Avoiding Collision with Obstacles

#### Static Obstacle

#### Dynamic Obstacle

## 4. Optimal Velocity Decision

#### 4.1. Random Probability Method

**Corollary**

**2.**

**Proof.**

#### 4.2. Optimum Available

Algorithm 1. Random Probability Exploration of the Optimal Velocity ${v}_{A}^{opt}$. |

Input: UAV $A$ maximal velocity ${v}_{A}^{\mathrm{max}}$, constrains of neighbor UAVs $ORC{V}_{A|*}^{\tau}$ Output: The optimal velocity decision ${v}_{A}^{opt}$ 1: Computational Rectangle Domain: $RandVelRange=Square(\Vert {v}_{A}^{\mathrm{max}}\Vert )$ 2: Random Velocity: ${v}_{rand}=RV(RandVelRange)$ 3: Set the Accuracy: $AN=1000$ 4: Initialization: $N=1$, $FN=0$, $FD=\mathsf{\Phi}$ 5: while $N\le AN$ do 6: if $\Vert {v}_{rand}\Vert \le \Vert {v}_{A}^{\mathrm{max}}\Vert $ then 7: if ${v}_{rand}\subset ORC{V}_{A|*}^{\tau}$ then 8: ${v}_{rand}\to FD$ 9: $FN=FN+1$ 10: end if 11: end if 12: $N=N+1$ 13: end while 14: Output ${v}_{A}^{opt}=AVE(FD)$ $\u22b3$ The optimal velocity has been explored. 15: return. |

#### 4.3. Vacant Optimal Velocity Space

Algorithm 2. Lounger strategy. |

Input: UAV A maximal velocity ${v}_{A}^{\mathrm{max}}$, constrains of neighbor UAVs $ORC{V}_{A|*}^{\tau}$ Output: The optimal velocity decision ${v}_{A}^{opt}$ Process 1~13 is same as Algorithm 1 14: if $FN=0$ 15: Output ${v}_{A}^{opt}=IdleVel()$ $\u22b3$ Adopt idle velocity. 16: end if 17: return. |

#### 4.4. Numerical Test

#### 4.4.1. Available Set

#### 4.4.2. Null Set

## 5. Simulation and Results

#### 5.1. Small-Scale

#### 5.2. Large-Scale

#### 5.3. Robotic Operation System (ROS) Simulation

## 6. Conclusions and Future Work

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**The visual display of UAVs $A$ and $B$, and the weak coverage velocity $WC{V}_{A|B}^{\tau}$. (

**a**) Display of two UAVs $A$ and $B$ in configuration space; (

**b**) Visualization of $WCV{L}_{A|B}^{\tau}$ and weak coverage velocity set $WC{V}_{A|B}^{\tau}$ in velocity space; (

**c**) Minkowski sum sets $WC{V}_{A|B}^{\tau}\oplus {V}_{B}$ owing to the fluctuation of UAV $B$’s velocity.

**Figure 4.**The construction of optimal velocity space. (

**a**) Visual display of UAVs’ situation; (

**b**) The geometrical expression of $ORC{V}_{A}^{\tau}$.

**Figure 5.**Two situations of optimal velocity space. (

**a**) Available situation; (

**b**) Available space; (

**c**) Vacant situation; (

**d**) Vacant space.

**Figure 7.**Two cases of visual display of UAV $A$, obstacle $O$ and $ORC{V}_{A|O}^{\tau}$. (

**a**) The most weak coverage point $o$ is on the edge of the segment $O$; (

**b**) The most weak coverage point $o$ is the endpoint of the segment $O$.

**Figure 8.**Three representative cases of optimization set. (

**a**) ORCV is a shape of sector; (

**b**) ORCV is a shape of triangle; (

**c**) ORCV is an irregular shape.

**Figure 10.**Two situations of null set. (

**a**) $ORC{V}_{A}^{\tau}\cap C(0,{v}_{\mathrm{max}})=\mathsf{\Phi}$; (

**b**) $ORC{V}_{A}^{\tau}=\mathsf{\Phi}$.

**Figure 12.**The entire process of UAVs’ coverage in a closed environment ${\mathsf{\Omega}}_{e}$ without obstacles. (

**a**) the initial positions; (

**b**) the moving trajectories; (

**c**) the optimal coverage.

**Figure 14.**The process of coverage with obstacle ${\mathsf{\Omega}}_{o}$. (

**a**) the initial positions; (

**b**) The moving trajectories; (

**c**) The optimal coverage.

**Figure 17.**The coverage situations of the V-based and VFA methods. (

**a**) The V-based coverage ($k=0$); (

**b**) The recorded trajectories of UAVs by the V-based method ($k=0~574$); (

**c**) The V-based coverage at $k=574$; (

**d**) The VFA coverage ($k=0$); (

**e**) The recorded trajectories of UAVs by the VFA method ($k=0~574$); (

**f**) The VFA coverage at $k=574$.

**Figure 18.**The recorded trajectories of UAVs generated by the simulation step $k=0~574$ by the RD, V-based and VFA methods. (

**a**) The RD method’s trajectories; (

**b**) The V-based method’s trajectories; (

**c**) The VFA method’s trajectories.

**Figure 19.**The comparison of coverage rate and deadweight loss. (

**a**) Comparison of coverage rate; (

**b**) Comparison of deadweight loss.

**Figure 21.**Cooperation coverage by 1000 UAVs. (

**a**) Coverage ($t=0$); (

**b**) Trajectory ($t=0~5226$); (

**c**) Coverage ($t=5226$).

**Figure 23.**Three typical moments of multi-UAVs sensing coverage: (

**a**) Initial coverage ($t=0$); (

**b**) Scatter moment ($t=2$ s); (

**c**) Steady-state coverage ($t=10$ s).

Symbol | Description |
---|---|

${v}_{opt}$ | The optimal velocity decision. |

$PR$ | The permitted region with unknown shape. |

$Square(x)$ | Centered at $0$, the length of edge is twice that of $x$. |

$RV(S)$ | Random velocity in the set of $S$. |

$AVE(G)$ | The center of the set of $G$ in Euclidean Space. |

$IdleVel()$ | The velocity of $0$ |

NUM(S) | The number of point in the set of S. |

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

$T$ | $0.25\text{}\mathrm{s}$ | simulation step size |

$\zeta $ | ${10}^{-5}$ | algorithm terminated value |

${l}_{e}$, ${l}_{a}$ | $250\text{}\mathrm{m}$, $50\text{}\mathrm{m}$ | length of square region ${\mathsf{\Omega}}_{e}$, ${\mathsf{\Omega}}_{a}$ |

$n$, ${n}^{\prime}$ | $25$, $1000$ | number of UAVs |

${v}_{i}^{\mathrm{max}}$ | $2\text{}\mathrm{m}/\mathrm{s}$ | maximum velocity of UAVs |

$r$, $R$, $CR$ | $0.5\text{}\mathrm{m}$, $25\text{}\mathrm{m}$, $70\text{}\mathrm{m}$ | radius of UAVs’ shape, sensor and communication |

${n}_{i}^{\mathrm{max}}$, ${R}_{i}^{\mathrm{max}}$ | $4$, $51\text{}\mathrm{m}$ | maximum considered neighbor and distance |

Method | Case 1 | Case 2 | Case 3 | Ave Time (ms) |
---|---|---|---|---|

RD | 10.857 | 20.280 | 13.266 | 14.807 |

V-Based | 591.148 | 605.856 | 632.880 | 609.961 |

VFA | 36.749 | 48.072 | 43.573 | 42.798 |

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**MDPI and ACS Style**

Chen, R.; Xu, N.; Li, J.
A Self-Organized Reciprocal Decision Approach for Sensing Coverage with Multi-UAV Swarms. *Sensors* **2018**, *18*, 1864.
https://doi.org/10.3390/s18061864

**AMA Style**

Chen R, Xu N, Li J.
A Self-Organized Reciprocal Decision Approach for Sensing Coverage with Multi-UAV Swarms. *Sensors*. 2018; 18(6):1864.
https://doi.org/10.3390/s18061864

**Chicago/Turabian Style**

Chen, Runfeng, Ning Xu, and Jie Li.
2018. "A Self-Organized Reciprocal Decision Approach for Sensing Coverage with Multi-UAV Swarms" *Sensors* 18, no. 6: 1864.
https://doi.org/10.3390/s18061864