# Multi-Robot Exploration of Unknown Space Using Combined Meta-Heuristic Salp Swarm Algorithm and Deterministic Coordinated Multi-Robot Exploration

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Problem Formulation and Proposed Method

#### 3.1. Coordinated Multi-Robot Exploration

#### 3.1.1. Cost Function

- Initialization.

- 2.
- Update loop for all grid cells (x, y).

#### 3.1.2. Utility Value

#### 3.2. Salp Swarm Algorithm

Algorithm 1 Salp Swarm Algorithm SSA |

1: $InitializethesalppopulationXi\left(i=1,\dots ,n\right)consideringupperandlowerbounds$ |

2: $\hspace{0.17em}whileiterationisnotoverdo$ |

3: $\hspace{1em}\hspace{1em}\hspace{0.17em}Calculatethecostfunctionofeachsearchagent\left(salp\right)$ |

4: $\hspace{1em}\hspace{1em}\hspace{0.17em}Food=thebestsearchagent$ |

5: $\hspace{1em}\hspace{1em}\hspace{0.17em}Updatec1byEquation\left(7\right)$ |

6: $\hspace{1em}\hspace{1em}\hspace{0.17em}foreachsalp\left(Xi\right)$ |

7: $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}if(i=Xi/2)$ |

8: Evaluate Equation (6) to update the salp leader position |

9: else |

10: Evaluate Equation (9) to update the position of the salp follower |

11: end |

12: end |

13: Amend the salps based on the upper and lower bounds of variables |

14: end while |

#### 3.3. Hybrid CME-SSA

Algorithm 2 Coordinated Multi-Robot Exploration with Salp Swarm Algorithm CME-SSA |

1: Initialization$\left\{\begin{array}{c}NumberofRobotsN,sensorrange\\ Iterationi,Initialposition\\ Settheutilityofallcellsto1\end{array}\right.$ |

2:$Whileiterationisnotoverdo$ |

3:$\hspace{1em}\hspace{0.17em}\hspace{0.17em}ForNrobot$ |

4:$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}Setcoordinatesofcost{V}_{Cell}$ |

5:$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Calculatecostof{V}_{Cell}$ |

6: Update $Utilit{y}_{cell}^{iteration}$and cost of${V}_{Cell}$ |

7: Calculate ${c}_{1}$,${c}_{2}$and${c}_{3}$ |

8: Find leaders $salpLeade{r}_{1}$,$salpLeade{r}_{2}$,$salpLeade{r}_{3}$,$salpLeade{r}_{4}$(Line 7 Algorithm 1) |

9: Find ${X}_{Leader1}$,${X}_{Leader2}$,${X}_{Leader3}$,${X}_{Leader4}$ |

10: Find the next position for $Robo{t}_{i}$as max (${X}_{Leader1}$,${X}_{Leader2}$,${X}_{Leader3}$,${X}_{Leader4}$) |

11: Reduce utility on a new position |

12: end for |

13: end while |

_{1}). Moreover, it is easy to implement and has lower memory requirement compared to other techniques, making the exploration process achievable in less time. Finally, because the SSA mimics the salp’s behavior in the chain of leaders and followers, it is easier for the robots to explore tight corridors and corners efficiently. Its main cons are when the exploration space is free of obstacles, it requires extra 10 to 20 iterations to explore most of it.

## 4. Results and Discussions

- Original coordinated multi-robot exploration (CME);
- Coordinated multi-robot exploration and grey wolf optimizer algorithms (CME-GWO);
- Coordinated multi-robot exploration and the sine cosine algorithm (CME-SCA);
- Coordinated multi-robot exploration and grey wolf optimizer algorithms combined with salp swarm algorithm (CME-GWOSSA) has been implemented under similar conditions.

#### 4.1. Simple Map

- CME-GWO showed an exploration average of 88.44% in simple map 1 with an std of 2.5 and 91.7% in simple map 2 with an std of 3.2
- CME-GWOSSA provided an exploration average of 87.84% in simple map 1 with an std of 5.2 and 87.63% in simple map 2 with an std of 7.4
- CME-SCA delivered an exploration average of 82.94% in simple map 1 with an std of 7.4 and 88.48% in simple map 2 with an std of 8.3

#### 4.2. Complex Space Map

#### 4.3. Results, Analysis, and Discussion

#### 4.4. Analysis Results Summary

#### 4.5. Implementation on Hardware

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Senor view range in the grid cells: (

**a**) sensor range cover $\left[V1,\dots ,V8\right]$ around the robot; (

**b**) eight cells around the robot and cell 9 is the robot position; (

**c**) robot moving from right to left showing the sensor range does not cover the cost $V1,V7,V8$.

**Figure 5.**Percentage of the explored area after implementing the CME-SSA and the other approaches on simple map 1. Simple map 1: (

**a**) CME 93%, (

**b**) CME-SSA 90%, (

**c**) CME-GWO 84%, (

**d**) CME-SCA 73%, (

**e**) CME-GWOSSA 80%.

**Figure 6.**Percentage of the explored area after implementing the CME-SSA and the other approaches on simple map 2. Simple map 2: (

**a**) CME 97%, (

**b**) CME-SSA 92%, (

**c**) CME-GWO 72%, (

**d**) CME-GWOSSA 61%, (

**e**) CME-SCA 74%.

**Figure 7.**Percentage of the explored area after implementing the CME-SSA and the other approaches on complex map 1. Complex map 1: (

**a**) CME, 39.24% (Iteration 21); (

**b**) SSA, 98.36%; (

**c**) CME-GWO, 86.88%; (

**d**) CME-GWOSSA, 71.47%; (

**e**) CME-SCA, 74.56%.

**Figure 8.**Percentage of the explored area after implementing the CME-SSA and the other approaches on complex map 2. Complex map 2: (

**a**) CME 52.16% (Iteration 33); (

**b**) CME-SSA, 96.45%; (

**c**) CME-GWO, 80.61%; (

**d**) CME-GWOSSA, 89.13%; (

**e**) CME-SCA, 76.57%.

**Figure 9.**Percentage of the explored area after implementing the CME-SSA and the other approaches on complex map 3. Complex map 3: (

**a**) CME, 36.48% (Iteration 15); (

**b**) CME-SSA, 98.49%; (

**c**) CME-GWO, 90.51%; (

**d**) CME-GWOSSA, 86.32%; (

**e**) CME-SCA, 78.44%.

**Figure 10.**Percentage of the explored area after implementing the CME-SSA and the other approaches on complex map 4. Complex map 4: (

**a**) CME, 69.45% (Iteration 50); (

**b**) CME-SSA, 97.25%; (

**c**) CME-GWO, 86.57%; (

**d**) CME-GWOSSA, 81.44%; (

**e**) CME-SCA, 79.12%.

**Figure 11.**Percentage of the explored area after implementing the CME-SSA and the other approaches on complex map 5. Complex map 5: (

**a**) CME, 54.23% (Iteration 31); (

**b**) CME-SSA, 96.59%; (

**c**) CME-GWO, 53.85% (Iteration 51); (

**d**) CME-GWOSSA, 58.32% (Iteration 58); (

**e**) CME-SCA, 44.56% (Iteration 49).

MAP | CME-SSA | CME-GWO | CME-GWOSSA | CME-SCA | CME | |||||
---|---|---|---|---|---|---|---|---|---|---|

ave | std | ave | std | ave | std | ave | std | ave | std | |

Map 1 | 89.72 | 3.13 | 88.45 | 2.54 | 87.84 | 5.27 | 82.95 | 7.42 | 93.08 | 0.00 |

Map 2 | 96.22 | 2.58 | 91.75 | 3.28 | 87.63 | 7.47 | 88.49 | 8.32 | 97.31 | 0.00 |

MAP | CME-SSA | CME-GWO | CME-GWOSSA | CME-SCA | CME | |||||
---|---|---|---|---|---|---|---|---|---|---|

ave | std | ave | std | ave | std | ave | std | ave | std | |

Map 1 | 10.97 | 0.10 | 12.98 | 0.14 | 13.08 | 0.38 | 14.22 | 0.50 | 15.26 | 0.00 |

Map 2 | 11.01 | 0.29 | 13.12 | 0.24 | 13.10 | 0.25 | 14.59 | 0.78 | 13.40 | 0.00 |

**Table 3.**The number of failed simulations before completing 100 iterations of exploration on two simple environments (map 1, map 2).

MAP | CME-SSA | CME-GWOSSA | CME-GWO | CME-SCA | CME |
---|---|---|---|---|---|

Map 1 | 0 | 5 | 2 | 5 | 0 |

Map 2 | 0 | 3 | 2 | 8 | 0 |

**Table 4.**Avg and std of the percentage of the explored area in a complex environment for each algorithm.

MAP | CME-SSA | CME-GWO | CME-GWOSSA | CME-SCA | CME | |||||
---|---|---|---|---|---|---|---|---|---|---|

ave | std | ave | std | ave | std | ave | std | ave | std | |

Map 1 | 92.84 | 2.62 | 85.57 | 11.57 | 87.31 | 9.11 | 87.13 | 8.95 | 39.24 | 0 |

Map 2 | 95.66 | 2.39 | 90.77 | 6.52 | 92.79 | 8.70 | 87.88 | 10.57 | 52.17 | 0 |

Map 3 | 95.20 | 2.52 | 88.80 | 8.11 | 87.45 | 7.68 | 87.04 | 8.70 | 36.48 | 0 |

Map 4 | 92.66 | 3.41 | 82.82 | 8.73 | 89.71 | 6.19 | 86.46 | 11.66 | 69.46 | 0 |

Map 5 | 96.34 | 1.90 | 73.42 | 12.23 | 70.34 | 14.48 | 65.30 | 15.93 | 54.23 | 0 |

Map Type | Map No | CME-SSA | CME-GWOSSA | CME-GWO | CME-SCA | CME |
---|---|---|---|---|---|---|

Simple | Map 1 | 2.92 × 10^{−9} | 7.47 × 10^{−10} | 1.43 × 10^{−8} | 1.33 × 10^{−8} | N/A |

Map 2 | 0.6411 | 1.21 × 10^{−12} | 1.21 × 10^{−12} | 1.21 × 10^{−12} | N/A | |

Complex | Map 1 | N/A | 0.0138 | 0.0315 | 0.0035 | Null |

Map 2 | N/A | 0.00 | 0.24 | 0.01 | Null | |

Map 3 | N/A | 0.00 | 0.00 | 0.00 | Null | |

Map 4 | N/A | 0.0261 | 0.0271 | 0.0451 | Null | |

Map 5 | N/A | 5.57 × 10^{−10} | 3.02 × 10^{−11} | 1.46 × 10^{−10} | Null |

MAP | CME-SSA | CME-GWO | CME-GWOSSA | CME-SCA | CME | |||||
---|---|---|---|---|---|---|---|---|---|---|

ave | std | ave | std | ave | std | ave | std | ave | std | |

Map 1 | 10.89 | 0.39 | 12.62 | 0.42 | 12.55 | 0.34 | 14.07 | 1.26 | ∞ | 0.00 |

Map 2 | 10.54 | 0.43 | 13.11 | 0.44 | 13.10 | 0.43 | 13.16 | 0.54 | ∞ | 0.00 |

Map 3 | 10.10 | 0.21 | 13.17 | 0.35 | 13.11 | 0.35 | 13.77 | 0.76 | ∞ | 0.00 |

Map 4 | 9.95 | 0.18 | 12.98 | 0.26 | 12.98 | 0.17 | 13.84 | 0.84 | ∞ | 0.00 |

Map 5 | 10.42 | 0.24 | 12.83 | 0.36 | 12.98 | 0.42 | 14.74 | 1.23 | ∞ | 0.00 |

Map Type | Map No | CME-SSA | CME-GWO | CME-GWOSSA | CME-SCA | CME |
---|---|---|---|---|---|---|

Simple | Map 1 | N/A | 4.20 × 10^{−10} | 2.61 × 10^{−10} | 3.02 × 10^{−11} | 1.17 × 10^{−7} |

Map 2 | N/A | 0.00 | 0.00 | 0.00 | 0.00 | |

Complex | Map 1 | N/A | 0.00 | 0.00 | 0.00 | NULL |

Map 2 | N/A | 0.00 | 0.00 | 0.00 | NULL | |

Map 3 | N/A | 0.00 | 0.00 | 0.00 | NULL | |

Map 4 | N/A | 1.21 × 10^{−10} | 2.37 × 10^{−10} | 1.96 × 10^{−10} | NULL | |

Map 5 | N/A | 1.10 × 10^{−8} | 6.72 × 10^{−10} | 3.34 × 10^{−11} | NULL |

**Table 8.**The number of failed simulations to complete 100 iterations of the hybrid exploration methods on five complex environment maps.

Complex MAP | CME-SSA | CME-GWOSSA | CME-GWO | CME-SCA | CME |
---|---|---|---|---|---|

Map 1 | 0.00 | 54.00 | 47.00 | 44.00 | ∞ |

Map 2 | 0.00 | 5.00 | 3.00 | 5.00 | ∞ |

Map 3 | 0.00 | 14.00 | 12.00 | 17.00 | ∞ |

Map 4 | 1.00 | 125.00 | 98.00 | 167.00 | ∞ |

Map 5 | 2.00 | 97.00 | 183.00 | 415.00 | ∞ |

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Romeh, A.E.; Mirjalili, S.
Multi-Robot Exploration of Unknown Space Using Combined Meta-Heuristic Salp Swarm Algorithm and Deterministic Coordinated Multi-Robot Exploration. *Sensors* **2023**, *23*, 2156.
https://doi.org/10.3390/s23042156

**AMA Style**

Romeh AE, Mirjalili S.
Multi-Robot Exploration of Unknown Space Using Combined Meta-Heuristic Salp Swarm Algorithm and Deterministic Coordinated Multi-Robot Exploration. *Sensors*. 2023; 23(4):2156.
https://doi.org/10.3390/s23042156

**Chicago/Turabian Style**

Romeh, Ali El, and Seyedali Mirjalili.
2023. "Multi-Robot Exploration of Unknown Space Using Combined Meta-Heuristic Salp Swarm Algorithm and Deterministic Coordinated Multi-Robot Exploration" *Sensors* 23, no. 4: 2156.
https://doi.org/10.3390/s23042156