# A Path-Planning Performance Comparison of RRT*-AB with MEA* in a 2-Dimensional Environment

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methodology

#### 3.1. MEA* Algorithm

Algorithm 1: $path\leftarrow MEA\ast (start,goal)$ [20]. |

Algorithm 2: path ← postSmoothPath(pathFound) [20]. |

#### 3.2. RRT*-AB Algorithm

Algorithm 3: $T\leftarrow RR{T}^{*}AB({z}_{init},{z}_{goal})$ [12]. |

#### 3.3. Complexity Analysis

#### 3.4. Data Set

- Simple Structured Environment: M1 is the case of a structured environment map such as a turning passage.
- Concave Structured Environment: M2 represents an environment with concave shape obstacle.
- Narrow Structured Environment: M3 is the case of a narrow structured environment.
- Dense Structured Environment: M4 signifies a highly dense environment.
- Complex Unstructured Environment: M5 is an example of a complex indoor and unstructured scenario.

#### 3.5. Performance Metrics

- Total Path Length: The total coverage length determines the total operational time required to perform the coverage task and the total energy consumption of the mobile robot. The path- planning algorithm is considered optimal if it generates the shortest path, thus leading to energy efficiency. Therefore, it is an important parameter for real-world solutions.
- Computational Time: The time required to compute the solution is preeminent for real-world applications. Hence, is a prominent efficiency indicator of the proposed approach.
- Memory Requirements: Memory requirements indicate the total number of vertices visited while performing the coverage task. This directly influences the total computational time required by the algorithm to find a solution.

## 4. Results

#### 4.1. Comparison with Sampling-BASED Algorithms

#### 4.2. Statistical Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

MEA* | Memory-Efficient A* |

RRT | Rapidly Exploring Random Tree |

RRT* | Rapidly Exploring Random Tree Star |

RRT*-AB | RRT*-Adjustable Bounds |

UAV | Unmanned Aerial Vehicle |

GA | Genetic Algorithm |

PSO | Particle Swarm Optimization |

ACO | Ant Colony Optimization |

SBP | Sampling-Based Planning |

IDA* | Iterative Deepening A* |

FD* | Field D* |

HPA* | Hierarchical A* |

A*PS | A* Post Smoothing |

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**Figure 1.**Path constrained to edges vs true shortest path in grid [20].

**Figure 2.**Cost Matrix of A* after grid expansion [20].

**Figure 3.**Cost Matrix of MEA* after grid expansion [20].

**Figure 4.**Global path pruning [20].

**Figure 5.**Fewer waypoints in MEA* generated path than A* generated path [20].

**Figure 6.**Process of RRT*-Adjustable Bounds [12].

**Figure 9.**Comparison of MEA * with grid-based approaches for processed grid cells and turns in the final path.

**Figure 11.**Plot of path lengths and computational time of all planners for all environment maps M1 to M5.

Map | A* | HPA* | RRT | RRT* | RRT*-AB | MEA* |
---|---|---|---|---|---|---|

M1 (Simple Case) | 12.54 | 12.453 | 69 | 164 | 26 | 0.0129 |

M2 (Concave Case) | 7.8821 | 7.9059 | 66 | 161 | 29.35 | 0.0205 |

M3 (Narrow Case) | 3.5571 | 3.5475 | 65 | 148 | 27 | 0.0094 |

M4 (Dense Case) | 4.42 | 5.235 | 72 | 166 | 25.5 | 0.0494 |

M5 (Complex Unstructured Case) | 3.0618 | 2.9953 | 66 | 157 | 25 | 0.0207 |

Total | 31.461 | 32.1367 | 338 | 796 | 132.85 | 0.1129 |

Mean | 6.2922 | 6.42734 | 67.6 | 159.2 | 26.57 | 0.02258 |

Std Dev | 3.9681 | 3.8726 | 2.8809 | 7.1203 | 1.7210 | 0.0157 |

Std Dev Err | 1.7746 | 1.7318 | 1.2884 | 3.1843 | 0.7696 | 0.0071 |

Map | A* | HPA* | RRT | RRT* | RRT*-AB | MEA* |
---|---|---|---|---|---|---|

M1 (Simple Case) | 153.23 | 109.97 | 199 | 137 | 107 | 107.70 |

M2 (Concave Case) | 110.97 | 93.09 | 117 | 128 | 95 | 91.67 |

M3 (Narrow Case) | 141.31 | 139.25 | 164 | 177 | 138 | 136.67 |

M4 (Dense Case) | 154.50 | 152.06 | 172 | 169 | 156 | 149.05 |

M5 (Complex Un-structure Case) | 99.71 | 97.20 | 129 | 130 | 96.34 | 96.91 |

Total | 659.7147 | 591.5614 | 781 | 741 | 592.34 | 582.007 |

Mean | 131.94294 | 118.31228 | 156.2 | 148.2 | 118.468 | 116.4014 |

Std Dev | 25.1410 | 26.1193 | 33.2370 | 23.0586 | 27.2124 | 25.2182 |

Std Dev Err | 11.2434 | 11.6809 | 14.8640 | 10.3121 | 12.1697 | 11.2779 |

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**MDPI and ACS Style**

Noreen, I.; Khan, A.; Asghar, K.; Habib, Z.
A Path-Planning Performance Comparison of RRT*-AB with MEA* in a 2-Dimensional Environment. *Symmetry* **2019**, *11*, 945.
https://doi.org/10.3390/sym11070945

**AMA Style**

Noreen I, Khan A, Asghar K, Habib Z.
A Path-Planning Performance Comparison of RRT*-AB with MEA* in a 2-Dimensional Environment. *Symmetry*. 2019; 11(7):945.
https://doi.org/10.3390/sym11070945

**Chicago/Turabian Style**

Noreen, Iram, Amna Khan, Khurshid Asghar, and Zulfiqar Habib.
2019. "A Path-Planning Performance Comparison of RRT*-AB with MEA* in a 2-Dimensional Environment" *Symmetry* 11, no. 7: 945.
https://doi.org/10.3390/sym11070945