# A UAV Path Planning Method for Building Surface Information Acquisition Utilizing Opposition-Based Learning Artificial Bee Colony Algorithm

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## Abstract

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## 1. Introduction

- A target information entropy ratio (IER) model based on observation angles is established. Considering the constraints on flight, IER is an index of information loss, which is a function of observation angles.
- An opposition-based learning ABC algorithm is proposed. By introducing the concept of vague opposition-based learning into the ABC algorithm, the algorithm is able to search a larger solution space with high-quality solutions preserved.
- The activation mechanism of the scout bees has been upgraded. The novel mechanism is based on the individual’s relative position to the population, allowing the scout bees to adaptively abandon the individual.

## 2. Problem Definition

#### 2.1. Definition of Drone Observation Angles

_{S}, which points from the imaging center of the sensor to the ground center of the target all the time. The ground center position of the target can be determined by previous positioning and detection. Since the ground center position of the target is known, the position of each waypoint can be determined by RAA and RDA. The definition and schematic diagram of RAA and RDA are shown in Figure 1.

_{S}on the horizontal plane and the positive direction of the X-axis. The value range is [0, 90] with a unit of degrees (°). When viewed from the positive half-axis of the Z-axis to the XOY plane, the angle increases counterclockwise.

_{S}and its projection vector on the horizontal plane. The value range is [0, 90] with a unit of degree (°). When viewed from the positive Y-axis of the XOZ plane, the angle increases counterclockwise.

#### 2.2. Analysis of Constraints for UAV Observations

#### 2.2.1. Constraints on RDA

_{min}should be limited to a small value.

#### 2.2.2. Constraints on RAA

#### 2.3. A Multi-Angle Target Information Acquisition Model

_{S}) composed of all N surfaces (m top surfaces, n side surfaces, N = n + m). G is shown in the following equation:

_{s_i}, φ

_{s_i}), where θ

_{s_i}∈ [0°, 360°], φ

_{s_i}∈ [−90°, 0°]. The information acquisition situation of the current surface can be expressed as follows:

_{s}|, β = |φ − φ

_{s}|. ${E}_{ort}$ represents the entropy of the frontal view of the observed surface, and $E(\alpha ,\beta )$ represents the entropy of the tilted view at the corresponding viewing angle. ${P}_{\alpha \beta \_i}$ and ${P}_{ort\_i}$ represent the distribution probabilities of each gray level in the two images. Obviously, IER is a dimensionless ratio that measures the difference between the information obtained at different viewing angles and the information of the frontal view image. The value range of IER is [0, 1]. The closer IER is to 0, the less information is lost. When IER = 1, there is no information acquired. Let IER(α,β) = 1 − ${I}_{{F}_{i}}\left(\theta ,\phi ,{T}_{S\_i}\right)$, which can be used to describe the information loss rate of the observed surface at the viewing angle (θ, φ). Due to the existence of occlusion, only when α is between 90° and 270°, IER(α, β) ≠ 1. The goal function is to find the minimum IER of all surfaces; therefore, all solutions that make IER = 1 are abandoned in the process of iteration. The trend of IER is that the observation angle is closer to the front view, the corresponding IER(α, β) value is smaller.

_{K×N}:

## 3. Proposed Method

#### 3.1. Artificial Bee Colony Algorithm

#### 3.2. Opposition-Based Learning Artificial Bee Colony Algorithm

#### 3.2.1. Opposition-Based Learning Mechanism

#### 3.2.2. Improved S-Bee Search Mechanism

## 4. Experiment

#### 4.1. Controlled Experiment

#### 4.1.1. Experiment Design

#### 4.1.2. Experiment Results

#### 4.2. 3D Reconstruction Experiment

#### 4.2.1. Experiment Design

#### 4.2.2. Visual Comparison of Models

#### 4.2.3. Quantitative Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Examples of simulated images at different viewing angles. The numbers represent visible surfaces of the target. ‘1’ represents the top surface, and ‘2’, ‘3’, ‘4’, ‘5’ represent the other four visible surfaces of the target.

**Figure 6.**Schematic diagram of waypoints generated to capture information of target surfaces in Scene 1.

**Figure 7.**(

**a**) Means of different algorithms as the population size varies; (

**b**) standard deviations of different algorithms as the population size varies; (

**c**) average runtimes of iterations in Scene 1.

**Figure 8.**Schematic diagram of waypoints generated to capture information of target surfaces in Scene 2.

**Figure 9.**(

**a**) Means of different algorithms as the population size varies; (

**b**) standard deviations of different algorithms; (

**c**) average runtimes of iterations in Scene 2.

Population Size | Algorithm | Mean | Std | Time (s) |
---|---|---|---|---|

10 | EA | 3.6854 | 0.1352 | 56.17 |

ACO | 1.9787 | 0.0368 | 53.18 | |

ABC | 1.5870 | 0.0358 | 51.33 | |

ABC1 | 1.3406 | 0.0271 | 53.01 | |

ABC2 | 1.2696 | 0.0289 | 48.62 | |

OABC | 1.2313 | 0.0154 | 46.98 | |

20 | EA | 3.425 | 0.1277 | 87.59 |

ACO | 1.8390 | 0.0423 | 71.63 | |

ABC | 1.4135 | 0.0312 | 73.88 | |

ABC1 | 1.3048 | 0.0229 | 73.94 | |

ABC2 | 1.2501 | 0.0247 | 79.16 | |

OABC | 1.2309 | 0.0124 | 66.51 | |

30 | EA | 3.1183 | 0.1049 | 123.88 |

ACO | 1.7581 | 0.0364 | 121.68 | |

ABC | 1.3537 | 0.0291 | 127.80 | |

ABC1 | 1.2425 | 0.0119 | 126.36 | |

ABC2 | 1.2310 | 0.0202 | 124.97 | |

OABC | 1.2309 | 0.0103 | 104.32 | |

50 | EA | 2.8609 | 0.1124 | 348.98 |

ACO | 1.6872 | 0.0387 | 215.08 | |

ABC | 1.3431 | 0.0272 | 226.95 | |

ABC1 | 1.2356 | 0.0119 | 209.64 | |

ABC2 | 1.2309 | 0.0182 | 199.02 | |

OABC | 1.2310 | 0.0112 | 175.94 | |

100 | EA | 2.5439 | 0.0847 | 580.61 |

ACO | 1.4598 | 0.0301 | 422.50 | |

ABC | 1.2315 | 0.0243 | 450.13 | |

ABC1 | 1.2310 | 0.0089 | 426.98 | |

ABC2 | 1.2309 | 0.0104 | 412.52 | |

OABC | 1.2308 | 0.0092 | 384.39 |

Population Size | Algorithm | Mean | Std | Time (s) |
---|---|---|---|---|

10 | EA | 2.1192 | 0.1488 | 59.64 |

ACO | 0.9463 | 0.0618 | 53.49 | |

ABC | 0.7732 | 0.0472 | 52.97 | |

ABC1 | 0.7763 | 0.0366 | 49.32 | |

ABC2 | 0.6289 | 0.0291 | 47.40 | |

OABC | 0.6051 | 0.0209 | 47.96 | |

20 | EA | 1.8970 | 0.1358 | 89.84 |

ACO | 0.9234 | 0.0589 | 81.06 | |

ABC | 0.7156 | 0.0433 | 82.58 | |

ABC1 | 0.6949 | 0.0315 | 77.20 | |

ABC2 | 0.6593 | 0.0256 | 75.98 | |

OABC | 0.6050 | 0.0182 | 73.44 | |

30 | EA | 1.2312 | 0.1586 | 178.48 |

ACO | 0.8865 | 0.0378 | 137.29 | |

ABC | 0.6954 | 0.0395 | 142.65 | |

ABC1 | 0.6617 | 0.0292 | 126.89 | |

ABC2 | 0.6201 | 0.0226 | 102.76 | |

OABC | 0.6049 | 0.0136 | 102.88 | |

50 | EA | 0.9873 | 0.0973 | 354.36 |

ACO | 0.7839 | 0.0423 | 229.10 | |

ABC | 0.6723 | 0.0250 | 262.16 | |

ABC1 | 0.6130 | 0.0217 | 218.22 | |

ABC2 | 0.6050 | 0.0127 | 194.61 | |

OABC | 0.6049 | 0.0129 | 173.20 | |

100 | EA | 0.9857 | 0.0925 | 572.65 |

ACO | 0.6982 | 0.0247 | 461.60 | |

ABC | 0.6154 | 0.0187 | 484.73 | |

ABC1 | 0.6050 | 0.0151 | 462.53 | |

ABC2 | 0.6049 | 0.0130 | 377.52 | |

OABC | 0.6048 | 0.0127 | 343.85 |

Surface 1 | Surface 2 | Surface 3 | Surface 4 | |
---|---|---|---|---|

OABC | ||||

ABC | ||||

ABC1 | ||||

ABC2 | ||||

Five-directional flight |

Number of Images | Time Consumption of UAV Working | Time Consumption of 3D Reconstruction | |
---|---|---|---|

OABC | 25 | 2 min 10 s | 25 min 46 s |

ABC | 52 | 10 min 13 s | 50 min 20 s |

ABC1 | 30 | 3 min 21 s | 34 min 02 s |

ABC2 | 28 | 2 min 43 s | 30 min 27 s |

Five-Directional Flight | 89 | 25 min 46 s | 3 h 48 min |

3D Models | X-Direction RMSE | Y-Direction RMSE | Planar RMSE | Height RMSE |
---|---|---|---|---|

From OABC | 0.0515 | 0.0898 | 0.1036 | 0.1470 |

From ABC | 0.0683 | 0.1023 | 0.1230 | 0.1522 |

From ABC1 | 0.0576 | 0.0917 | 0.1083 | 0.1497 |

From ABC2 | 0.0618 | 0.0984 | 0.1162 | 0.1633 |

From Five-Directional Flight | 0.0521 | 0.0835 | 0.0984 | 0.1395 |

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## Share and Cite

**MDPI and ACS Style**

Chen, H.; Liang, Y.; Meng, X.
A UAV Path Planning Method for Building Surface Information Acquisition Utilizing Opposition-Based Learning Artificial Bee Colony Algorithm. *Remote Sens.* **2023**, *15*, 4312.
https://doi.org/10.3390/rs15174312

**AMA Style**

Chen H, Liang Y, Meng X.
A UAV Path Planning Method for Building Surface Information Acquisition Utilizing Opposition-Based Learning Artificial Bee Colony Algorithm. *Remote Sensing*. 2023; 15(17):4312.
https://doi.org/10.3390/rs15174312

**Chicago/Turabian Style**

Chen, Hao, Yuheng Liang, and Xing Meng.
2023. "A UAV Path Planning Method for Building Surface Information Acquisition Utilizing Opposition-Based Learning Artificial Bee Colony Algorithm" *Remote Sensing* 15, no. 17: 4312.
https://doi.org/10.3390/rs15174312