# UAV Path Planning Based on Improved Artificial Potential Field Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Traditional Artificial Potential Field Method

_{att}(goal) the target location generates a field of gravitational attraction toward the drone, and U

_{rep}(obs) is the barrier that generates the repulsive potential field. The letter “m” denotes the number of barriers.

_{att}(goal) and the repulsive potential field U

_{rep}(obs) functions, respectively, are shown.

_{att}and keeps to represent the attractive potential gain coefficient and repulsive potential gain coefficient, respectively. It also uses P

_{u}to represent the drone’s position, P

_{goal}to represent the target point’s position, ρ(P

_{u}, P

_{goal}) to represent the Euclidean distance between the two, P

_{obs}to represent the obstacle’s position, ρ(P

_{u}, P

_{obs}) to represent the Euclidean distance between the two, and ρ

_{eff}to represent the obstacle’s influence distance. As stated in Equations (4) and (5), the attractive force F

_{att}(goal) and the repulsive force F

_{rep}(obs) can be calculated by calculating the negative gradient of the potential field function.

_{all}that it is currently experiencing during flight by adding the attractive force from the point of the goal and the repulsive force generated by the obstacles.

- (1)
- The local minimum value problem [25]. Figure 1a illustrates what happens when the drone, obstacle, and target point are all situated in a straight line: the drone will be in a state of force balance, unable to progress to the next position, and unable to reach the target point. As seen in Figure 1b, the drone encounters equal and opposing repulsive and attractive forces from the obstacles at a given point, forcing it to stall at this location.

- (2)

- (3)
- Unreasonable motions are made to avoid obstacles. Even though the position of obstacles in front of the drone has no bearing on its forward path, as illustrated in Figure 3, when the forward path reaches within the obstacle’s influence range, the drone will produce obstacle avoidance movements, lengthening the path.

## 3. Improvement of Artificial Potential Field Method

#### 3.1. The Mechanism for Calculating Crash Risk Based on Safety Distance

_{safe}was added to the obstacle model, as illustrated in Figure 5, to predict the collision between drones and obstacles [27]. As a buffer zone between the drone and the obstacle, the safety distance d

_{safe}added to the radius of the drone outside of the obstacle.

_{safe}is defined as follows:

_{o}and d

_{u}is the obstacle radius. Using Formula (8), the angle ψ of the drone’s current flight path is compared to the angle (θ

_{R}, θ

_{L}) of the obstacle’s boundary to assess the probability of collision:

#### 3.2. Virtual Sub-Target Setting

_{cur_uav}(x

_{u}, y

_{u}) is the origin, and the detected distance d

_{pre}is the radius to detect the obstacle within the angle β in front of the UAV. When the detection of obstacles ahead P

_{r_col}(x

_{obs}, y

_{obs}) has the risk of collision or in the case of local minima, a virtual sub-target is generated to guide the UAV to the target point. The specific method is to make the UAV and the obstacle line L

_{1}of the vertical line L

_{2}, L

_{2}, and the safe distance d

_{safe}intersect with two points for P

_{dum_i}(i = 1, 2); that is, the virtual sub-target coordinates to be determined. The slope of the UAV obstacle line L

_{1}is k

_{1}, and the coordinates of the virtual sub-target P

_{dum_i}(x

_{dum_i}, y

_{dum_i}) (i = 1, 2) are given by Equations (9) and (10).

#### 3.3. Virtual Sub-Target Evaluation

_{dum_i}(i = 1, 2) was set and connected with the target point by line L

_{dum_i}(i = 1, 2), and the distances from the obstacles in front of line L

_{2}to line L

_{dum_i}(i = 1, 2) were represented as ρ(P

_{obs_j}, L

_{dum_i}). When the line L

_{dum_i}fell within the influence range of obstacles 1 and 3, the drone needed to generate obstacle avoidance actions to avoid them. At the same time, considering the effect of scenario a formed by obstacles 1 and 2 on the line, the obstacles within the range of 4ρ

_{eff}from line L

_{dum_i}were included in the evaluation calculation. All these descriptions are in the past tense because it is explaining what has already been proposed and done in the article.

_{dum_i}(i = 1, 2) is defined as ω. The relative distance ω is determined to determine how impediments (such as obstacles 1 and 3) affect the line L

_{dum_i}. After that, the effectiveness of establishing virtual sub-goals is assessed using the assessment factor J. Equation (12) is the expression for the evaluation factor J.

_{dum_i}, as represented by distance ρ(P

_{obs_j}, L

_{dum_i}), is greater than 4ρ

_{eff}(ρ + α) is the evaluation distance and α is the evaluation constant.

_{dum_i}evaluation distance. When ω ≥ 0, it meant that the obstacle was outside of the line L

_{dum_i}evaluation range and that the drone did not need to avoid it. Based on the value of ω, the value of J might is i determined. When a particular virtual sub-goal assessment factor J is smaller, it means that the obstacles close to the line L

_{dum}have less of an effect on the drone’s future flight route; thus, a reasonable virtual sub-target coordinate can be derived P

_{dum}(x

_{dum}, y

_{dum}).

#### 3.4. Artificial Potential Field Model Modification

_{dum}(x

_{dum}, y

_{dum}) has no obstacles between its location and the current position of the drone. Therefore, it is possible to eliminate the repulsive force generated by obstacles in traditional artificial potential field methods and only retain the attraction generated by the target point. The attraction in traditional artificial potential field methods is only based on the distance between the drone and the target point. As the drone gets closer to the target point, the value of the attraction also decreases, which can make it difficult for the drone to accurately reach the target point.

_{s}, P

_{goal}) between the drone’s starting point and the target point and ρ(P

_{cur_uav}, P

_{goal}) between the drone’s current position and the target point. The enhanced attraction force F

_{imp_att}(goal) can offer more attraction as the drone gets closer to the target point, enabling it to be reached precisely. Equation (13) provides the expression for the enhanced attraction force F

_{imp_att}(goal).

_{imp_att}(goal) of the virtual sub-target is given by Equation (15). It is derived depending on the distance ρ(P

_{cur}, P

_{dum}) between the drone and the virtual sub-target.

_{att}on the drone following Equations (13) and (15).

#### 3.5. Adaptive Step Size

_{pre}to accomplish fast flight. The step size should be decreased to avoid obstacles when there is a chance of collision in front of the drone.

_{T}, the fixed step size S

_{t}, the virtual sub-target boundary angle $\delta $, and the current angle L. Equation (17) gives L the step length expression.

_{T}) represents the collision angle.

_{max}= 1.8S

_{t}and a lower limit for the step size l

_{min}= 0.8S

_{t}:

## 4. Comparison of Simulation Results

_{length}), energy consumption (E) during flight, number of iterations (N), angle changes, and number of angle changes in the drone flight path.

_{length}:

#### 4.1. Local Minimal Value Test Verification

#### 4.2. Target Unreachable Test Validation

#### 4.3. Complex Environment Test Verification

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Majeed, A.; Hwang, S.O. A Multi-Objective Coverage Path Planning Algorithm for UAVs to Cover Spatially Distributed Regions in Urban Environments. Aerospace
**2021**, 8, 343. [Google Scholar] [CrossRef] - Hassanalian, M.; Abdelkefi, A. Classifications, applications, and design challenges of drones: A review. Prog. Aerosp. Sci.
**2017**, 91, 99–131. [Google Scholar] [CrossRef] - Gugan, G.; Haque, A. Path Planning for Autonomous Drones: Challenges and Future Directions. Drones
**2023**, 7, 169. [Google Scholar] [CrossRef] - Li, M.; Zhang, H. AUV 3D Path Planning Based On a Algorithm. In 2020 Chinese Automation Congress (CAC); IEEE: Piscataway, NJ, USA, 2020; pp. 11–16. [Google Scholar]
- Chen, X.; Gao, P. Path planning and control of soccer robot based on genetic algorithm. J. Ambient. Intell. Humaniz. Comput.
**2019**, 11, 6177–6186. [Google Scholar] [CrossRef] - Qian, Q.; Wu, J.; Wang, Z. Optimal path planning for two-wheeled self-balancing vehicle pendulum robot based on quan-tum-behaved particle swarm optimization algorithm. Pers. Ubiquitous Comput.
**2019**, 23, 393–403. [Google Scholar] [CrossRef] - Wang, L.; Kan, J.; Guo, J.; Wang, C. 3D Path Planning for the Ground Robot with Improved Ant Colony Optimization †. Sensors
**2019**, 19, 815. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wang, D.; Zheng, S.; Ren, Y.; Du, D. Path Planning Based on the Improved RRT * Algorithm for the Mining Truck. Comput. Mater. Contin.
**2022**, 71, 3571–3587. [Google Scholar] [CrossRef] - Ren, J.; Zhang, J.; Cui, Y. Autonomous Obstacle Avoidance Algorithm for Unmanned Surface Vehicles Based on an Improved Velocity Obstacle Method. ISPRS Int. J. Geo-Inf.
**2021**, 10, 618. [Google Scholar] [CrossRef] - Jenie, Y.I.; van Kampen, E.-J.; de Visser, C.C.; Chu, Q.P. Velocity Obstacle Method for Non-cooperative Autonomous Collision Avoidance System for UAVs. In Proceedings of the AIAA Guidance, Navigation, and Control Conference, Grapevine, TX, USA, 13 January 2014; American Institute of Aeronautics and Astronautics: National Harbor, MD, USA, 2014. [Google Scholar]
- Choi, J.; Lee, G.; Lee, C. Reinforcement learning-based dynamic obstacle avoidance and integration of path planning. Intell. Serv. Robot.
**2021**, 14, 663–677. [Google Scholar] [CrossRef] [PubMed] - Li, A.; Liu, Z.; Wang, W.; Zhu, M.; Li, Y.; Huo, Q.; Dai, M. Reinforcement Learning with Dynamic Movement Primitives for Obstacle Avoidance. Appl. Sci.
**2021**, 11, 11184. [Google Scholar] [CrossRef] - Yao, J.; Li, X.; Zhang, Y.; Ji, J.; Wang, Y.; Zhang, D.; Liu, Y. Three-Dimensional Path Planning for Unmanned Helicopter Using Memory-Enhanced Dueling Deep Q Network. Aerospace
**2022**, 9, 417. [Google Scholar] [CrossRef] - He, Z.; Chu, X.; Liu, C.; Wu, W. A novel model predictive artificial potential field based ship motion planning method con-sidering COLREGs for complex encounter scenarios. ISA Trans.
**2023**, 134, 58–73. [Google Scholar] [CrossRef] [PubMed] - Feng, S.; Qian, Y.; Wang, Y. Collision avoidance method of autonomous vehicle based on improved artificial potential field algorithm. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2021**, 235, 3416–3430. [Google Scholar] [CrossRef] - Yang, W.; Wu, P.; Zhou, X.; Lv, H.; Liu, X.; Zhang, G.; Hou, Z.; Wang, W. Improved Artificial Potential Field and Dynamic Window Method for Amphibious Robot Fish Path Planning. Appl. Sci.
**2021**, 11, 2114. [Google Scholar] [CrossRef] - Feng, J.; Zhang, J.; Zhang, G.; Xie, S.; Ding, Y.; Liu, Z. UAV Dynamic Path Planning Based on Obstacle Position Prediction in an Unknown Environment. IEEE Access
**2021**, 9, 154679–154691. [Google Scholar] [CrossRef] - Azzabi, A.; Nouri, K. An advanced potential field method proposed for mobile robot path planning. Trans. Inst. Meas. Control.
**2019**, 41, 3132–3144. [Google Scholar] [CrossRef] - Fedele, G.; D’alfonso, L.; Chiaravalloti, F.; D’aquila, G. Obstacles Avoidance Based on Switching Potential Functions. J. Intell. Robot. Syst.
**2017**, 90, 387–405. [Google Scholar] [CrossRef] - Fan, X.; Guo, Y.; Liu, H.; Wei, B.; Lyu, W. Improved Artificial Potential Field Method Applied for AUV Path Planning. Math. Probl. Eng.
**2020**, 2020, 1–21. [Google Scholar] [CrossRef] - Jiang, L.; Liu, S.; Cui, Y.; Jiang, H. Path Planning for Robotic Manipulator in Complex Multi-Obstacle Environment Based on Improved_RRT. IEEE/ASME Trans. Mechatron.
**2022**, 27, 4774–4785. [Google Scholar] [CrossRef] - Li, F.-F.; Du, Y.; Jia, K.-J. Path planning and smoothing of mobile robot based on improved artificial fish swarm algorithm. Sci. Rep.
**2022**, 12, 659. [Google Scholar] [CrossRef] - Zelek, J.; Levine, M. Local-global concurrent path planning and execution. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum.
**2000**, 30, 865–870. [Google Scholar] [CrossRef] - Khatib, O. Real-Time Obstacle Avoidance for Manipulators and Mobile Robots. In Autonomous Robot Vehicles; Springer: New York, NY, USA, 1986; pp. 396–404. [Google Scholar]
- Chen, Y.; Bai, G.; Zhan, Y.; Hu, X.; Liu, J. Path Planning and Obstacle Avoiding of the USV Based on Improved ACO-APF Hybrid Algorithm With Adaptive Early-Warning. IEEE Access
**2021**, 9, 40728–40742. [Google Scholar] [CrossRef] - Szczepanski, R.; Tarczewski, T.; Erwinski, K. Energy Efficient Local Path Planning Algorithm Based on Predictive Artificial Potential Field. IEEE Access
**2022**, 10, 39729–39742. [Google Scholar] [CrossRef] - Hao, K.; Zhao, J.; Wang, B.; Liu, Y.; Wang, C. The Application of an Adaptive Genetic Algorithm Based on Collision Detection in Path Planning of Mobile Robots. Comput. Intell. Neurosci.
**2021**, 2021, 1–20. [Google Scholar] [CrossRef] [PubMed] - Stojaković, P.; Velimirović, K.; Rašuo, B. Power optimization of a single propeller airplane take-off run on the basis of lateral maneuver limitations. Aerosp. Sci. Technol.
**2018**, 72, 553–563. [Google Scholar] [CrossRef] - Stojakovic, P.; Rasuo, B. Single propeller airplane minimal flight speed based upon the lateral maneuver condition. Aerosp. Sci. Technol.
**2016**, 49, 239–249. [Google Scholar] [CrossRef] - Zheng, H.X.B. Trajectory Planning of Improved Artificial Potential Field Method. Electron. Opt. Control
**2023**, 30, 38–41. (In Chinese) [Google Scholar] - Luo, Q.; Wang, H.B.; Cui, X.; He, J.C. Autonomous Mobile Robot Path Planning Based on Improved Artificial Potential Method. Control Eng. China
**2019**, 26, 1091–1098. (In Chinese) [Google Scholar] - Long, Z. Virtual target point-based obstacle-avoidance method for manipulator systems in a cluttered environment. Eng. Optim.
**2019**, 52, 1957–1973. [Google Scholar] [CrossRef] - Luo, Q.; Wang, H.B.; Cui, X.; He, J.C. Robot Path Planning Based on Improved Potential Field Method. Comput. Sci.
**2022**, 49, 196–203. (In Chinese) [Google Scholar] - Zhao, L.; Yan, L.; Hu, X.; Yuan, J.; Liu, Z. Efficient and High Path Quality Autonomous Exploration and Trajectory Planning of UAV in an Unknown Environment. ISPRS Int. J. Geo-Inf.
**2021**, 10, 631. [Google Scholar] [CrossRef] - Duhé, J.-F.; Victor, S.; Melchior, P. ContribUtions on Artificial Potential Field Method for Effective Obstacle Avoidance. Fract. Calc. Appl. Anal.
**2021**, 24, 421–446. [Google Scholar] [CrossRef] - Battulwar, R.; Winkelmaier, G.; Valencia, J.; Naghadehi, M.Z.; Peik, B.; Abbasi, B.; Parvin, B.; Sattarvand, J. A Practical Methodology for Generating High-Resolution 3D Models of Open-Pit Slopes Using UAVs: Flight Path Planning and Optimization. Remote Sens.
**2020**, 12, 2283. [Google Scholar] [CrossRef]

Name | Symbol | Value |
---|---|---|

gravitational gain coefficient | k_{att} | 30 |

obstacle radius/m | d_{o} | 1 |

fixed step size/m | S_{t} | 0.1 |

Name | Symbol | Value |
---|---|---|

safe distance/m | d_{safe} | 1.3 |

detection distance/m | d_{pre} | 4.5 |

evaluation constants | α | 0.5 |

distance factor | n | 1.2 |

distance parameters | $\gamma $ | 16 |

Scenarios | Algorithm | Energy Consumption [kJ] | Path Length [m] | Iteration Number [N] |
---|---|---|---|---|

Scenario 1 | T-APF | - | - | - |

B-APF | 35.67 | 34.10 | 342 | |

IM-APF | 23.70 | 33.83 | 200 | |

Scenario 2 | T-APF | - | - | - |

B-APF | 31.27 | 27.20 | 273 | |

IM-APF | 21.10 | 27.06 | 156 | |

Scenario 3 | T-APF | - | - | - |

B-APF | 36.18 | 35.80 | 359 | |

IM-APF | 24.01 | 35.45 | 201 |

Scenarios | Algorithm | Energy Consumption [kJ] | Path Length [m] | Iteration Number [N] |
---|---|---|---|---|

Scenario 1 | T-APF | - | - | - |

B-APF | 21.13 | 20.6 | 203 | |

IM-APF | 13.78 | 20.20 | 116 | |

Scenario 2 | T-APF | - | - | - |

B-APF | 21.24 | 20.30 | 204 | |

IM-APF | 14.37 | 20.12 | 125 | |

Scenario 3 | T-APF | - | - | - |

B-APF | 35.67 | 34.60 | 347 | |

IM-APF | 23.78 | 34.32 | 196 |

Scenarios | Algorithm | Energy Consumption [kJ] | Path Length [m] | Iteration Number [N] |
---|---|---|---|---|

Scenario 1 | T-APF | 103.86 | 39.60 | 397 |

B-APF | 35.33 | 34.40 | 345 | |

IM-APF | 22.45 | 33.88 | 192 | |

Scenario 2 | T-APF | - | - | - |

B-APF | 35.64 | 35.40 | 355 | |

IM-APF | 22.98 | 34.20 | 196 | |

Scenario 3 | T-APF | 43.93 | 42 | 421 |

B-APF | 35.64 | 35.00 | 351 | |

IM-APF | 23.36 | 34.89 | 198 |

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**MDPI and ACS Style**

Hao, G.; Lv, Q.; Huang, Z.; Zhao, H.; Chen, W.
UAV Path Planning Based on Improved Artificial Potential Field Method. *Aerospace* **2023**, *10*, 562.
https://doi.org/10.3390/aerospace10060562

**AMA Style**

Hao G, Lv Q, Huang Z, Zhao H, Chen W.
UAV Path Planning Based on Improved Artificial Potential Field Method. *Aerospace*. 2023; 10(6):562.
https://doi.org/10.3390/aerospace10060562

**Chicago/Turabian Style**

Hao, Guoqiang, Qiang Lv, Zhen Huang, Huanlong Zhao, and Wei Chen.
2023. "UAV Path Planning Based on Improved Artificial Potential Field Method" *Aerospace* 10, no. 6: 562.
https://doi.org/10.3390/aerospace10060562