# Research on 2D Laser Automatic Navigation Control for Standardized Orchard

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. System Composition

^{2}of the regression equation of the left and right turn response curves of the test platform was 0.9938 and 0.9918, respectively, indicating that the system obtains the rotation angle as linear.

#### 2.2. Fruit Tree Position Information Determination

_{i}is the distance between the laser scanner’s emission point and the target. The λ

_{i}is the angle formed laser beam with the coordinate axis. The point (x

_{i}, y

_{i}) is the Cartesian coordinates of the i-th point scanned by the 2D laser.

_{i}. Its eigenvector is shown in Equation (2). Set the distance thresholds to ρ

_{max}and x

_{max}. If ρ

_{i}< ρ

_{max}and x

_{i}< x

_{max}, q

_{i}is retained. Otherwise it is eliminated.

_{i}is the Euclidean distance from point q

_{i}to any point. The D

_{avr-i}is the average distance of q

_{i}to all its k neighbors and the H

_{i}is the standard range of calculation.

_{i}. When D

_{avr-i}> H

_{i}, the point is regarded as a discrete point and culled. Otherwise it is retained.

_{i,i+1}is the Euclidean distance of the laser data points q

_{i}and q

_{i+1}. The cluster search radius is r and its value is related to the average radius of the fruit trees.

_{i,i+1}< r, we think that two points come from the same fruit tree and gather into one kind; when M

_{i,i+1}> r, we think that two points come from different fruit trees.

_{n}, λ

_{n}), the n consecutive data points of the trunk cluster are q

_{n}, the point with the smallest ρ value is selected as the feature point (ρ

_{min}, λ

_{min}) and the R

_{ave}is expressed as the average radius of the fruit tree trunk. The Equation (5) can be obtained through geometric derivation.

#### 2.3. Navigation Control Parameter Acquisition

_{li}, y

_{li}) and (x

_{ri}, y

_{ri}). In this experiment, the coordinates of the center points of the three fruit trees on the left and right sides of the vehicle are selected to form two groups, forming 9 groups. Use the following equation to find the midpoint coordinates (x

_{c}, y

_{c}).

#### 2.4. Navigation Controller Design

#### 2.4.1. Calculating the Target Front Wheel Angle

_{g}in the car body coordinate system can be obtained:

#### 2.4.2. Adaptive Pure Tracking Model Controller Design

_{d}was used as the output. The L

_{d}was adjusted in real time by the fuzzy controller. When d and θ were large, the smaller L

_{d}was used to make the vehicle approach the tracking path quickly, reduce the system adjustment time and improve the system response speed. When d and θ were small, a larger L

_{d}was used to prevent system overshoot and improve system stability.

_{d}= 0.12. The basic domain of the heading deviation θ was [−π/6, π/6], which is divided into 13 levels with quantization levels: {−6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6}, quantization factor K

_{θ}= 0.087. The basic domain of the forward-looking distance L

_{d}is [1 m, 6 m], which is divided into 6 levels, the quantization levels: {1, 2, 3, 4, 5, 6}, and the quantization factor K

_{Ld}= 1.

_{d}is divided into seven levels: very small (VS), small (S), little small (LS), medium (M), little big (LB), big (B), very big (VB). Then, the distribution of this fuzzy variable membership function can be seen in the following Figure 12.

## 3. Results and Discussion

#### 3.1. Path-Tracking Simulation Test

_{0}= 0.45 m/s and the fixed forward-looking distance 2 m, the initial position of the controlled object is (0 m, 0.1 m), the tracking distance is 30 m. Set two kinds of simulation tracking trajectories. The linear tracking path is shown in Equation (13), and the curve tracking path is shown in Equation (14). The path-tracking simulation results are shown in Figure 15.

#### 3.2. Feature Map and Navigation Parameter Acquisition Accuracy Test

_{max}= 10 m, x

_{max}= 2.5 m, the number of adjacent points k = 5. The laser point cloud figure after distance threshold processing was shown in Figure 17a; the laser point cloud figure after filter processing was shown in Figure 17b. As shown in Figure 17c, the red points were actual points of trunk, the black points were prediction points of trunk. The method of Section 2.3 was used to fit navigation path and obtain navigation control parameter, as show in Figure 17d.

^{2}of the navigation path was 0.988, which is close to 1. The results show that the method of extracting the navigation path was accurate and reliable.

#### 3.3. Path-Tracking Accuracy Test

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Zhao, Y.; Xiao, H.; Mei, S.; Song, Z.; Ding, W.; Jin, Y.; Hang, Y.; Xia, X.; Yang, G. Current status and development strategies of orchard mechanization production in China. J. Chin. Agric. Univ.
**2017**, 22, 116–127. [Google Scholar] - Gao, X.; Li, J.; Fan, L.; Zhou, Q.; Yin, K.; Wang, J.; Song, C.; Huang, L.; Wang, Z. Review of Wheeled Mobile Robots’ Navigation Problems and Application Prospects in Agriculture. IEEE Access
**2018**, 6, 49248–49268. [Google Scholar] [CrossRef] - Shamshiri, R.R.; Weltzien, C.; Hameed, I.A.; Yule, I.J.; Grift, T.E.; Balasundram, S.K.; Pitonakova, L.; Ahmad, D.; Chowdhary, G. Research and development in agricultural robotics: A perspective of digital farming. Int. J. Agric. Biol. Eng.
**2018**, 11, 1–14. [Google Scholar] [CrossRef] - Blok, P.M.; Van Boheemen, K.; Van Evert, F.K.; IJsselmuiden, J.; Kim, G.H. Robot navigation in orchards with localization based on Particle filter and Kalman filter. Comput. Electron. Agric.
**2019**, 157, 261–269. [Google Scholar] [CrossRef] - Radcliffe, J.; Cox, J.; Bulanon, D.M. Machine vision for orchard navigation. Comput. Ind.
**2018**, 98, 165–171. [Google Scholar] [CrossRef] - Ye, Y.; He, L.; Wang, Z.; Jones, D.; Hollinger, G.A.; Taylor, M.E.; Zhang, Q. Orchard manoeuvring strategy for a robotic bin-handling machine. Biosyst. Eng.
**2018**, 169, 85–103. [Google Scholar] [CrossRef] - Keicher, R.; Seufert, H. Automatic guidance for agricultural vehicles in Europe. Comput. Electron. Agric.
**2000**, 25, 169–194. [Google Scholar] [CrossRef] - Yayan, U.; Yucel, H.; Yazici, A. A Low Cost Ultrasonic Based Positioning System for the Indoor Navigation of Mobile Robots. J. Intell. Robot. Syst.
**2015**, 78, 541–552. [Google Scholar] [CrossRef] - Ortiz, B.V.; Balkcom, K.B.; Duzy, L.; Van Santen, E.; Hartzog, D.L. Evaluation of agronomic and economic benefits of using RTK-GPS-based auto-steer guidance systems for peanut digging operations. Precis. Agric.
**2013**, 14, 357–375. [Google Scholar] [CrossRef] - Yin, X.; Du, J.; Noguchi, N.; Yang, T.; Jin, C. Development of autonomous navigation system for rice transplanter. Int. J. Agric. Biol. Eng.
**2018**, 11, 89–94. [Google Scholar] [CrossRef] [Green Version] - Xiong, B.; Zhang, J.; Qu, F.; Fan, Z.; Wang, D.; Li, W. Navigation Control System for Orchard Spraying Machine Based on Beidou Navigation Satellite System. Trans. Chin. Soc. Agric. Mach.
**2017**, 48, 45–50. [Google Scholar] - Liu, L.; Mei, T.; Niu, R.; Wang, J.; Liu, Y.; Chu, S. RBF-Based Monocular Vision Navigation for Small Vehicles in Narrow Space below Maize Canopy. Appl. Sci.
**2016**, 6, 182. [Google Scholar] [CrossRef] [Green Version] - Bengochea-Guevara, J.M.; Conesa-Muñoz, J.; Andújar, D.; Ribeiro, A. Merge Fuzzy Visual serving and GPS-based planning to obtain a proper navigation behavior for a small crop-inspection robot. Sensors
**2016**, 16, 276. [Google Scholar] [CrossRef] - Matthies, L.; Kelly, A.; Litwin, T.; Tharp, G. Obstacle Detection for Unmanned Ground Vehicles: A Progress Report. In Proceedings of the Intelligent Vehicles 95 Symposium, Detroit, MI, USA, 25–26 September 1995; IEEE: Barcelona, Spain, 1995; pp. 66–71. [Google Scholar]
- Zhai, Z.; Zhu, Z.; Du, Y.; Song, Z.; Mao, E. Multi-crop-row detection algorithm based on binocular vision. Biosyst. Eng.
**2016**, 150, 89–103. [Google Scholar] [CrossRef] - Zhang, S.; Wang, Y.; Zhu, Z.; Li, Z.; Du, Y.; Mao, E. Tractor Path Tracking Control Based on Binocular Vision. Inf. Process. Agric.
**2018**, 5, 422–432. [Google Scholar] [CrossRef] - Milella, A.; Reina, G. 3D reconstruction and classification of natural environments by an autonomous vehicle using multi-baseline stereo. Intell. Serv. Robot.
**2014**, 7, 79–92. [Google Scholar] [CrossRef] - Zhao, H.; Shibasaki, R. Reconstructing a textured CAD model of an urban environment using vehicle-borne laser range scanners and line cameras. Mach. Vis. Appl.
**2003**, 14, 35–41. [Google Scholar] [CrossRef] - Narvaez, F.J.Y.; Del Pedregal, J.S.; Prieto, P.A.; Torres-Torriti, M.; Cheein, F.A.A. LiDAR and thermal images fusion for ground-based 3D characterisation of fruit trees. Biosyst. Eng.
**2016**, 151, 479–494. [Google Scholar] [CrossRef] - Wang, C.; Wang, J.; Li, C.; Ho, D.; Cheng, J.; Yan, T.; Meng, L.; Meng, M.Q.H. Safe and Robust Mobile Robot Navigation in Uneven Indoor Environments. Sensors
**2019**, 19, 2993. [Google Scholar] [CrossRef] [Green Version] - Asvadi, A.; Premebida, C.; Peixoto, P.; Nunes, U. 3D Lidar-based static and moving obstacle detection in driving environments: An approach based on voxels and multi-region ground planes. Robot. Auto Syst.
**2016**, 83, 299–311. [Google Scholar] [CrossRef] - Tuley, J.; Vandapel, N.; Hebert, M. Analysis and removal of artifacts in 3-D LADAR data. In Proceedings of the 2005 IEEE International Conference on Robotics and Automation (ICRA 2005), Barcelona, Spain, 18–22 April 2005; IEEE: Barcelona, Spain, 2005; pp. 2203–2210. [Google Scholar]
- Hrubos, M.; Nemec, D.; Janota, A.; Pirnik, R.; Bubenikova, E.; Gregor, M.; Juhasova, B.; Juhas, M. Sensor fusion for creating a three-dimensional model for mobile robot navigation. Int. J. Adv. Robot. Syst.
**2019**, 16, 1–12. [Google Scholar] [CrossRef] - Zhao, T.; Noguchi, N.; Yang, L.; Ishii, K.; Chen, J. Development of uncut crop edge detection system based on laser rangefinder for combine harvesters. Int. J. Agric. Biol. Eng.
**2016**, 9, 21–28. [Google Scholar] - Barawid, O.C.; Mizushima, A.; Ishii, K.; Noguchi, N. Development of an Autonomous Navigation System using a Two-dimensional Laser Scanner in an Orchard Application. Biosyst. Eng.
**2007**, 96, 139–149. [Google Scholar] [CrossRef] - Liu, P.; Chen, J.; Zhang, M. Automatic control system of orchard tractor based on laser navigation. Trans. Chin. Soc. Agric. Eng.
**2011**, 27, 196–199. [Google Scholar] - Chen, J.; Jiang, H.; Liu, P.; Zhang, Q. Navigation Control for Orchard Mobile Robot in Curve Path. Trans. Chin. Soc. Agric. Mach.
**2012**, 43, 179–182+187. [Google Scholar] - Thanpattranon, P.; Ahamed, T.; Takigawa, T. Navigation of autonomous tractor for orchards and plantations using a laser range finder: Automatic control of trailer position with tractor. Biosyst. Eng.
**2016**, 147, 90–103. [Google Scholar] [CrossRef] - Bayar, G.; Bergerman, M.; Koku, A.B.; Konukseven, E.I. Localization and control of an autonomous orchard vehicle. Comput. Electron. Agric.
**2015**, 115, 118–128. [Google Scholar] [CrossRef] [Green Version] - Kukko, A.; Kaasalainen, S.; Litkey, P. Effect of incidence angle on laser scanner intensity and surface data. Appl. Optics.
**2008**, 47, 986–992. [Google Scholar] [CrossRef] - Soudarissanane, S.; Lindenbergh, R.; Menenti, M.; Teunissen, P. Scanning geometry: Influencing factor on the quality of terrestrial laser scanning points. ISPRS J. Photogramm. Remote Sens.
**2011**, 66, 389–399. [Google Scholar] [CrossRef] - Lichti, D.D.; Harvey, B.R. The effects of reflecting surface properties on time-off light laser scanner measurements. In Geospatial Theory, Processing and Applications; ISPRS: Ottawa, ON, Canada, 2002; Volume XXXIV, Part 4-IV. [Google Scholar]
- Voegtle, T.; Schwab, I.; Landes, T. Influences of different materials on the measurements of a terrestrial laser scanner (TLS). In Proceedings of the International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Beijing, China, 3–11 July 2008; Volume XXXVII, Part B5. pp. 1061–1066. [Google Scholar]
- Urbančič, T.; Koler, B.; Stopar, B.; Kosmatin Fras, M. Quality analysis of the sphere parameters determination in terrestrial laser scanning. Geod. Vestn.
**2014**, 58, 11–27. [Google Scholar] [CrossRef] - Ai, C.; Lin, H.; Wu, D.; Feng, Z. Path planning algorithm for plant protection robots in vineyard. Trans. Chin. Soc. Agric. Eng.
**2018**, 34, 77–85. [Google Scholar] - Xue, J.; Zhang, S. Navigation of an Agricultural Robot Based on Laser Radar. Trans. Chin. Soc. Agric. Mach.
**2014**, 45, 55–60. [Google Scholar] - Zhang, C.; Yong, L.; Chen, Y.; Zhang, S.; Ge, L.; Wang, S.; Li, W. A Rubber-Tapping Robot Forest Navigation and Information Collection System Based on 2D LiDAR and a Gyroscope. Sensors
**2019**, 19, 2136. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kayacan, E.; Kayacan, E.; Ramon, H.; Saeys, W. Towards agrobots: Identification of the yaw dynamics and trajectory tracking of an autonomous tractor. Comput. Electron. Agric.
**2015**, 115, 78–87. [Google Scholar] [CrossRef] [Green Version] - Xue, J.; Zhang, L.; Grift, T.E. Variable field-of-view machine vision based row guidance of an agricultural robot. Comput. Electron. Agric.
**2012**, 84, 85–91. [Google Scholar] [CrossRef] - Zhang, S.; Liu, J.; Du, Y.; Zhu, Z.; Mao, E.; Song, Z. Method on automatic navigation control of tractor based on speed adaptation. Trans. Chin. Soc. Agric. Eng.
**2017**, 33, 48–55. [Google Scholar] - Conlter, R.C. Implementation of the Pure Pursuit Path Tracking Algorithm: Technical Report; Camegie Mellon University: Pittsburgh, PA, USA, 1992. [Google Scholar]
- Liu, J.K. Intelligent Control, 4th ed.; Electronic Industry Press: Beijing, China, 2017; pp. 39–41. [Google Scholar]

**Figure 1.**Test platform composition: (

**A**) 2D laser; (

**B**) Stm32F103; (

**C**): automatic travel switches; (

**D**) main controller PC; (

**E**) tracking device; (

**F**) 121 power supply; (

**G**) steering system; (

**H**) front wheel angle system.

**Figure 6.**Laser data interference point type: (

**a**) laser data cross-line interference point, (

**b**) orbital noise between orchards.

**Figure 10.**Vehicle kinematics model. Note: M (x

_{r}, y

_{r}) and N (x

_{f}, y

_{f}) are the coordinates of the axle of the rear axle and the front axle of the vehicle respectively; P is the instantaneous steering center of the vehicle; Φ is the heading angle of the current position of the vehicle (rad); δ is the front turning angle (rad); v

_{r}is the center speed of the rear axle of the vehicle (m·s

^{−1}); v

_{f}is the center speed of the front axle of the vehicle (m·s

^{−1}); l is the wheelbase (m); R is the turning radius of the vehicle (m).

**Figure 11.**Pure pursuit model. Note: S is the navigation tracking path; G (x

_{g}, y

_{g}) is the target point on the path; O is the turning center; γ is the turning rate of the vehicle (m

^{−1}); L

_{d}is the forward looking distance (m); R is the instantaneous turning radius (m); d is Lateral deviation (m); θ is the heading deviation (rad); v is the forward speed of the vehicle (m·s

^{−1}); l is the vehicle wheelbase (m); δ is the front wheel angle (rad); Ψ is the angle of course change when the vehicle reaches the target point along the steering arc (rad).

**Figure 12.**The distribution of the membership function. (

**a**) lateral deviation membership function expression. (

**b**) heading deviation membership function expression. (

**c**) forward-viewing distance membership function expression.

**Figure 15.**Simulation results test charts. (

**a**) Straight path-tracking simulation results. (

**b**) Curved path-tracking simulation results. (

**c**) Linear path-tracking simulation error graph. (

**d**) Curved path-tracking simulation error graph.

**Figure 17.**Navigation path acquisition process. (

**a**) laser point cloud image after distance threshold processing. (

**b**) laser point cloud image after statistical filtering. (

**c**) feature map of center point of fruit tree trunk. (

**d**) navigation path fit results.

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

Light source | Semiconductor laser (905 nm) |

Measuring range | 0.06 (m)–8 (m) Maximum detection distance 60 (m) |

Ranging accuracy | 40 (mm) |

Angular resolution | 0.25° |

Maximum scanning range | 270° |

Scanning period | 25 (ms) |

θ | d | ||||||
---|---|---|---|---|---|---|---|

LB | LM | LS | Z | RS | RM | RB | |

LB | VS | S | S | VS | S | S | VS |

LM | VS | LS | M | LS | M | M | VS |

LS | VS | M | LB | LB | LB | M | VS |

Z | VS | LB | VB | VB | VB | LB | VS |

RS | VS | M | LB | LB | LB | M | VS |

RM | VS | LS | M | LS | M | LS | VS |

RB | VS | S | S | VS | LS | S | VS |

L_{d} (m) | d (m) | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

−6 | −5 | −4 | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||

θ (rad) | −6 | 1.38 | 1.38 | 1.70 | 2.25 | 2.25 | 2.06 | 1.38 | 2.06 | 2.25 | 2.25 | 1.70 | 1.38 | 1.38 |

−5 | 1.38 | 1.38 | 1.70 | 2.25 | 2.25 | 2.06 | 1.38 | 2.06 | 2.25 | 2.25 | 1.70 | 1.38 | 1.38 | |

−4 | 1.43 | 1.43 | 1.72 | 2.27 | 2.30 | 2.05 | 1.46 | 2.05 | 2.29 | 2.28 | 1.74 | 1.43 | 1.43 | |

−3 | 1.39 | 1.39 | 1.95 | 3.00 | 3.34 | 3.40 | 3.00 | 3.40 | 3.50 | 3.50 | 2.12 | 1.39 | 1.39 | |

−2 | 1.46 | 1.46 | 2.34 | 3.26 | 3.57 | 3.57 | 3.51 | 3.57 | 3.76 | 3.50 | 2.24 | 1.46 | 1.46 | |

−1 | 1.39 | 1.39 | 2.37 | 3.58 | 4.28 | 4.32 | 4.31 | 4.32 | 4.28 | 3.58 | 2.37 | 1.39 | 1.39 | |

0 | 1.38 | 1.38 | 2.28 | 4.00 | 5.05 | 5.61 | 5.62 | 5.61 | 5.05 | 4.00 | 2.28 | 1.38 | 1.38 | |

1 | 1.39 | 1.39 | 2.37 | 3.58 | 4.28 | 4.32 | 4.31 | 4.32 | 4.28 | 3.58 | 2.37 | 1.39 | 1.39 | |

2 | 1.46 | 1.46 | 2.34 | 3.26 | 3.57 | 3.57 | 3.51 | 3.57 | 3.57 | 3.26 | 2.34 | 1.46 | 1.46 | |

3 | 1.39 | 1.39 | 1.95 | 3.00 | 3.34 | 3.40 | 3.00 | 3.40 | 3.34 | 3.00 | 1.95 | 1.39 | 1.39 | |

4 | 1.43 | 1.43 | 1.72 | 2.27 | 2.30 | 2.05 | 1.46 | 2.54 | 2.75 | 2.27 | 1.72 | 1.43 | 1.43 | |

5 | 1.38 | 1.38 | 1.70 | 2.25 | 2.25 | 2.06 | 1.38 | 2.61 | 2.74 | 2.25 | 1.70 | 1.38 | 1.38 | |

6 | 1.38 | 1.38 | 1.70 | 2.25 | 2.25 | 2.06 | 1.38 | 2.61 | 2.74 | 2.25 | 1.70 | 1.38 | 1.38 |

Serial Number | θ (°) | Δd (cm) | ||
---|---|---|---|---|

Actual Value | Measurements | Error | ||

1 | −30 | −30.13 | 0.13 | 2.75 |

2 | −25 | −25.40 | −0.40 | −2.18 |

3 | −20 | −19.09 | −0.91 | 1.62 |

4 | −15 | −14.34 | −0.66 | 1.04 |

5 | −10 | −10.57 | 0.57 | −2.00 |

6 | −5 | −5.88 | 0.88 | −2.14 |

7 | 0 | 0.89 | 0.89 | 4.66 |

8 | 5 | 4.45 | −0.55 | −1.06 |

9 | 10 | 10.58 | 0.58 | −1.14 |

10 | 15 | 14.24 | −0.76 | 2.88 |

11 | 20 | 19.05 | −0.95 | −2.71 |

12 | 25 | 24.17 | −0.83 | 2.20 |

13 | 30 | 30.75 | 0.75 | −1.17 |

MAD (m) | 0.682 | 2.119 | ||

SD (m) | 0.237 | 1.010 |

Number | Maximum Deviation (m) | AVG Deviation (m) | SD Deviation (m) |
---|---|---|---|

1 | 0.09 | 0.05 | 0.05 |

2 | 0.13 | 0.08 | 0.04 |

3 | −0.07 | −0.04 | 0.03 |

4 | −0.10 | 0.04 | 0.03 |

5 | 0.09 | −0.03 | 0.02 |

MAD (m) | 0.096 | 0.048 | 0.034 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, S.; Guo, C.; Gao, Z.; Sugirbay, A.; Chen, J.; Chen, Y.
Research on 2D Laser Automatic Navigation Control for Standardized Orchard. *Appl. Sci.* **2020**, *10*, 2763.
https://doi.org/10.3390/app10082763

**AMA Style**

Zhang S, Guo C, Gao Z, Sugirbay A, Chen J, Chen Y.
Research on 2D Laser Automatic Navigation Control for Standardized Orchard. *Applied Sciences*. 2020; 10(8):2763.
https://doi.org/10.3390/app10082763

**Chicago/Turabian Style**

Zhang, Shuo, Chengyang Guo, Zening Gao, Adilet Sugirbay, Jun Chen, and Yu Chen.
2020. "Research on 2D Laser Automatic Navigation Control for Standardized Orchard" *Applied Sciences* 10, no. 8: 2763.
https://doi.org/10.3390/app10082763