# Autonomous Surveying of Plantation Forests Using Multi-Rotor UAVs

^{*}

## Abstract

**:**

## 1. Introduction

- A method for online waypoint placement for autonomous coverage planning in plantation forests
- A nonlinear optimization-based trajectory generation method to rapidly plan constant-speed, dynamically feasible, and safe trajectories within complex environments
- Experimental flight testing results in both simulation and a local plantation forest to verify the proposed method

## 2. Materials and Methods

#### 2.1. Waypoint Generation

**j**, ${n}_{j}$ denotes the number of trees in cluster j, ${n}_{v}$ denotes the number of clusters with more than five trees, and ${n}_{c}$ denotes the number of clusters. Since row estimates are generated based on identified cluster information, the accuracy of the $\theta $ estimate does not need to be high. Because this work does not consider initial traversal to the survey starting location, an assumption is made that the inertial frame $\left\{{I}_{x}\right\}$ is approximately aligned with the row direction. Therefore, a coarse search is performed for $\theta \in [-{30}^{\circ},{30}^{\circ}]$ in 1° increments. The cluster labels from the minimum cost $\theta $ value are used to label the unmodified tree locations

**C**, resulting in clusters of tree locations corresponding to independent rows. Finally, a least-squares fit is used to determine the estimated rows present within the scene and converted into the $r,\theta $ representation, as shown in Equations (3) and (4).

**A**x =

**B**

#### 2.2. Trajectory Generation

^{N-1}continuity, and the strong convex hull property. A degree 3 B-Spline guarantees C

^{2}continuity at all points, which means that the trajectory is guaranteed to be continuous up to the 2nd derivative. The convex hull property also guarantees that any points of the spline will fall within the convex hull formed by the neighboring control points. Specifically, if $t\in [{t}_{i},{t}_{i}+1)$, all points in that piecewise portion of the B-Spline are contained entirely in the convex hull formed by control points ${P}_{i-2},{P}_{i-1},{P}_{i}$. These properties greatly simplify the enforcement of collision constraints and dynamic limits.

^{2}continuous, the velocity at any point can be determined by inspecting the derivative of the B-Spline. The control point defining the velocity profile at index i can be computed based on the position control points ${\mathit{P}}_{i}$ and ${\mathit{P}}_{i+1}$ using the derivative of the position B-Spline. Because the convex hull property similarly constrains the velocity B-Spline, the profile’s maximum velocity is also constrained by the magnitude of the velocity control points. The velocity control points are defined by:

#### 2.3. Trajectory Following

#### 2.4. Runtime

## 3. Simulation Tests

#### 3.1. Branching

#### 3.2. Slope and Roughness

**Ax**=

**b**be an over-constrained system

#### 3.3. Simulation Environments

#### 3.4. Survey Time

#### 3.5. Coverage

#### 3.6. Effects of Survey Speed

#### 3.7. Comparison to Existing Methods

## 4. Flight Tests

- Attempted corridors—the number of identified corridors and an attempt to traverse these corridors have been made
- Completed corridors—the number of correctly traversed corridors

#### 4.1. Large Flights

#### 4.2. Small Flights

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Deadman, M.W.; Goulding, C.J. A method for assessment of recoverable volume by log types. N. Z. J. For. Sci.
**1979**, 9, 225–239. [Google Scholar] - Interpine Innovation. PlotSafe Overlapping Feature Crusing Forest Inventory Procedures; Interpine Innovation: Rotorua, New Zealand, 2007; p. 49. [Google Scholar]
- Hudak, A.T.; Crookston, N.L.; Evans, J.S.; Hall, D.E.; Falkowski, M.J. Nearest neighbor imputation of species-level, plot-scale forest structure attributes from LiDAR data. Remote Sens. Environ.
**2008**, 112, 2232–2245. [Google Scholar] [CrossRef] - Puliti, S.; Dash, J.P.; Watt, M.S.; Breidenbach, J.; Pearse, G.D. A comparison of UAV laser scanning, photogrammetry and airborne laser scanning for precision inventory of small-forest properties. For. Int. J. For. Res.
**2020**, 93, 150–162. [Google Scholar] [CrossRef] - Mielcarek, M.; Kamińska, A.; Stereńczak, K. Digital Aerial Photogrammetry (DAP) and Airborne Laser Scanning (ALS) as Sources of Information about Tree Height: Comparisons of the Accuracy of Remote Sensing Methods for Tree Height Estimation. Remote Sens.
**2020**, 12, 1808. [Google Scholar] [CrossRef] - Bauwens, S.; Bartholomeus, H.; Calders, K.; Lejeune, P. Forest inventory with terrestrial LiDAR: A comparison of static and hand-held mobile laser scanning. Forests
**2016**, 7, 127. [Google Scholar] [CrossRef] - Kukko, A.; Kaijaluoto, R.; Kaartinen, H.; Lehtola, V.V.; Jaakkola, A.; Hyyppä, J. Graph SLAM correction for single scanner MLS forest data under boreal forest canopy. ISPRS J. Photogramm. Remote Sens.
**2017**, 132, 199–209. [Google Scholar] [CrossRef] - Wang, Y.; Kukko, A.; Hyyppä, E.; Hakala, T.; Pyörälä, J.; Lehtomäki, M.; El Issaoui, A.; Yu, X.; Kaartinen, H.; Liang, X.; et al. Seamless integration of above- and under-canopy unmanned aerial vehicle laser scanning for forest investigation. For. Ecosyst.
**2021**, 8, 10. [Google Scholar] [CrossRef] - Hyyppä, E.; Hyyppä, J.; Hakala, T.; Kukko, A.; Wulder, M.A.; White, J.C.; Pyörälä, J.; Yu, X.; Wang, Y.; Virtanen, J.P.; et al. Under-canopy UAV laser scanning for accurate forest field measurements. ISPRS J. Photogramm. Remote Sens.
**2020**, 164, 41–60. [Google Scholar] [CrossRef] - Hyyppä, J.; Yu, X.; Hakala, T.; Kaartinen, H.; Kukko, A.; Hyyti, H.; Muhojoki, J.; Hyyppä, E. Under-Canopy UAV Laser Scanning Providing Canopy Height and Stem Volume Accurately. Forests
**2021**, 12, 856. [Google Scholar] [CrossRef] - Del Perugia, B.; Krisanski, S.; Taskhiri, M.S.; Turner, P. Below-canopy UAS photogrammetry for stem measurement in radiata pine plantation. Proc. Remote Sens. Agric. Ecosyst. Hydrol.
**2018**, 11, 1078309. [Google Scholar] [CrossRef] - Krisanski, S.; Taskhiri, M.S.; Turner, P. Enhancing Methods for Under-Canopy Unmanned Aircraft System Based Photogrammetry in Complex Forests for Tree Diameter Measurement. Remote Sens.
**2020**, 12, 1652. [Google Scholar] [CrossRef] - Kuželka, K.; Surový, P. Mapping Forest Structure Using UAS inside Flight Capabilities. Sensors
**2018**, 18, 2245. [Google Scholar] [CrossRef] [PubMed] - Jiang, S. Towards Autonomous Flights of an Unmanned Aerial Vehicle (UAV) in Plantation Forests. Master’s Thesis, The University of Auckland, Auckland, New Zealand, 2016. [Google Scholar]
- Chiella, A.C.B.; Machado, H.N.; Teixeira, B.O.S.; Pereira, G.A.S. GNSS/LiDAR-Based Navigation of an Aerial Robot in Sparse Forests. Sensors
**2019**, 19, 4061. [Google Scholar] [CrossRef] - Chisholm, R.A.; Cui, J.; Lum, S.K.Y.; Chen, B.M. UAV LiDAR for below-canopy forest surveys. J. Unmanned Veh. Syst.
**2013**, 1, 61–68. [Google Scholar] [CrossRef] - Cui, J.Q.; Lai, S.; Dong, X.; Liu, P.; Chen, B.M.; Lee, T.H. Autonomous navigation of UAV in forest. In Proceedings of the 2014 International Conference on Unmanned Aircraft Systems, ICUAS 2014—Conference Proceedings, Orlando, FL, USA, 27–30 May 2014. [Google Scholar] [CrossRef]
- Thrun, S.; Montemerlo, M. The graph SLAM algorithm with applications to large-scale mapping of urban structures. Int. J. Robot. Res.
**2006**, 25, 403–429. [Google Scholar] [CrossRef] - Zucker, M.; Ratliff, N.; Dragan, A.D.; Pivtoraiko, M.; Klingensmith, M.; Dellin, C.M.; Bagnell, J.A.; Srinivasa, S.S. CHOMP: Covariant Hamiltonian optimization for motion planning. Int. J. Robot. Res.
**2013**, 32, 1164–1193. [Google Scholar] [CrossRef] - Oleynikova, H.; Burri, M.; Taylor, Z.; Nieto, J.; Siegwart, R.; Galceran, E. Continuous-time trajectory optimization for online UAV replanning. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems 2016, Daejeon, Korea, 9–14 October 2016; pp. 5332–5339. [Google Scholar] [CrossRef]
- Usenko, V.; Von Stumberg, L.; Pangercic, A.; Cremers, D. Real-time trajectory replanning for MAVs using uniform B-splines and a 3D circular buffer. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Vancouver, BC, Canada, 24–28 September 2017; pp. 215–222. [Google Scholar] [CrossRef]
- Zhou, B.; Pan, J.; Gao, F.; Shen, S. RAPTOR: Robust and Perception-Aware Trajectory Replanning for Quadrotor Fast Flight. IEEE Trans. Robot.
**2021**, 37, 1992–2009. [Google Scholar] [CrossRef] - Mellinger, D.; Kumar, V. Minimum snap trajectory generation and control for quadrotors. In Proceedings of the IEEE International Conference on Robotics and Automation, Shanghai, China, 9–13 May 2011; pp. 2520–2525. [Google Scholar] [CrossRef]
- Tordesillas, J.; Lopez, B.T.; How, J.P. FASTER: Fast and Safe Trajectory Planner for Flights in Unknown Environments. In Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Macau, China, 3–8 November 2019; pp. 1934–1940. [Google Scholar] [CrossRef]
- Deits, R.; Tedrake, R. Efficient mixed-integer planning for UAVs in cluttered environments. In Proceedings of the IEEE International Conference on Robotics and Automation, Seattle, WA, USA, 26–30 May 2015; pp. 42–49. [Google Scholar] [CrossRef]
- Gao, F.; Wang, L.; Zhou, B.; Zhou, X.; Pan, J.; Shen, S. Teach-Repeat-Replan: A Complete and Robust System for Aggressive Flight in Complex Environments. IEEE Trans. Robot.
**2020**, 36, 1526–1545. [Google Scholar] [CrossRef] - Meng, Z.; Qin, H.; Chen, Z.; Chen, X.; Sun, H.; Lin, F.; Ang, M.H. A Two-Stage Optimized Next-View Planning Framework for 3-D Unknown Environment Exploration, and Structural Reconstruction. IEEE Robot. Autom. Lett.
**2017**, 2, 1680–1687. [Google Scholar] [CrossRef] - Zhou, B.; Zhang, Y.; Chen, X.; Shen, S. FUEL: Fast UAV Exploration using Incremental Frontier Structure and Hierarchical Planning. IEEE Robot. Autom. Lett.
**2021**, 6, 779–786. [Google Scholar] [CrossRef] - Dharmadhikari, M.; Dang, T.; Solanka, L.; Loje, J.; Nguyen, H.; Khedekar, N.; Alexis, K. Motion Primitives-based Path Planning for Fast and Agile Exploration using Aerial Robots. In Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France, 31 May–31 August 2020; pp. 179–185. [Google Scholar] [CrossRef]
- Bircher, A.; Kamel, M.; Alexis, K.; Oleynikova, H.; Siegwart, R. Receding Horizon “Next-Best-View” Planner for 3D Exploration. In Proceedings of the 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, 16–21 May 2016; pp. 1462–1468. [Google Scholar] [CrossRef]
- Schmid, L.; Pantic, M.; Khanna, R.; Ott, L.; Siegwart, R.; Nieto, J. An Efficient Sampling-Based Method for Online Informative Path Planning in Unknown Environments. IEEE Robot. Autom. Lett.
**2020**, 5, 1500–1507. [Google Scholar] [CrossRef] - Papachristos, C.; Khattak, S.; Alexis, K. Uncertainty-aware receding horizon exploration and mapping using aerial robots. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 29 May–3 June 2017; pp. 4568–4575. [Google Scholar] [CrossRef]
- Xu, Z.; Deng, D.; Shimada, K. Autonomous UAV Exploration of Dynamic Environments Via Incremental Sampling and Probabilistic Roadmap. IEEE Robot. Autom. Lett.
**2021**, 6, 2729–2736. [Google Scholar] [CrossRef] - Lin, T.J.; Stol, K.A. Faster Navigation of Semi-Structured Forest Environments using Multi-Rotor UAVs. Robotica
**2022**. submitted. [Google Scholar] - Stanford Artificial Intelligence Laboratory. Robotic Operating System. Available online: https://www.ros.org (accessed on 15 June 2022).
- Lin, J.; Zhang, F. R3LIVE: A Robust, Real-Time, RGB-Colored, LiDAR-Inertial-Visual Tightly-Coupled State Estimation and Mapping Package. In Proceedings of the 2022 International Conference on Robotics and Automation (ICRA), Philadelphia, PA, USA, 23–27 May 2022; pp. 10672–10678. [Google Scholar] [CrossRef]
- Zhang, W.; Qi, J.; Peng, W.; Wang, H.; Xie, D.; Wang, X.; Yan, G. An Easy-to-Use Airborne LiDAR Data Filtering Method Based on Cloth Simulation. Remote Sens.
**2016**, 8, 501. [Google Scholar] [CrossRef] - Ester, M.; Kriegel, H.P.; Sander, J.; Xu, X. A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise; AAAI Press: Palo Alto, CA, USA, 1996; pp. 226–231. [Google Scholar]
- Han, L.; Gao, F.; Zhou, B.; Shen, S. FIESTA: Fast Incremental Euclidean Distance Fields for Online Motion Planning of Aerial Robots. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Macau, China, 3–8 November 2019; pp. 4423–4430. [Google Scholar] [CrossRef]
- Hart, P.E.; Nilsson, N.J.; Raphael, B. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Trans. Syst. Sci. Cybern.
**1968**, 4, 100–107. [Google Scholar] [CrossRef] - Agarwal, S.; Mierle, K.; Team, T.C.S. Ceres Solver. Available online: https://github.com/ceres-solver/ceres-solver (accessed on 15 June 2022).
- Lin, T.J.; Stol, K.A. Fast Trajectory Tracking of Multi-Rotor UAVs using First-Order Model Predictive Control. In Proceedings of the 2021 Australian Conference on Robotics and Automation (ACRA), Melbourne, Australia, 6–8 December 2021. [Google Scholar]
- Houska, B.; Ferreau, H.J.; Diehl, M. ACADO toolkit—An open-source framework for automatic control and dynamic optimization. Optim. Control Appl. Methods
**2011**, 32, 298–312. [Google Scholar] [CrossRef] - Perlin, K. An Image Synthesizer. In Proceedings of the SIGGRAPH ’85: 12th Annual Conference on Computer Graphics and Interactive Techniques, San Francisco, CA, USA, 22–26 July 1985; Association for Computing Machinery: New York, NY, USA, 1985; pp. 287–296. [Google Scholar] [CrossRef]

**Figure 1.**Examples of plantation forests which are (

**a**) traversable, and (

**b**) untraversable on foot in Kaingaroa Forest, Rotorua, New Zealand. Note the presence of an available flight corridor in both environments.

**Figure 2.**UAV used for flight testing. The carried payload consists of a Livox MID-70 LiDAR, Intel Realsense T265, and an Intel NUC. The body and inertial frames are denoted as $\left\{B\right\}$ and $\left\{I\right\}$ respectively.

**Figure 3.**Overall task flow during the survey process. Pose estimation and mapping are not within the scope of this work.

**Figure 4.**Horizontal slice of a point cloud in a typical New Zealand plantation forest with rows labeled. Note the lack of consistent structure in the orthogonal direction.

**Figure 6.**Top-down views of (

**a**) good, and (

**b**) poor alignment between $\left\{{I}_{X}\right\}$ and the principle row directions of the plantation forest.

**Figure 7.**Sample environment consisting of two rows with $r,\theta $ labeled. The dotted yellow line denotes the traversable corridor.

**Figure 9.**Worst case B-Spline collision scenario with degree 3. The trajectory is guaranteed to be collision-free if the three convex hulls shown in blue, orange, and green are obstacle free.

**Figure 10.**Top down view of a typical replanning event, showing the elements of a newly observed obstacle and a splice event.

**Figure 11.**Simplified version of the forward paths of the cascaded multi-rotor controller with unified and airframe-specific portions highlighted.

**Figure 13.**Illustration of parameters modeled in Table 1.

**Figure 14.**Simulation test environments. The three numbers in the subfigure captions correspond to the branching, roughness, and slope metrics.

**Figure 15.**Summary of survey time for each test environment. Trials that did not produce full coverage are not included. Circles denote outliers in the survey time.

**Figure 19.**Averaged coverage maps for trials in environments (

**a**–

**h**), normalized to the maximum of each specific sample. Blue hues indicate trees with fewer observed points, and green hues indicate more observed points. Non-uniformity is shown as the difference in hues.

**Figure 20.**Effects on survey time (

**left**) and coverage (

**right**) with varying speed. Exponential fit through all results is shown as a red line.

**Figure 21.**Plot of mean speed vs. target survey speed. Note the plateau in mean speed at 3 m/s and 4 m/s. The averaged mean speed across all samples for each target speed is indicated by a horizontal line.

**Figure 23.**(

**a**) Single row view of the plantation site used for flight testing, note the presence of some low-hanging branches, and (

**b**) 3D scan of the proposed test site showing the survey region; the scan area is approx. 25 m by 30 m.

**Figure 24.**Simplified views of the large-scale test flights (

**a**–

**d**), the path followed is shown as a solid line overlaid with stem locations within the environment. Greener hues indicate a flight speed closer to the 1 m/s target speed, while red hues indicate slower speeds taken.

**Figure 25.**Top-down views of large-scale test flights (

**a**–

**d**), with the path taken overlaid on the reconstructed point cloud.

**Figure 27.**Top-down views of path taken during small-scale test flights (

**a**–

**f**) overlaid on the reconstructed point clouds. The path taken during the survey is shown as the line.

Parameter | Distribution Type | Mean(m)/a | SD(m)/b |
---|---|---|---|

Row spacing (m) | Gaussian | 4.42 | 0.37 |

Row deviation (m) | Gaussian | 0.01 | 0.78 |

Tree spacing (m) | Gamma | 2.61 | 2.24 |

Branch length (Low-branching) (m) | Gamma | 2.94 | 0.37 |

Branch length (High-branching) (m) | Gamma | 7.31 | 0.37 |

Branch height (m) | Gaussian | 4.76 | 1.01 |

Branch Elevation Angle (rad) | Gaussian | 0.23 | 0.62 |

Tree diameter (m) | Gaussian | 0.52 | 0.14 |

**Table 2.**Summary of parameters of the generated forest environments shown in Figure 14.

Label | Branching | Roughness | Slope | Type |
---|---|---|---|---|

(a) | 44.1 | 0.074 | 0.120 | High Branching |

(b) | 38.4 | 3.19 | 0.192 | Mixed Difficult |

(c) | 6.68 | 1.30 | 0.154 | Mixed Medium |

(d) | 6.66 | 0.081 | 0.134 | Medium Slope |

(e) | 6.45 | 1.55 | 0.122 | Medium Roughness |

(f) | 6.91 | 0.065 | 0.255 | High Slope |

(g) | 6.57 | 3.57 | 0.103 | High Roughness |

(h) | 6.48 | 0.079 | 0.076 | Baseline |

Label | Trails | Incomplete | Mean (s) | SD (s) | Min (s) | Max (s) |
---|---|---|---|---|---|---|

(a) | 26 | 4 | 143 | 10.0 | 123 | 163 |

(b) | 26 | 11 | 147 | 16.9 | 112 | 173 |

(c) | 28 | 1 | 137 | 5.2 | 121 | 144 |

(d) | 30 | 0 | 136 | 4.5 | 125 | 141 |

(e) | 30 | 0 | 139 | 1.5 | 133 | 142 |

(f) | 28 | 0 | 138 | 2.3 | 133 | 141 |

(g) | 29 | 0 | 139 | 3.7 | 133 | 144 |

(h) | 26 | 0 | 134 | 1.7 | 127 | 136 |

Theoretical Minimum * | - | 0 | 120 | 0 | 120 | - |

Label | Mean (s) | SD (s) | Min (s) | Max (s) |
---|---|---|---|---|

(a) | 2055 | 687 | 1099 | 3453 |

(b) | 757 | 492 | 139 | 2218 |

(c) | 1477 | 600 | 532 | 2629 |

(d) | 1188 | 748 | 137 | 3551 |

(e) | 1830 | 797 | 707 | 3894 |

(f) | 1540 | 617 | 631 | 3044 |

(g) | 1094 | 289 | 435 | 1500 |

(h) | 1625 | 682 | 699 | 3400 |

Label | Attempted | Completed | Survey Time (s) | Return Time (s) |
---|---|---|---|---|

(a) | 3 | 2 | 114.5 | - |

(b) | 4 | 3 | 135.5 | 25.5 |

(c) | 4 | 4 | 106.4 | 18.7 |

(d) | 5 | 5 | 157.8 | - |

Label | Attempted | Completed | Survey Time (s) | Return Time (s) |
---|---|---|---|---|

(a) | 3 | 3 | 49.8 | 15.3 |

(b) | 3 | 3 | 66.7 | 20.4 |

(c) | 3 | 3 | 61.8 | 20.2 |

(d) | 3 | 3 | 62.9 | 23.1 |

(e) | 3 | 3 | 52.6 | 20.4 |

(f) | 3 | 3 | 69.7 | - |

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**MDPI and ACS Style**

Lin, T.-J.; Stol, K.A.
Autonomous Surveying of Plantation Forests Using Multi-Rotor UAVs. *Drones* **2022**, *6*, 256.
https://doi.org/10.3390/drones6090256

**AMA Style**

Lin T-J, Stol KA.
Autonomous Surveying of Plantation Forests Using Multi-Rotor UAVs. *Drones*. 2022; 6(9):256.
https://doi.org/10.3390/drones6090256

**Chicago/Turabian Style**

Lin, Tzu-Jui, and Karl A. Stol.
2022. "Autonomous Surveying of Plantation Forests Using Multi-Rotor UAVs" *Drones* 6, no. 9: 256.
https://doi.org/10.3390/drones6090256