# A Versatile Control Method for Multi-Agricultural Machine Cooperative Steering Applicable to Two Steering Modes

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## Abstract

**:**

## 1. Introduction

- (1)
- This article proposes a versatile multi-machine control architecture, applicable to two typical agricultural machine steering modes, including U-turn and T-turn.
- (2)
- Building upon the control architecture, a cooperative control approach for multiple agricultural machines in both straight-line and headland turn steering scenarios is proposed. This method, while ensuring the safety of agricultural machines, aims to enhance operational efficiency and fuel economy.

## 2. Problem Description

_{1}T

_{2}and T

_{3}T

_{4}, and a connecting line segment, T

_{2}T

_{3}. T

_{1}marks the commencement of the turn, while T

_{4}indicates the completion. Centers O

_{1}and O

_{2}correspond to the turning circular arcs T

_{1}T

_{2}and T

_{3}T

_{4}, respectively, with r representing the turning radius, and w indicating the working width. A U-turn approach is used when the working width w is greater than or equal to twice the turning radius, signified as w ≥ 2r; conversely, a T-turn method is preferred when the working width w is less than double the turning radius, denoted as w < 2r [25].

## 3. Methodology

#### 3.1. Integral Control Framework

#### 3.2. Kinematic Model

#### 3.2.1. Lateral Kinematics

#### 3.2.2. Longitudinal Kinematics

_{g}is the engine power transmission ratio; N

_{0}is the engine-to-wheel transmission ratio; η

_{t}is the mechanical efficiency of the transmission system; M

_{e}is the engine output torque; K

_{p}is the scaling factor; P

_{b}is the brake pressure; r

_{w}is the wheel radius; v

_{f}is the speed of the following agricultural machine; m is the weight of the following agricultural machine; C

_{A}is the aerodynamic drag coefficient; g is the acceleration due to gravity; and f is the rolling resistance coefficient.

_{d}, can be derived using the collision risk detection module. For detailed derivation, refer to Section 3.3.2. The derived longitudinal kinematic model for agricultural machinery following is as follows:

_{r}is the actual following distance; ∆v is the following speed error; and v

_{m}is the speed of the leading machine.

#### 3.3. Controller Design

#### 3.3.1. Straight-Line Formation-Keeping Controller

_{i}’ is fed into the PID as an error term. This error is then subjected to a linear combination of proportional, integral, and differential calculations to produce the control variable. The model is illustrated in Figure 6.

_{i}’ yields the desired acceleration for the subject machine. The module ‘H

_{i}’ represents the spacing strategy, which determines the desired spacing between the subject machine and the lead machine. The ‘G

_{i}’ module is the longitudinal machine controller, which provides the subject machine’s velocity as the input to the spacing strategy module.

#### 3.3.2. Headland-Turn Cooperative Steering Optimization Controller

- (1)
- Collision Risk Detection

_{1}P

_{2}P

_{3}P

_{4}serves as the enclosing surface of the safety model, as illustrated in Figure 7. The dimensions of this rectangle are the combined aggregate of the length and width of the machine’s ground projection including its implements, with an additional minimum safety margin incorporated. The heading angle of the machine is represented by θ, and a minimum safety distance of 0.5 m is established to uphold the standard of operational safety.

_{A}and O

_{B}are identified as the geometric centers of the OBB for machine 1 and 2, respectively.

_{A}as the origin, where the separating axis is parallel to the lateral symmetry axis of the OBB of machine 1. L

_{AB}denotes the projection length of the geometric center distance between the OBB of the two machines on the separating axis. R

_{A}and R

_{B}are the half-lengths of the maximum projection lengths on the separating axis of machine 1 and 2’s OBB section, which can be referred to as the projection radius. The formulas for calculating R

_{A}, R

_{B}, and L

_{AB}are as follows:

_{A}is the width of the OBB for agricultural machine 1; θ

_{B}is the heading angle of agricultural machine 2 relative to agricultural machine 1; L

_{B}is the length of the OBB for agricultural machine 2; and W

_{B}is the width of agricultural machine 2.

_{AB}) exceed the sum of the projection lengths of the geometric center distances on the separating axis (denoted as R

_{A}+ R

_{B}), it indicates that there is no collision between the machines, hence, no risk of collision.

- (2)
- U-turn Cooperative Steering

- (3)
- T-turn Cooperative Steering

^{2}), needs to satisfy:

_{ahead}denotes the travel distance of the preceding machine during the deceleration process, measured in meters (m); S

_{ego}signifies the travel distance of the ego vehicle, which refers to the machine under consideration or the machine executing the maneuver, also measured in meters (m).; L

_{ABmin}is the minimum safe distance for the agricultural machine; V

_{ahead}is the lead machine speed; V

_{ego}is the machine speed before it decelerates; V

_{desire}is the machine speed after it decelerates; t

_{1}is the duration of the deceleration phase; and t

_{2}is the duration of the V

_{desire}.

#### 3.3.3. Path-Tracking Controller

- (1)
- U-turn Cooperative Steering

_{d}is the look-ahead distance.

- (2)
- T-turn Cooperative Steering

_{e}), a more substantial lateral tracking error results in a greater steering angle of the front wheel. Assuming that the vehicle’s anticipated trajectory intersects with the tangent of the nearest point on the given path at a distance d(t) ahead of the front wheel, the following nonlinear proportional function is deduced based on the geometric relationships:

## 4. Simulation Validation

#### 4.1. Scenario Design

_{1}B

_{1}and A

_{2}B

_{2}correspond to the paths of the following machines. The coordinates of the path points are entered into the path-tracking controller. It is stipulated that the machines maintain a stable working speed of 10 km/h, while the speed during reverse motion is set to 5 km/h. Furthermore, the acceleration during the entire process is to be confined within the limits of ±1.5 m/s

^{2}.

#### 4.2. Analysis of Results

#### 4.2.1. U-Type Cooperative Steering

#### 4.2.2. T-Type Cooperative Steering

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, M.; Ji, Y.; Li, S.; Cao, R.; Xu, H.; Zhang, Z. Research Progress of Agricultural Machinery Navigation Technology. Trans. Chin. Soc. Agric. Mach.
**2020**, 51, 1–18. [Google Scholar] - Jin, S.; Liu, G.; Yan, X.; Shi, H.; Cheng, L. Necessity and Application Prospects of Precision Agriculture Development in China. Zhejiang Agric. Sci.
**2010**, 2, 414–416. [Google Scholar] [CrossRef] - Hu, J.; Gao, L.; Bai, X.; Li, T.; Liu, X. Review of research on automatic guidance of agricultural vehicles. Trans. Chin. Soc. Agric. Eng.
**2015**, 31, 1–10. [Google Scholar] [CrossRef] - Chen, X.; Wen, H.; Zhang, W.; Pan, F.; Zhao, Y. Advances and progress of agricultural machinery and sensing technology fusion. Smart Agric.
**2020**, 2, 1–16. [Google Scholar] [CrossRef] - Ju, C.; Kim, J.; Seol, J.; Son, H.I. A review on multirobot systems in agriculture. Comput. Electron. Agric.
**2022**, 202, 107336. [Google Scholar] [CrossRef] - Zhu, Z.; Song, Z.; Xie, B.; Chen, J.; Wutian, C.; Mao, E. Automatic Control System of Tractors Platooning. Trans. Chin. Soc. Agric. Mach.
**2009**, 40, 149–154. [Google Scholar] - Rigatos, G.G. Derivative-free distributed nonlinear Kalman filtering for cooperating agricultural robots. In Proceedings of the 2013 IEEE International Symposium on Industrial Electronics, Taipei, Taiwan, 28–31 May 2013; pp. 1–6. [Google Scholar] [CrossRef]
- Li, S.; Xu, H.; Ji, Y.; Cao, R.; Zhang, M.; Li, H. Development of a following agricultural machinery automatic navigation system. Comput. Electron. Agric.
**2019**, 158, 335–344. [Google Scholar] [CrossRef] - Mao, W.; Liu, H.; Hao, W.; Yang, F.; Liu, Z. Development of a Combined Orchard Harvesting Robot Navigation System. Remote Sens.
**2022**, 14, 675. [Google Scholar] [CrossRef] - Martin, A.; Dionysis, B.; Claus, G.; Morten, R.; Kasper, L. In-field and inter-field path planning for agricultural transport units. Comput. Ind. Eng.
**2012**, 63, 1054–1061. [Google Scholar] [CrossRef] - Conesa-Muñoz, J.; Bengochea-Guevara, J.M.; Andujar, D.; Ribeiro, A. Efficient Distribution of a Fleet of Heterogeneous Vehicles in Agriculture: A Practical Approach to Multi-path Planning. In Proceedings of the 2015 IEEE International Conference on Autonomous Robot Systems and Competitions, Vila Real, Portugal, 8–10 April 2015; pp. 56–61. [Google Scholar] [CrossRef]
- Blender, T.; Buchner, T.; Fernandez, B.; Pichlmaier, B.; Schlegel, C. Managing a Mobile Agricultural Robot Swarm for a seeding task. In Proceedings of the IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society, Florence, Italy, 23–26 October 2016; pp. 6879–6886. [Google Scholar] [CrossRef]
- Bai, X.; Wang, Z.; Hu, J.; Gao, L.; Xiong, F. Harvester Group Corporative Navigation Method Based on Leader-Follower Structure. Trans. Chin. Soc. Agric. Mach.
**2017**, 48, 14–21. [Google Scholar] [CrossRef] - Zhang, C.; Noguchi, N. Development of a multi-robot tractor system for agriculture field work. Comput. Electron. Agric.
**2017**, 142, 79–90. [Google Scholar] [CrossRef] - Noguchi, N.; Will, J.; Reid, J.; Zhang, Q. Development of a master–slave robot system for farm operations. Comput. Electron. Agric.
**2004**, 44, 1–19. [Google Scholar] [CrossRef] - Xu, G.; Chen, M.; Miao, H.; Yao, W.; Diao, P.; Wang, W. Control Method of Agricultural Machinery Master-Slave Following Operation Based on Model Predictive Control. Trans. Chin. Soc. Agric. Mach.
**2020**, 51, 11–20. [Google Scholar] [CrossRef] - Wang, Z. Design and Realization on Autonomous Following Control System for Agricultural Vehicles. Master’s Thesis, Nanjing Agricultural University, Nanjing, China, 2014. [Google Scholar]
- Zhang, C.; Noguchi, N.; Yang, L. Leader–follower system using two robot tractors to improve work efficiency. Comput. Electron. Agric.
**2016**, 121, 269–281. [Google Scholar] [CrossRef] - Stavros, G.; Vougioukas, A. distributed control framework for motion coordination of teams of autonomous agricultural vehicles. Biosyst. Eng.
**2012**, 113, 284–297. [Google Scholar] [CrossRef] - Zhang, W.; Zhang, Z.; Luo, X.; He, J.; Hu, L.; Yue, B. Position-velocity coupling control method and experiments for longitudinal relative position of harvester and grain truck. Trans. Chin. Soc. Agric. Eng.
**2021**, 37, 1–11. [Google Scholar] [CrossRef] - Zheng, X. Master-Slave Cooperative Control Method Harvester-Grain Carrier. Master’s Thesis, Shenyang University of Technology, Shenyang, China, 2021. [Google Scholar] [CrossRef]
- Abe, G.; Mizushima, A.; Noguchi, N. Mizushima and Noboru Noguchi. Study on a Straight Follower Control Algorithm based on a Laser Scanner. J. Jpn. Soc. Agric. Mach.
**2005**, 67, 65–71. [Google Scholar] [CrossRef] - Iida, M.; Kudou, M.; Ono, K.; Umeda, M. Automatic following control for agricultural vehicle. In Proceedings of the 6th International Workshop on Advanced Motion Control. Proceedings (Cat. No.00TH8494), Nagoya, Japan, 30 March–1 April 2000; pp. 158–162. [Google Scholar] [CrossRef]
- Zhang, X.; Geimer, M.; Grandl, L.; Kammerbauer, B. Method for an electronic controlled platooning system of agricultural vehicles. In Proceedings of the 2009 IEEE International Conference on Vehicular Electronics and Safety (ICVES), Pune, India, 11–12 November 2009; pp. 156–161. [Google Scholar] [CrossRef]
- Zhai, Z.; Wang, X.; Wang, L.; Zhu, Z.; Du, Y.; Mao, E. Collaborative Path Planning for Autonomous Agricultural Machinery of Master-Slave Cooperation. Trans. Chin. Soc. Agric. Mach.
**2021**, 52, 542–547. [Google Scholar] [CrossRef] - Hu, Z.; Qin, Q. Algorithm for Finding Minimum Volume Oriented Bounding Boxes Based on Convex Hull. J. Hunan Univ. Nat. Sci.
**2019**, 46, 105–111. [Google Scholar] [CrossRef] - Liu, C.; Jiang, X.; Shi, H. Improved Collision Detection Algorithm Based on Oriented Bounding Box. Comput. Technol. Dev.
**2018**, 28, 43–48. [Google Scholar] [CrossRef]

**Figure 14.**U-type cooperative steering trajectory diagram: (

**a**) global trajectory and (

**b**) local trajectory.

**Figure 17.**T-turn cooperative steering trajectory diagram: (

**a**) global trajectory and (

**b**) local trajectory.

Parameter | Value | |
---|---|---|

Model | YTO-LX800 | |

Dimensions (mm) | 4250 × 2090 × 2850 | |

Minimum turning radius (m) | 4 | |

Wheelbase (mm) | 2342 | |

Total vehicle weight (kg) | 2725 | |

Speed range (km/h) | Forward | 1.92 to 31.72 |

Reverse | 5 to 15.01 | |

Maximum traction force (kN) | ≥22.4 |

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**MDPI and ACS Style**

Zhu, W.; Zhang, Y.; Kong, W.; Jiang, F.; Ji, P.
A Versatile Control Method for Multi-Agricultural Machine Cooperative Steering Applicable to Two Steering Modes. *World Electr. Veh. J.* **2024**, *15*, 126.
https://doi.org/10.3390/wevj15040126

**AMA Style**

Zhu W, Zhang Y, Kong W, Jiang F, Ji P.
A Versatile Control Method for Multi-Agricultural Machine Cooperative Steering Applicable to Two Steering Modes. *World Electric Vehicle Journal*. 2024; 15(4):126.
https://doi.org/10.3390/wevj15040126

**Chicago/Turabian Style**

Zhu, Weizhen, Yuhao Zhang, Weiwei Kong, Fachao Jiang, and Pengxiao Ji.
2024. "A Versatile Control Method for Multi-Agricultural Machine Cooperative Steering Applicable to Two Steering Modes" *World Electric Vehicle Journal* 15, no. 4: 126.
https://doi.org/10.3390/wevj15040126