# An Approach for Autonomous Feeding Robot Path Planning in Poultry Smart Farm

^{*}

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

^{3}hopper, two vertical churns, discharge belts on both sides, am infinitely adjustable speed control belt and a mixing enhancer, which acts as a fully automatic feeding system in conjunction with a stationary feed mixer [14]. The aerial conveyor feeding system, produced by PELLON in Tampere, Finland, consists of filler unit and concentrate tower to put the feed group into the fixed feed mixing device. The mixed feed is sent to the feed conveyor by the lifting conveyor, and under the thrust of the sliding plow device on the conveyor, it is evenly sprinkled on the feeding surface to complete the feeding operation [15].

## 2. Materials and Methods

#### 2.1. Problem Description and Analysis

#### 2.2. Path Planning for Small-Scale Feeding Point

#### 2.2.1. Theory of the Branch and Bound Algorithm

#### 2.2.2. Boundary Constraints of Branch and Bound Algorithms

#### 2.2.3. Solution of the Global Lower Bound

_{0}is the starting and the final return point of the feeding robot, v

_{1}, v

_{2},…, v

_{n}represents the set of feed buckets in the farm and E is the set of edges of the complete graph G. Any two points are connected by an edge. For any edge in G, the path from v

_{i}to v

_{j}is e

_{ij}. The path of the feeding robot satisfies the symmetric property that the distance between any two feeding points satisfies e

_{ij}= e

_{ji}(i, j ∈ V). Thus, the distance between any two points can be expressed as the following symmetric matrix.

_{m}= (V

_{0}, E

_{0}) could be defined: ${V}_{0}=\left\{{v}_{0},{v}_{1},{v}_{2},\cdots ,{v}_{m}\right\}$, v

_{0}is the starting and the final return point of the feeding robot, ${V}_{1}=\left\{{v}_{1},{v}_{2},\cdots ,{v}_{m}\right\}$ represents the set of feed buckets in the farm and the weight of feed required for each bucket is $F=\left\{{q}_{1},{q}_{2},\cdots ,{q}_{m}\right\}$. E

_{0}is the set of edges of the complete graph G

_{m}. The robot’s path is represented by the following: $B=\left\{{e}_{01},{e}_{12},\cdots ,{e}_{ij},\cdots ,{e}_{(m-1)\begin{array}{c}m\end{array}},{e}_{m0}\right\}$, where e

_{ij}is the edge from v

_{i}to v

_{j}and the length of e

_{ij}is d

_{i}. The energy consumed by the feeding robot for the path B could be expressed as Equation (2):

_{m}, there are m edges connected to v

_{i}. From the path B, it is known that the feeding robot needs to pass through m + 1 points and m + 1 edges to finish the feeding task. In order to find the lower bound of the energy consumption of the feeding robot, it is necessary to find the lower bound by choosing m + 1 suitable and relatively short edges. The approach of preferred selection of the set of shortest edges is as follows:

_{i}from the m edges corresponding to each point as an edge in set H. The shortest edges could be chosen from the distance matrix E, the minimum value of each row is the shortest edge corresponding to the point and the edges chosen are then added to the set H. To further select the most suitable shortest edge, duplicate selection of edges is prohibited. Since e

_{ij}and e

_{ji}are the same edge, when the shortest edge e

_{ij}of an edge point v

_{i}∈ V

_{1}is selected, e

_{ji}cannot be selected as the shortest edge again. Therefore, if the shortest edge of point v

_{j}is e

_{ij}and e

_{ji}has been selected, the secondary short edge in the two set of edges corresponding to v

_{i}and v

_{j}is added to set H. Finally, $H=\left\{{h}_{0},{h}_{1},\cdots ,{h}_{m}\right\}$ is obtained, and it could be expressed as an increasing sequence matrix ${H}^{*}=\left[{h}_{0}^{*},{h}_{1}^{*},\cdots ,{h}_{m}^{*}\right]$.

^{*})

^{T}·M

^{*}is the lower bound of the current path, not the lower bound of all paths. For a complete work process of the feeding robot, regardless of how the feeding robot plans the path, the weight of the feed bucket shortage is fixed, so M

^{*}in Equation (4) is determined. To find the lower bound of energy consumption of all paths, we need to find the relatively short edge sequence; for each item within A

^{*}and each item in H

^{*}, there is such a relationship:

_{i}in the set H is shortest corresponding to v

_{i}(i.e., e

_{ij}is the shortest edge in the set corresponding to v

_{i}, and e

_{ij}is not shortest corresponding to v

_{j}), and d

_{i}is one of the edges in the set A corresponding to v

_{i}, so for each element of the same index number in both sequences, there is d

_{i}≥ h

_{i}. When there exist edges in the set A that are the shortest edges of their corresponding points, and the edges corresponding to these points in the set H are also the shortest edges, it is obvious that d

_{i}≥ h

_{i}. Sometimes, there exist edges in set A that are the shortest edges of their corresponding points, and these edges in set H are not the shortest edges of their corresponding points, i.e., e

_{ij}in set A is the shortest edge (d

_{i}= e

_{ij}) corresponding to point v

_{i}, but in set H, e

_{ij}is not the shortest edge corresponding to point v

_{i}, and e

_{ji}must be the shortest edge corresponding to v

_{j}, i.e., d

_{i}= e

_{ji}. Therefore, although d

_{i}< h

_{i}, d

_{j}≥ h

_{i}and d

_{i}= h

_{j}must also be true.

#### 2.2.4. Solution of the Partial Lower Bound for the Energy Consumption

_{1}, v

_{4}and v

_{6}is undetermined. If the global LB is still used for the process of branching and bounding, the efficiency of the branch and bound algorithm will be greatly reduced, so the partial lower bound (PLB) for possible paths need to be calculated.

_{k}) of the determined path, and the second part is the calculation of lower bound LB

_{m−k}of the energy consumption of the undetermined path, so the PLB could be expressed as Equation (10):

_{k}contains at least two points (i.e., k ≥ 1), and the sequence of the weight of feed required for each bucket is ${F}_{k}=\left\{{q}_{0},{q}_{1},\cdots ,{q}_{k}\right\}$. The C(B

_{k}) could be calculated by Equation (11):

_{m−k}is ${H}_{m-k}^{*}={\left[{h}_{k}^{\ast},{h}_{k+1}^{\ast},\cdots ,{h}_{m-1}^{\ast},{h}_{m}^{\ast}\right]}^{T}$. Therefore, the LB

_{m−k}could be calculated by Equation (13):

#### 2.2.5. Solution of the Upper Bound of Energy Consumption

_{x}) and C(S

_{y}), respectively. We assume that the path S is $\left\{{e}_{01},\cdots ,{e}_{(m-1)m},{e}_{m0}\right\}$, d

_{i}is the length of e

_{ij}and the weight set of the missing feed for each feed bucket is ${F}_{m}=\left\{{q}_{0},{q}_{1},{q}_{2},\cdots ,{q}_{m}\right\}$(q

_{0}= 0). Therefore, the C(S

_{x}) could be expressed as follows:

_{x}) could be expressed as follows:

_{x}) ≤ C(S

_{y}), so we can derive the following relation:

^{*}is $\left\{{e}_{01}^{\ast},\cdots ,{e}_{(m-1)m}^{\ast},{e}_{m0}^{\ast}\right\}$, ${d}_{i}^{*}$ is the length of ${e}_{i}^{*}$(${e}_{i}^{*}\in {S}^{*}$), the weight set of the missing feed for each feed bucket is ${F}_{m}^{*}=\left\{{q}_{1}^{*},{q}_{2}^{*},\cdots ,{q}_{m-1}^{*}\right\}$, and the minimum value of the elements in the set ${F}_{m}^{*}$ is ${q}_{\mathrm{min}}^{\ast}$. The C(S

^{*}) could be expressed as follows:

#### 2.3. Large Scale Feeding Point Path Planning

#### 2.3.1. Determination of the Fitness Function

#### 2.3.2. Double Choice Operator

#### 2.3.3. Double Cross Operator Based on Upper Bound on Energy Consumption

#### 2.3.4. Based on the Energy Consumption Upper Bound Mutation Operator

_{1}= 0.02. For individuals with fitness function values smaller than the upper bound, the mutation probability wil1 be set to P

_{2}= 0.05.

#### 2.3.5. Flow of the Large Scale Feeding Point Path Planning Approach

_{c}= 0.8, the mutation probabilities is P

_{1}and P

_{2}and the maximum number of iterations is T

_{max}= 1000, with a population size S = 500.

_{1}= 0.02. The individuals with value of fitness smaller than the value of upper bound are subjected to exchange mutation with a probability of P

_{2}= 0.05.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

G | a complete graph representing the smart farm |

V | the set of feed buckets in the farm |

E | the set of edges of the complete graph G |

LB | the lower bound |

UB | the upper bound |

G_{m} | a complete graph representing the smart farm with feed buckets lacking feed |

V_{m} | the set of feed buckets lacking feed in the farm, include the starting and the final return point of the feeding robot |

V_{1} | the set of feed buckets in the farm |

E_{m} | the set of edges of the complete graph G_{m} |

B | a complete path of the feeding robot |

PLB | partial lower bound |

LB_{m−k} | lower bound of energy consumption of non driving path points |

C(B_{k}) | energy consumption of the determined path |

V_{k} | the determined path that feeding robot has traveled |

B_{k} | the undetermined path that feeding robot has not traveled |

OX | order crossover operator |

CX | cycle crossover operator |

LB1 | the lower bound obtained by using the approach proposed in this study |

LB2 | the lower bound of energy consumption obtained by the minimum spanning tree algorithm |

R | the exact result of energy consumption |

UB1 | the upper bound of energy consumption obtained by the Christofides’s Heuristic algorithm |

UB2 | the upper bound of energy consumption obtained by greedy algorithm |

B-B1 | the branch and bound algorithm proposed in this study |

B-B2 | change the calculation method of obtaining the upper bound of B-B1 to the greedy algorithm, and the rest is same as B-B2 |

B-B3 | change the calculation method of obtaining the lower bound of B-B1 to the minimum spanning tree method, and the rest is same as B-B2 |

GA-1 | the double-crossing operator genetic algorithm based on the upper bound of energy consumption described in this study |

GA-2 | genetic algorithm with only use order crossover operator as its crossover operator |

## References

- Uehleke, R.; Seifert, S.; Hüttel, S. Do animal welfare schemes promote better animal health? An empirical investigation of german pork production. Livest. Sci.
**2021**, 247, 104481. [Google Scholar] [CrossRef] - Iannetti, L.; Neri, D.; Santarelli, G.A.; Cotturone, G.; Vulpiani, M.P.; Salini, R.; Antoci, S.; Di Serafino, G.; Di Giannatale, E.; Pomilio, F.; et al. Animal welfare and microbiological safety of poultry meat: Impact of different at-farm animal welfare levels on at-slaughterhouse Campylobacter and Salmonella contamination. Food Control
**2020**, 109, 106921. [Google Scholar] [CrossRef] - Temple, D.; Manteca, X.; Velarde, A.; Dalmau, A. Assessment of animal welfare through behavioural parameters in Iberian pigs in intensive and extensive conditions. Appl. Anim. Behav. Sci.
**2011**, 131, 29–39. [Google Scholar] [CrossRef] - Wang, T.; Xu, X.; Wang, C.; Li, Z.; Li, D. From smart farming towards unmanned farms: A new mode of agricultural production. Agriculture
**2021**, 11, 145. [Google Scholar] [CrossRef] - Wicaksono, M.G.S.; Suryani, E.; Hendrawan, R.A. Increasing productivity of rice plants based on IoT (Internet Of Things) to realize Smart Agriculture using System Thinking approach. Procedia Comput. Sci.
**2022**, 197, 607–616. [Google Scholar] [CrossRef] - Tao, W.; Zhao, L.; Wang, G.; Liang, R. Review of the internet of things communication technologies in smart agriculture and challenges. Comput. Electron. Agric.
**2021**, 189, 106352. [Google Scholar] [CrossRef] - Osinga, S.A.; Paudel, D.; Mouzakitis, S.A.; Athanasiadis, I.N. Big data in agriculture: Between opportunity and solution. Agric. Syst.
**2022**, 195, 103298. [Google Scholar] [CrossRef] - Torky, M.; Hassanein, A.E. Integrating blockchain and the internet of things in precision agriculture: Analysis, opportunities, and challenges. Comput. Electron. Agric.
**2020**, 178, 105476. [Google Scholar] [CrossRef] - Eli-Chukwu, N.C. Applications of artificial intelligence in agriculture: A review. Eng. Technol. Appl. Sci. Res.
**2019**, 9, 4377–4383. [Google Scholar] [CrossRef] - da Silveira, F.; Lermen, F.H.; Amaral, F.G. An overview of agriculture 4.0 development: Systematic review of descriptions, technologies, barriers, advantages, and disadvantages. Comput. Electron. Agric.
**2021**, 189, 106405. [Google Scholar] [CrossRef] - Wan, J.; Li, J.; Hua, Q.; Celesti, A.; Wang, Z. Intelligent equipment design assisted by Cognitive Internet of Things and industrial big data. Neural Comput. Appl.
**2020**, 32, 4463–4472. [Google Scholar] [CrossRef] - Shi, Y.L. Application of artificial intelligence technology in modern agricultural production. S. Agric. Mach.
**2019**, 50, 14–73. [Google Scholar] - Aquilani, C.; Confessore, A.; Bozzi, R.; Sirtori, F.; Pugliese, C. Precision Livestock Farming technologies in pasture-based livestock systems. Animal
**2022**, 16, 100429. [Google Scholar] [CrossRef] [PubMed] - Vaintrub, M.O.; Levit, H.; Chincarini, M.; Fusaro, I.; Giammarco, M.; Vignola, G. Precision livestock farming, automats and new technologies: Possible applications in extensive dairy sheep farming. Animal
**2021**, 15, 100143. [Google Scholar] [CrossRef] [PubMed] - Ren, G.; Lin, T.; Ying, Y.; Chowdhary, G.; Ting, K.C. Agricultural robotics research applicable to poultry production: A review. Comput. Electron. Agric.
**2020**, 169, 105216. [Google Scholar] [CrossRef] - Wang, Z.; Zeng, Q. A branch-and-bound approach for AGV dispatching and routing problems in automated container terminals. Comput. Ind. Eng.
**2022**, 166, 107968. [Google Scholar] [CrossRef] - Meneguzzi, C.C.; da Silva, G.F.; Mauri, G.R.; de Mendonça, A.R.; de Barros Junior, A.A. Routing model applied to forest inventory vehicles planning. Comput. Electron. Agric.
**2020**, 175, 105544. [Google Scholar] [CrossRef] - Thakar, S.; Malhan, R.K.; Bhatt, P.M.; Gupta, S.K. Area-coverage planning for spray-based surface disinfection with a mobile manipulator. Robot. Auton. Syst.
**2021**, 147, 103920. [Google Scholar] [CrossRef] - Xie, X.; Tang, Z.; Cai, J. The multi-objective inspection path-planning in radioactive environment based on an improved ant colony optimization algorithm. Prog. Nucl. Energy
**2021**, 144, 104076. [Google Scholar] [CrossRef] - Mahmud, M.S.A.; Abidin, M.S.Z.; Mohamed, Z.; Abd Rahman, M.K.I.; Iida, M. Multi-objective path planner for an agricultural mobile robot in a virtual greenhouse environment. Comput. Electron. Agric.
**2019**, 157, 488–499. [Google Scholar] [CrossRef] - Zacharia, P.T.; Aspragathos, N.A. Optimal robot task scheduling based on genetic algorithms. Robot. Comput. Integr. Manuf.
**2005**, 21, 67–79. [Google Scholar] [CrossRef] - Zajac, S.; Huber, S. Objectives and approachs in multi-objective routing problems: A survey and classification scheme. Eur. J. Oper. Res.
**2021**, 290, 1–25. [Google Scholar] [CrossRef] - Laporte, G. The vehicle routing problem: An overview of exact and approximate algorithms. Eur. J. Oper. Res.
**1992**, 59, 345–358. [Google Scholar] [CrossRef] - Bukata, L.; Šůcha, P.; Hanzálek, Z. Optimizing energy consumption of robotic cells by a Branch & Bound algorithm. Comput. Oper. Res.
**2019**, 102, 52–66. [Google Scholar] - Hardy, G.H.; Littlewood, J.E.; Pólya, G.; Pólya, G. Inequalities; Cambridge University Press: Cambridge, UK, 1952. [Google Scholar]
- Cook, W.; Lovász, L.; Seymour, P.D. (Eds.) Combinatorial Optimization: Papers from the DIMACS Special Year; American Mathematical Society: Providence, RI, USA, 1995; Volume 20. [Google Scholar]
- Qu, L.; Sun, R. A synergetic approach to genetic algorithms for solving traveling salesman problem. Inf. Sci.
**1999**, 117, 267–283. [Google Scholar] [CrossRef] - Xue, Y.; Zhu, H.; Liang, J.; Słowik, A. Adaptive crossover operator based multi-objective binary genetic algorithm for feature selection in classification. Knowl.-Based Syst.
**2021**, 227, 107218. [Google Scholar] [CrossRef] - Kaya, M. The effects of two new crossover operators on genetic algorithm performance. Appl. Soft Comput.
**2011**, 11, 881–890. [Google Scholar] [CrossRef] - Kumar, N.; Karambir, R.K. A comparative analysis of pmx, cx and ox crossover operators for solving traveling salesman problem. Int. J. Latest Res. Sci. Technol.
**2012**, 1, 98–101. [Google Scholar] - Herrera, F.; Lozano, M. Gradual distributed real-coded genetic algorithms. IEEE Trans. Evol. Comput.
**2000**, 4, 43–63. [Google Scholar] [CrossRef] [Green Version] - Morais, V.; da Cunha, A.S.; Mahey, P. A Branch-and-cut-and-price algorithm for the Stackelberg Minimum Spanning Tree Game. Electron. Notes Discret. Math.
**2016**, 52, 309–316. [Google Scholar] [CrossRef] [Green Version] - Karabulut, K.; Tasgetiren, M.F. A variable iterated greedy algorithm for the traveling salesman problem with time windows. Inf. Sci.
**2014**, 279, 383–395. [Google Scholar] [CrossRef] - Sandamurthy, K.; Ramanujam, K. A hybrid weed optimized coverage path planning technique for autonomous harvesting in cashew orchards. Inf. Process. Agric.
**2020**, 7, 152–164. [Google Scholar] [CrossRef] - Dell’Amico, M.; Montemanni, R.; Novellani, S. Algorithms based on branch and bound for the flying sidekick traveling salesman problem. Omega
**2021**, 104, 102493. [Google Scholar] [CrossRef] - Ha, Q.M.; Deville, Y.; Pham, Q.D.; Hà, M.H. On the min-cost traveling salesman problem with drone. Transp. Res. Part C Emerg. Technol.
**2018**, 86, 597–621. [Google Scholar] [CrossRef]

**Figure 5.**Example of Christofides’s heuristic algorithm. (

**a**) Minimum spanning tree T, (

**b**) blue points are odd degrees in set O, (

**c**) minimum perfect matching R, (

**d**) re-graph I, (

**e**): Euler circuit X and (

**f**) final path S.

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## Share and Cite

**MDPI and ACS Style**

Zhang, Y.; Sun, W.; Yang, J.; Wu, W.; Miao, H.; Zhang, S.
An Approach for Autonomous Feeding Robot Path Planning in Poultry Smart Farm. *Animals* **2022**, *12*, 3089.
https://doi.org/10.3390/ani12223089

**AMA Style**

Zhang Y, Sun W, Yang J, Wu W, Miao H, Zhang S.
An Approach for Autonomous Feeding Robot Path Planning in Poultry Smart Farm. *Animals*. 2022; 12(22):3089.
https://doi.org/10.3390/ani12223089

**Chicago/Turabian Style**

Zhang, Yanjun, Weiming Sun, Jian Yang, Weiwei Wu, Hong Miao, and Shanwen Zhang.
2022. "An Approach for Autonomous Feeding Robot Path Planning in Poultry Smart Farm" *Animals* 12, no. 22: 3089.
https://doi.org/10.3390/ani12223089