A Novel Multirobot System for Plant Phenotyping^{ †}
Abstract
:1. Introduction
2. Materials and Methods
 Smaller light weight robots equipped with low resolution sensors that acquire frequent measurements, and infer changes that take place at smalltime scales. We refer to them as rover.
 A mobile platform carrying high resolution sensors for accurate plant disease detection and analysis of spread of disease. The platform can be autonomous or guided by a human. For example, in [14], we present the construction of a Modular Autonomous Rover for Sensing (MARS) that uses the information provided by the rovers to capture hyperspectral images of plants.
2.1. Robot Configurations
System Requirements for Rover
2.2. System Architecture
2.3. MicroController and Sensors
2.4. Middleware and Architecture
2.5. Current Application
2.5.1. Gaussian Process
 $X=[{({x}^{1})}^{T};{({x}^{2})}^{T};\cdots ;{({x}^{n})}^{T}]\in {\mathbb{R}}^{n\times d}$ be training input;
 ${X}_{*}=[{({x}_{*}^{1})}^{T};{({x}_{*}^{2})}^{T};\cdots ;{({x}_{*}^{m})}^{T}]\in {\mathbb{R}}^{m\times d}$ be test input;
 ${\mathbf{f}}_{*}=[f({x}_{*}^{1});f({x}_{*}^{2});\cdots ;f({x}_{*}^{m})]\in {\mathbb{R}}^{m}$ be function values corresponding to test input;
 $\mathbf{y}=[{y}^{1};{y}^{2};\cdots ;{y}^{n}]\in {\mathbb{R}}^{n}$ be training output;
2.5.2. Estimation of Hyperparameters
2.5.3. Informative Motions
Algorithm 1 Informative Motions and Nonparametric Learning 

2.5.4. Path Planning
2.5.5. Robot–Target Assignment
2.5.6. Tasks Scheduling
 If $m>n$, then there is a unique reassignment that allows $mn$ robots to leave the row, and the remaining n robots to reach their goals without any collision.
 If $n>m$, then there is a unique reassignment that allows $nm$ robots to enter the row, and the remaining m robots in the row to reach the m goal points without any collision.
 Let us consider a labeling of robots $\{{r}_{1},\dots ,{r}_{m}\}$ from left to right with the first robot on the left numbered as 1. Goals are labeled from left to right $\{{g}_{1},\dots ,{g}_{n}\}$ in a similar manner. Goal ${g}_{n}$ is assigned to robot ${r}_{m}$, ${g}_{n1}$ is assigned to ${r}_{m1}$, ${g}_{n2}$ is assigned to ${r}_{m2}$, and so on, until ${g}_{1}$ is assigned to ${r}_{mn+1}$. The leftover $mn$ robots can leave the row without any collision with other robots. This reassignment does not change the sum of the path lengths. Between any two robots being reassigned, the original travel distance for robot ${r}_{i}$ and ${r}_{j}$ are ${d}_{i}$ and ${d}_{j}$. The distance between ${r}_{i}$ and ${r}_{j}$ is d. After reassignment, the traveling distance for ${r}_{i}$ is ${d}_{j}d$, and the traveling distance of ${R}_{j}$ is $d+{d}_{i}$. The total traveling distance is still ${d}_{i}+{d}_{j}$. Since the total traveling distance remains unchanged, the total time required to complete the task will not increase either.
 Consider the same labeling as in the previous case. Goal ${g}_{n}$ is assigned to robot ${r}_{m}$, ${g}_{n1}$ is assigned to ${r}_{m1}$, ${g}_{n2}$ is assigned to ${r}_{m2}$, and so on, until ${g}_{nm+1}$ is assigned to ${r}_{1}$. The leftover $nm$ goals can be taken care of by $nm$ robots entering from left path without collision. We sort these robots with increasing order by traveling distance to this row. Then, we assign the leftover $nm$ goals from right to left with the sorted robots. Similarly, this reassignment does not change the sum of path lengths, and does not increase the total time required to complete the task.
2.5.7. Time Complexity
Algorithm 2 Compute cost matrix given robots and goal points position 
Input: Two matrices. $\mathbf{A}$ and $\mathbf{B}$ are robots and goal points location sets Output: Cost matrix $\mathbf{C}$ 1: function CostMatrix($\mathbf{A},\mathbf{B}$) 2: for each ${r}_{ij}$ do 3: for each ${t}_{uv}$ do 4: ${\mathbf{C}}_{ij}=iu+min(j+v,2n(j+v)))$ 5: end for 6: end for return $\mathbf{C}$ 7: end function 
3. Results
3.1. Experimental Setup
3.2. Simulation
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Share and Cite
Gao, T.; Emadi, H.; Saha, H.; Zhang, J.; Lofquist, A.; Singh, A.; Ganapathysubramanian, B.; Sarkar, S.; Singh, A.K.; Bhattacharya, S. A Novel Multirobot System for Plant Phenotyping. Robotics 2018, 7, 61. https://doi.org/10.3390/robotics7040061
Gao T, Emadi H, Saha H, Zhang J, Lofquist A, Singh A, Ganapathysubramanian B, Sarkar S, Singh AK, Bhattacharya S. A Novel Multirobot System for Plant Phenotyping. Robotics. 2018; 7(4):61. https://doi.org/10.3390/robotics7040061
Chicago/Turabian StyleGao, Tianshuang, Hamid Emadi, Homagni Saha, Jiaoping Zhang, Alec Lofquist, Arti Singh, Baskar Ganapathysubramanian, Soumik Sarkar, Asheesh K. Singh, and Sourabh Bhattacharya. 2018. "A Novel Multirobot System for Plant Phenotyping" Robotics 7, no. 4: 61. https://doi.org/10.3390/robotics7040061