Wildlife Monitoring Using a MultiUAV System with Optimal Transport Theory
Abstract
:1. Introduction
2. Problem Description and Theoretical Background
 Wasserstein distance:
 Linear Programming problem: (for $p=1$)
3. Method
3.1. Animal Movement Modeling
 Group center movement model (CRW):
 Individual animal movement model (BRW):
3.2. OTBased MultiUAV Exploration: TimeInvariant Case
3.2.1. A ThreeStage Approach
 Next goal point (${}^{g}{x}_{T+1}^{k}$) determination stage:
 Weight update stage:
 Weight information exchange and update stage:
3.2.2. Algorithm
Algorithm 1 MultiAgent Exploration Algorithm 

3.3. Sample Point Generation and Propagation: TimeVarying Case
3.4. Other Exploration Strategy: Lawn Mower Method
4. Simulation Results
4.1. Unicycle Robot Dynamics
4.2. Variation in the Number of Agents
4.3. Variation in Exploration Time
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters  Parameter Values  

Exploration strategies  3 (OT (TVGauss), LM (TIUni), OT (TIUni))  
No. of agents  2, 3, 5 (for each strategy)  
No. of simulations  30 (for each strategy with a specific no. of agents)  
Exploration time  900 s  
Time delay  600 s  
No. of animal herds  9  
Initial locations (m) of the animal herds and populations in each herd  1: ${[300,400]}^{T},10$, 2: ${[800,800]}^{T},15$  
3: ${[400,650]}^{T},18$, 4: ${[750,550]}^{T},20$  
5: ${[150,750]}^{T},15$, 6: ${[\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}\phantom{\rule{0.166667em}{0ex}}0,400]}^{T},20$  
7: ${[500,500]}^{T},15$, 8: ${[700,300]}^{T},13$  
9: ${[200,200]}^{T},16$  
Initial GPS tracker information for 9 tracked animals (m)  1: ${[\phantom{\rule{0.166667em}{0ex}}0.58,402.60]}^{T}$, 2: ${[402.11,651.83]}^{T}$  
3: ${[296.22,398.91]}^{T}$, 4: ${[297.10,396.19]}^{T}$  
5: ${[151.90,747.73]}^{T}$, 6: ${[199.65,205.11]}^{T}$  
7: ${[503.16,496.32]}^{T}$, 8: ${[404.92,648.39]}^{T}$  
9: ${[305.28,403.58]}^{T}$  
Estimated herd center (m) from Section 3.3 with tracked animal no.  1: ${[299.53,399.56]}^{T}$, 3,4,9, 2: ${[151.90,747.73]}^{T}$, 5  
3: ${[\phantom{\rule{0.166667em}{0ex}}0.58,402.60]}^{T}$, 1, 4: ${[503.16,496.32]}^{T}$, 7  
5: ${[403.52,650.11]}^{T}$, 2,8, 6: ${[199.65,205.11]}^{T}$, 6  
Distribution parameters for animalherd movement  ${r}_{u,T+1},{r}_{k,T+1}\sim \Gamma ({\mu}_{\gamma}=0.4$ m/s, ${\sigma}_{\gamma}=1$ m/s)  
${v}_{u,T+1}\sim V({\mu}_{vm}=0$, ${k}_{vm}=100)$  
${v}_{k,T+1}\sim V({\mu}_{vm}=0$, ${k}_{vm}=2)$  
${90}^{\circ}\le {v}_{u,T+1}\le {90}^{\circ}$  
${\theta}_{u,0}={v}_{u,0}\sim V({\mu}_{vm}=0$, ${k}_{vm}=0)$  
Exploration domain size  2500 m × 3000 m  
Maximum velocity of the UAVs  30 m/s  
Minimum velocity of the UAVs  10 m/s  
Angular velocity limit  30 $\mathrm{deg}/s$  
Positional error gain, ${K}_{x}$  $0.4$  
Angular error gain, ${K}_{\theta}$  1  
UAV sensor range to detect animals, ${r}_{\mathrm{sensing}}$  15 m  
Specific parameters for OT (TVGauss)  Number of sample points, N  3600  
Number of UAV steps for each agent for exploration, ${M}_{a}$  900  
Initial covariance for the sample point clusters  $Q=\left(\right)open="["\; close="]">\begin{array}{cc}1000& 0\\ 0& 1000\end{array}$  
Herd threshold  50 m  
Horizon length, h  5  
Search radius, r  0.1 m  
Radius increment, $\delta $  0.05 m  
Initial robot positions  [100 m, 400 m]${}^{T}$  
[200 m, 600 m]${}^{T}$  
[200 m, 150 m]${}^{T}$  
[150 m, 400 m]${}^{T}$  
[400 m, 750 m]${}^{T}$  
Distribution parameters for the sample point propagation  ${r}_{j,T+1}\sim \Gamma ({\mu}_{\gamma}$ = 0.6 m/s, ${\sigma}_{\gamma}$ = 0.05 m/s)  
${v}_{j,T+1}\sim V({\mu}_{vm}=0$, ${k}_{vm}=150)$  
${\theta}_{j,0}$ = ${v}_{j,0}\sim V({\mu}_{vm}=0$, ${k}_{vm}=0)$  
Specific parameters for LM (TIUni)  Horizontal and vertical expansion factors, ${f}_{X}$, ${f}_{Y}$  1  
Distance between adjacent waypoints, ${d}_{w}$  10 m  
Spacing between adjacent vertical lines ${d}_{v}$  120 m, 70 m, 40 m for ${n}_{a}=2$, 3, 5, respectively  
Simulation output  No. of UAVs  Average Detection Rate (%)  
OT(TVGauss)  LM(TIUni)  OT(TIUni)  
2  40.45  21.08  19.86  
3  57.72  27.86  25.85  
5  74.34  40.31  36.22 
Parameters  Parameter Values  

Exploration strategies  3 (OT (TVGauss), LM (TIUni), OT (TIUni))  
Exploration time  900, 1800, 3600 s (for each strategy)  
No. of UAVs  3  
Time delay  600  
No. of simulations  30 (for each strategy with a specific exploration time  
Initial UAV positions (m) (OT(TVGauss) and OT(TIUni))  ${[100,900]}^{T}$  
${[200,600]}^{T}$  
${[500,150]}^{T}$  
Parameters varied with exploration time  Exploration Time  
900  1800  3600  
Exploration domain size(m^{2})  2500 × 2500  3000 × 4000  7000 × 7000  
Number of UAV steps for each agent for exploration, ${M}_{a}$ (OT(TVGauss))  900  1800  3600  
Horizontal and vertical expansion factors, ${f}_{X}$, ${f}_{Y}$ (LM(TIUni))  1  $0.7$  $0.5$  
Spacing between adjacent vertical lines ${d}_{v}\left(m\right)$ (LM(TIUni))  120  70  40  
Simulation output  Exploration Strategy  Average Detection Rate (%)  
900  1800  3600  
OT (TVGauss)  63.08  59.84  44.08  
LM (TIUni)  35.63  26.90  12.16  
OT (TIUni)  29.34  23.19  9.39 
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Kabir, R.H.; Lee, K. Wildlife Monitoring Using a MultiUAV System with Optimal Transport Theory. Appl. Sci. 2021, 11, 4070. https://doi.org/10.3390/app11094070
Kabir RH, Lee K. Wildlife Monitoring Using a MultiUAV System with Optimal Transport Theory. Applied Sciences. 2021; 11(9):4070. https://doi.org/10.3390/app11094070
Chicago/Turabian StyleKabir, Rabiul Hasan, and Kooktae Lee. 2021. "Wildlife Monitoring Using a MultiUAV System with Optimal Transport Theory" Applied Sciences 11, no. 9: 4070. https://doi.org/10.3390/app11094070