1. Introduction
2. Robot Reasoning Combined with Its Hedge Algebras
2.1. The Robot Coverage Path Planning Problem
 The coverage is complete: The robot must travel through all nodes in its working area;
 The overlapping area is minimized: In the ideal case, robot’s trajectory must contain no overlapping between different moves in the same working session. However, when the working area is made up of complicated shapes, overlapping is usually unavoidable to ensure a complete coverage. Also, no part of the trajectory should be repeated;
 The path is viable for a robot: The robot must be able to follow the path in a sequential and continuous manner, based upon simple primitive motions, such as going straight, turning left or right;
 Robots must be able to avoid all of the obstacles that they may encounter during their working session;
 Under the conditions experienced by the robot, achieving the optimal path is expected.
2.2. Robot Reasoning in Dynamic Environments
2.2.1. Robot Sensing in Dynamic Environments
2.2.2. Applied Hedge Algebra for Robot Sensing in Dynamic Environments
Concept of Hedge Algebra (HA)
 $\left(i\right)$ Let $\leftx\right=1$: We construct fuzzy space $J\left({c}^{}\right)$ and $J\left({c}^{+}\right)$, with $\leftJ\left(x\right)\right=fm\left(x\right)$, so that they form a differential range of [0,1], and are derived from the order of the parts ${c}^{}$ and ${c}^{+}$ in which we have $J\left({c}^{}\right)\le J\left({c}^{+}\right)$.
 $\left(ii\right)$ Assume that fuzzy space $J\left(x\right)$ with $\leftJ\left(x\right)\right=fm\left(x\right)$ has been constructed with $\forall x\in H\left(G\right),\leftx\right=n>1$. Let f be a subset of $J\left({h}_{i}x\right)$ $J\left(x\right)$, $\leftJ\left({h}_{i}x\right)\right=fm\left({h}_{i}x\right)$ in which they arise from the sequence between elements in $\left\{{h}_{i}x:q\le i\le p,i\ne 0\right\}.$
 $T\left(X\right)$: the set values linguistic ($dom\left(SUCESS\right)$;
 $G$: a set of elements ($sucess,false)$;
 $H$: a set hedge (very, more, little);
 $\le $: the semantic relation(s) on words (a fuzzy concept). The semantic relations are the order relations obtained from the natural meaning (false ≤ success, more success ≤ very success, very false ≤ more success, possible success ≤ success, little false ≤ false,$\dots $)
2.2.3. Rules Considered by Robot Direction in KnowledgeBased
 IF (Conditions) THEN (apply the actions with these automated rules)
 ELSE find a new rule in KB.
3. The Proposed Model
Procedure$\mathit{S}\mathit{T}\mathit{C}\left(\mathit{w},\mathit{x}\right)$. While $x$ is a root contained a starting cell, $w$ is a main cell. 

End of while. 

End of Procedure$\mathit{S}\mathit{T}\mathit{C}\left(\mathit{w},\mathit{x}\right)$ 
These steps of the proposed algorithm will be completed while the grid lines have been scanned where, 

{ 
Temp = GT; Vet = 0; 
Obstacle = Loc(Temp,R); 
while ((Obstacle ≠ 0) and (KL ⊄ GT)) do 
r ← Get(Obstacle) // r: left → q 
Vet = Vet ∪ {r}; R = R \ {r}; 
Temp = Temp ∪ {q}; 
Obstacle = Loc(Temp, R); 
end while 
if (KL ⊂ Temp) then 
exit(‘ Robot passed the obstacles’); 
else exit (‘Robot could not be successful’); 
} 
4. Experimental Result and Evaluation
4.1. Experimental Results
4.2. Experimental Results in a Real Case Study of Robot Coverage Path Planning
 (1)
 $A{H}_{Muc\_Do\_Dap\_Ung}\text{}=\left(T\left(X\right),\text{}G,H,\le \right)$
 (2)
 $G=\left\{low,\text{}high\right\},\text{}fm\left(low\right)=0.5,\text{}fm\left(high\right)=0.75$
 (3)
 ${H}^{+}=\left\{very\right\}=\left\{{h}_{2}\right\},\text{}q=1$
 (4)
 ${H}^{}=\left\{little\right\}=\left\{{h}_{1}\right\},\text{}p=1$
 (5)
 $\theta =W=0.5\text{}\mathrm{and}\text{}\alpha =0.75$
4.3. Evaluation
 ▪
 A_{t} is the total nodes of the environment
 ▪
 A_{o} is the total area of the obstacles and A_{p} is the total area covered by the robot’s path.
4.3.1. A Comparison of the Repetition Rate for Evaluation of the Methods
4.3.2. Comparison of Repetition Rate and Duration in Robot Coverage Path Planning with Moving Obstacles
4.3.3. Result Discussions
5. Concluding Observations
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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${\mathit{V}}_{1}$  ${\mathit{V}}_{2}$  ${\mathit{V}}_{3}$  ${\mathit{V}}_{4}$  

$({\mathrm{S}}_{1})$  $\mathrm{important}$  $\mathrm{important}$  $\mathrm{unImportant}$  $\mathrm{very}\text{}\mathrm{important}$ 
$({\mathrm{S}}_{2})$  $\mathrm{unImportant}$  $\mathrm{unImportant}$  $\mathrm{important}$  $\mathrm{unImportant}$ 
$({\mathrm{S}}_{3})$  $\mathrm{unImportant}$  $\mathrm{unImportant}$  $\mathrm{unImportant}$  $\mathrm{unImportant}$ 
$({\mathrm{S}}_{4})$  $\mathrm{little}\text{}\mathrm{important}$  $\mathrm{little}\text{}\mathrm{important}$  $\mathrm{very}\text{}\mathrm{unImportant}$  $\mathrm{little}\text{}\mathrm{important}$ 
Symbol  Conditions  Actions 

${a}_{1}$  Robot faces an obstacle  Stop waiting for the obstacle 
${a}_{2}$  Robot moves to the right to meet a moving obstacle  Move to the left to find a direction 
${a}_{3}$  Robot faces with moving irregular obstacles  Combine with the other rules ${a}_{1}$ & ${a}_{2}$ for an action moved the robot in the straight way 
${a}_{4}$  Robot faces with complex obstacles  Stop and move to the left to find a direction 
….  …………….  ……………………. 
….  …………….  ……………………. 
${a}_{7}$  …………….  ……………………. 
Methods  Obstacles in Static Environments  

Irregular  Regular  Multiple Irregular  Multiple Regular  
MRN  4.00%  4.10%  26.50%  22.50% 
BA*  5.30%  5.50%  16.50%  23.10% 
A*CPP  5.00%  5.40%  9.80%  23.40% 
Proposed model  2.20%  0.00%  2.50%  5.30% 
Methods  Obstacles in Static Environments  

Covered Area  Time (Minutes)  Coverage Rate  Repetition Rate  
MRN  70–90 m^{2}  6.00  75%  22.50% 
BA*  70–90 m^{2}  5.00  95%  23.10% 
A*CPP  70–90 m^{2}  5.25  93%  13.40% 
Proposed model  70–90 m^{2}  4.00  100%  4.30% 
Method  Duration (in Seconds)  

Regular  Irregular  Multiple Regular  Multiple Irregular  
MRN  142  162  148  151 
BA*  102  141  129  135 
A*CPP  87  107  97  125 
Proposed model  67  78  68  80 
Method  Repetition Rate (%)  

Regular  Irregular  Multiple Regular  Multiple Irregular  
MRN  15%  25%  36%  35% 
BA*  9%  23%  25%  30% 
A*CPP  12%  11%  16%  22% 
Proposed model  2%  4%  4%  7% 
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