Algorithm 3 Safety inspection of a frontier cell

Require: empty cell position ${\left[r,c\right]}^T$, size of window for detecting safe frontier cells $window\_size$, $gridmap=\left\{cell\left(i,j\right)\left|1\le i\le RowSize,1\le j\le ColSize\right.\right\}$

Ensure:  $fla{g}_{\mathrm{frontier}}$

1: function Inspect-Safe-Frontier-Cell(${\left[r,c\right]}^T$, $window\_size$, $gridmap$)

2:     $fla{g}_{\mathrm{frontier}}\leftarrow 0$

3:     $number\_of\_unknown\leftarrow 0$

4:     $number\_of\_occupied\leftarrow 0$

5:     for $p=r-\mathrm{round}\left(window\_size/2\right)$ to $r+\mathrm{round}\left(window\_size/2\right)$ do

6:         for $q=c-\mathrm{round}\left(window\_size/2\right)$ to $c+\mathrm{round}\left(window\_size/2\right)$ do

7:            if $cell\left(p,q\right)>th{}_{\mathrm{occupied}}$ then

8:                $number\_of\_occupied\leftarrow number\_of\_occupied+1$

9:            else if $cell\left(p,q\right)>th{}_{\mathrm{empty}}$ then

10:                $number\_of\_unknown\leftarrow number\_of\_unknown+1$

11:            end if

12:         end for

13:     end for

14:     if $number\_of\_occupied<1$and$number\_of\_unknown>t{h}_{\mathrm{num}\_\mathrm{unknown}}$ then

15:         $fla{g}_{\mathrm{frontier}}\leftarrow 1$

16:     end if

17:     return $fla{g}_{\mathrm{frontier}}$

18: end function