Algorithm 1 Registration of new nodes by frontier segmentation

Require:  current local grid map $gridma{p}_{cur}$, frontier-graph database $Node=\left\{nod{e}_{id}|1\le id\le N\right\}$, $Edge$, $Map=\left\{ma{p}_{id}|1\le id\le M-1\right\}$, size of window for detecting safe frontier cells $window\_size$ Ensure:  updated frontier-graph database, $Node,Edge,Map$ ▹ The algorithm assumes that the current node is $nod{e}_n$, the parent node is $nod{e}_{n-2}$, and the previous node is $nod{e}_{n-1}$. $nod{e}_n$ and $nod{e}_{n-1}$ are siblings to each other. The map IDs of the parent node and previous node are $M-2$ and $M-1$.

1: add $ma{p}_M=\left\{M,gridma{p}_M,\left\{M\right\},\left\{{\left[0,0,0\right]}^T\right\}\right\}$into $Map$

2: obtain $gridma{p}_{mg}$ by merging the adjacent local maps, $ma{p}_{M-2}$, $ma{p}_{M-1}$, $ma{p}_M$,

3: $gridmap\_frontier\leftarrow$ Detect-Frontier-Cell $\left(gridma{p}_{cur},window\_size\right)$    ▹$RowSize$ is the number of rows $gridmap\_frontier$ and $gridma{p}_{cur}$.    ▹$ColSize$ is the number of columns $gridmap\_frontier$ and $gridma{p}_{cur}$.

4: for $r=1$ to $RowSize$ do

5:     for $c=1$ to $ColSize$ do

6:         if $gridmap\_frontier\left(r,c\right)=1$ then

7:            ${\left[r_{mg},c_{mg}\right]}^T\leftarrow \mathrm{cell}\_\mathrm{coordinate}\_\mathrm{transform}\left({\left[r,c\right]}^T,gridma{p}_{cur},gridma{p}_{mg},Edge\right)$

8:            if Inspect-Safe-Frontier-Cell$\left({\left[r_{mg},c_{mg}\right]}^T,window\_size,gridma{p}_{mg}\right)=0$ then

9:                $gridmap\_frontier\left(r,c\right)\leftarrow 0$

10:            end if

11:         end if

12:     end for

13: end for

14: $frontier\_segment\leftarrow \mathrm{connected}\_\mathrm{component}\_\mathrm{labeling}\left(grifmap\_frontier\right)$

15: if $frontier\_segment\ne \varnothing$ then

16:     $relative\_trans\leftarrow \varnothing$

17:     $new\_Node\leftarrow \varnothing$

18:     for all $frontie{r}_i\in frontier\_segment$ do

19:         $\left\{nod{e}_{i{d}_{new}},\mathbf{t}{\mathbf{r}}_{n,i{d}_{new}}\right\}$←Initialize-New-Node$\left(frontie{r}_i,n,i{d}_{new}\right)$

20:         $new\_Node\leftarrow new\_Node\cup \left\{nod{e}_{i{d}_{new}}\right\}$

21:         $relative\_trans\leftarrow relative\_trans\cup \left\{\mathbf{t}{\mathbf{r}}_{n,i{d}_{new}}\right\}$

22:     end for

23:     $Edg{e}_{new}\leftarrow \mathrm{calculate}\_\mathrm{edge}\left(nod{e}_n,new\_Node,relative\_trans,gridma{p}_{cur}\right)$

24:     $new\_Node\_ordered\leftarrow \mathrm{TSP}\left(nod{e}_n,new\_Node,Edg{e}_{new}\right)$

25:     $\mathrm{update}\_\mathrm{node}\_\mathrm{DB}\left(Node,new\_Node\_ordered\right)$

26:     $\mathrm{update}\_\mathrm{edge}\_\mathrm{DB}\left(Edge,Edg{e}_{new}\right)$

27: end if