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Figure 4. Illustration of ANS method within a more specific sense, where an obstacle obstructing the connection path. (A) The multiple
connection paths have been obstructed by the obstacles. (B) It selects the nodes in the defined range. (C) It conducts IPSO point-to-point
algorithm to achieve the optimal path to the selected node.

Figure 5. Illustration of the ANS algorithm analysis. (A) From Figure 11 it is enclosed by a pink dashed box. (B) From Figure 13 it is enclosed
by a pink dashed box.

We carry out further discussions on our proposed ANS algorithm. Figure 5A and Figure 5B are parts of
Figure 11 and Figure 13 (enclosed in pink dashed boxes), respectively. As shown in Figure 5A, the solid circles
represent the search radius of the waypoints in the simulation and the red solid dots depict the nodes in the
workspace. In Figure 11, we end up with the trajectory that follows the generated safe-aware road. However, if
the space in the map is more sparse, our search radius R may increase to R , which may achieve the waypoints
0
in their respective search spaces. Thus, instead of following the safe-awareness road, a new connection path is
obtained through the improved PSO algorithm directly, as shown in dashed lines in Figure 5A. Moreover, the
sparseness of the overall workspace may not represent the complexity of local obstacles. Therefore, the choice
of the radius of the search space may require more mathematical proof and analysis.

With the increasing radius of the potential search range, more nodes are applicable for selection, such as the
nodes connected with dashed lines in Figure 5B. Enlarging the search space may avoid some unnecessary
detours and give a shorter path. Therefore, the trade-off between path length and safety of the autonomous
robot still requires more consideration.