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Sellers et al. Intell Robot 2022;2(4):333­54 I http://dx.doi.org/10.20517/ir.2022.21 Page 345

(2) The improved model generates a better curve by solely affecting the two lines within the corner of the orig-
inal trajectory. Each curve generated affects others within the lines.

(3)Theimprovedmodeleasilyadjuststothesmoothedpathbasedontheenvironmentconstraintsortherobot.

Algorithm 2: Pseudocode for the adjacent node selection (ANS) algorithm
Input: Edge list E, N nodes coordinates (N , N ), N × N distance matrix D and the location of the
waypoint , ( , ) and the waypoint , ( , ).
Output: The path length of the trajectory L
= (E); // Number of the edges in the workspace
[E , ] = (E); // Sort the edge list from low to high

= d e; // Exclude 10% of extraneous edge distance
10
E = 0;
for i = : do
E = E + E ( );
end

R = E ; // The radius of the search range
−
for j = 1 : N do
if (N , , N , in range of R from , ) then
A = [A ; N , , N , ]; // Add the potential adjacent nodes of
waypoint in the list
end
if (N , , N , in range of R from , ) then
A = [A ; N , , N , ]; // Add the potential adjacent nodes of
waypoint in the list
end
end
= (A ); = (A ); // Number of the points in the search range
Apply IPSO-based path planning algorithm;
Obtain the length of the connection path L and L in the search range;
L = ∞;
for = 1 : do
for = 1 : do
L = L ( ) + D(N , , N , ) + L ( ); // Calculate the total path
end
if L > L then
L = L ; // Achieve the minimum path length
end
end

5. REACTIVE LOCAL NAVIGATION
A crucial aspect in developing a multi-waypoint model is accounting for moving and unknown obstacles [39,40] .
In a real-world setting, not all objects are static and known. To develop a more efficient model, we propose the
use of a local navigator to remedy this issue.

In order to avoid dynamic and unknown obstacles, the proposed model employs the Vector Field Histogram