Page 113 - Innovations in Intelligent Machines

UAV Path Planning Using Evolutionary Algorithms 103
F = 0.99, C r = 0.85. The algorithm was defined to terminate after 700 gener-
ations, although feasible solutions can be reached in less than 30 generations.
The large number of generations was used in order to compare the convergence
behavior between the original DE algorithm and the RBFN assisted one. For
the 4 test cases presented here, 3 free-to-move control points were used for
each B-Spline path, resulting in a total number of control points equal to 5
for each B-Spline curve (along with the fixed starting and target points). For
3 different paths (corresponding to 3 UAVs) and 3 free-to-move control points
for each path, a total number of 27 design variables are needed (seg length k,j ,
seg angle k,j and c k,j , for each pathj and each control point k).
Figures 6 to 9 present simulation results for the four different test cases,
using the RBFN assisted DE. For all test cases safety distance d safe was set
equal to 12.5% of the length of each side of the rectangular terrain. For all test
cases, term f 4 of the cost function converged to zero, indicating no violation
of the safety distance constraint. Concerning the time intervals between the
first and the last arrival to the target, for all the test cases considered this
time interval was kept less than about 3% of the flight duration (0.71% for the
1st case, 3.08% for the 2nd case, 1.33% for the 3rd case and 1.41% for the 4th
case). As it can be observed, term f 3 of the fitness function managed to pro-
duce uniform distribution of UAVs around the target for all cases considered.
Even for the fourth test case a uniform distribution of UAV paths around the
target was achieved, although the target point was positioned very close to
an obstacle (island coast).
As it has been already stated, the main reason for introducing the RBFN
surrogate model was to speed-up the optimization procedure. However, as

Fig. 6. The first test case for the coordinated UAV path planning