Page 13 - Read Online

Zhu et al. Intell Robot 2022;2(3):200­222 I http://dx.doi.org/10.20517/ir.2022.13 Page 206

Figure 4. Path derived by the APF method on the 2D modeling map: (A) path planning based on the distribution of the APF on the map; (B)
APF path on the contour map; and (C) final APF path presented on the 2D modeling map [42] .

F ( ) = −∇U ( ) = ( , ) (1)

{
1 1 1
( − ) 2 ∇ ( , ), ( , ) <
F ( ) = −∇U ( ) = ( , ) ( , ) (2)
0, ( , ) ≥
where −∇U represents the negative gradient of the attractive field; −∇U represents the negative gradient
of the repulsive field; is the coefficient for attraction; ( , ) represents the distance between the current
position and the destination position ; is the repulsion coefficient; and ( , ) represents the distance
between the current position to the obstacle position and is the radius of the obstacle.

Therefore, the destination has the lowest gravity field but the highest gravity force for attraction, while the
gravity field for the obstacles performs higher such that the vehicle can flow along the gravity field descending
route to complete the optimal path planning, as the path deduced from the point in Figure 4A to the one in
Figure 4C.

The APF reduces the calculation complexity as well as performs outstanding real-time reactions, which is
widely applied in the area of vehicle path planning. The virtual gravitational potential field realizes a fast
calculationofthemostoptimalpathtothetargetwithoutcollisionsforthevehicle, byfollowingtheguidanceof
resultant forces given by the pre-designed attraction and repulsion [43] . Zhou et al. improved the APF method
with a particle swarm algorithm to increase the pathfinding efficiency for tangent navigating robots [44] . Lin
et al. designed a subgoal algorithm for the APF such that the path planning of the unmanned vehicle can
overcome the local minimum and track the most optimal path [45] . The decision tree was added to the APF to
form the efficient path planning algorithm without local minimum and collisions for vehicles [46] . Regarding
the environmental factors, the effect of ocean currents was then involved in the path planning of the UUV
while using the APF method [42] .

However, most of the APF research do not involve environmental disturbance in the design, thus affecting
the practical application of the APF. Moreover, the APF method for vehicle path planning often deduces the
problem of local minimum, where the vehicle might stick at halfway instead of reaching the target position
due to the larger resultant effect produced by the local minimum point [47] . The large computation complexity
caused by the increasing obstacle numbers also affects the planning efficiency of the APF method.

IntelligentPathPlanningMethod Moreandmoreartificialintelligencemethodshavebeenappliedinthestudies
of UUV path planning in recent years, covering the genetic algorithm, swarm intelligence, fuzzy logic, and