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Ocean Engineering 235 (2021) 109355
6
C. Cheng et al.
Fig. 5.
The flowchart of the particle swarm optimization algorithm.
introduced to solve the critical point problem. Simulated experimental
results verified the effectiveness of the proposed algorithm. In path
planning for AUV docking,
Li et al.
(
2019c
) proposed an adaptive
quantum particle swarm optimization algorithm based on B-spline
function. B-spline function allows AUV to obtain a smoother path by
setting multiple internal control points. Since the attitude of AUV is
controlled by rudder and propeller, the constraint of curvature radius
caused by kinematics of AUV is considered when the particle position is
updated in their method. In addition, the algorithm uses the quantum
behavior to update particles, considers the travel time in the fitness
function, and adds a mutation operator, which greatly improves the
search performance. To speed up the convergence,
Wang et al.
(
2020
)
proposed an improved quantum particle swarm optimization algorithm.
In their method, the safety, length and angle of the path are considered
for constructing the fitness function, and the cubic spline interpolation
algorithm
Hou and Andrews
(
1978
) is used to smooth the path. In
addition, since the translational velocity of AUV is affected by the eddy
flow field, the component of flow velocity is considered in the wave,
swing and heave of AUV.
Lim et al.
(
2020b
) proposed a particle swarm
optimization algorithm with selective differential evolution for off-line
path planning of AUV. Selecting the most suitable particle for differen-
tial evolution hybridization can greatly reduce the computation. The
proposed algorithm is simulated and tested in an environment with
known obstacles and time-invariant non-uniform currents.
Compared with other mobile robots, the particle swarm optimiza-
tion for AUV path planning mainly modifies the adaptability function
to resist the interference of current or changes the update process of
particles to adapt to the underactuated AUV. Particle swarm optimiza-
tion has no crossover and mutation operation and only needs to adjust
Fig. 6.
The mechanism of the ant colony algorithm.
Source:
Modified from
Dorigo et al.
(
1991
).
a few parameters. In addition, it has a memory function and can find
the optimal path in a short time. However, due to the lack of dynamic
regulation of particle velocity, particle swarm optimization is easy to
fall into local optimums.
3.5. Ant colony optimization
Similar to particle swarm optimization which is inspired by birds’
foraging behavior, the ant colony algorithm is a heuristic optimization
method proposed by simulating the foraging behavior of ant colony in
nature. The fundamental idea behind the ant colony algorithm is that
it uses the behavior of a single ant to represent one feasible solution
of the path optimization problem, and the behavior of the entire ant
colony constitutes the solution space of the problem. The mechanism
of the ant colony algorithm is shown in
Fig. 6
. To be specific, ants can
sense the chemicals released by groups called pheromones, and show
certain intelligent behaviors in the process of foraging (
Fig. 6
(a)). In the
presence of obstacles, ants will randomly crawl to both sides of the path
(
Fig. 6
(b)). As time goes, the pheromone concentrated on the short path
is larger than that on the long path (
Dorigo et al.
,
1991
). According to
the intensity of pheromone, they can be guided to bypass the obstacles
and find the shortest path to food sources (
Fig. 6
(c)).
Wang and Wei
(
2009
) improved the ant colony optimization algo-
rithm and applied it to AUV path planning. Specifically, they defined
the area covered or partially covered by obstacles as inaccessible region
with the grid method. In addition, a cutting operator and insertion
point operator are added to allow AUV to find a smooth path around
the inaccessible area quickly. However, the distance between AUV
and the obstacle might be very close, which poses a great threat to
the safety of the vehicle.
Zhang and Jia
(
2012
) used the distance
between AUV and obstacles as heuristic information and added a
penalty factor in the ant colony optimization algorithm to eliminate
the path close to the obstacle. Their simulation results show that the
proposed method may produce too large yaw angle, which does not
conform to the yaw characteristics of AUV. To avoid static obsta-
cles in three-dimensional space,
Yang et al.
(
2015
) proposed an ant
colony optimization algorithm based on pheromone elimination. In
their method, the pheromone is divided into two parts: attraction and
repulsion. So ants can explore first and then develop in the search path,
which can overcome the shortcoming of making AUV fall into local
extremum easily in traditional ant colony optimization algorithm. In
addition, in their method, the main running direction is determined
when initializing the population, and the maximum horizontal and
vertical moving ranges of AUV are limited.
To speed up the convergence,
Dong and Xu
(
2017
) proposed an
ant colony algorithm with a reinforcement idea from reinforcement
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