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Page 203 Zhu et al. Intell Robot 2022;2(3):200­222 I http://dx.doi.org/10.20517/ir.2022.13

In the agent-based task assignment algorithm, the whole system is assumed to be an economy entity, while
each vehicle works as an agent. The agent-based algorithms are regarded as decentralized approaches, as each
vehicle agent is supposed to know its requirement and limitation, and the final solution is deduced based on
the balance between them. The task assigned to each agent is balanced after the repeated computation and
comparison of the cost to their targets; therefore, the minor consumption and the largest profit for the whole
entity can be obtained at the end [19] . The agent-based algorithms such as the auction algorithm resolve the
taskassignmentproblemofknowntargetsefficiently; however, theydonotworkwellinthevehicleassignment
problem of unknown targets [20,21] . Yao applied the biased min-consensus (BMC) method, which introduces
the edge weight into the standard min-consensus protocol. Yao achieved the path planning of simultaneous
arrival for all UUVs through this agent-based task assignment algorithm, yet the situation of unknown targets
is still not developed [22,23] .

Intelligent methods such as swarm intelligence, genetic algorithm (GA), and neural network (NN) have been
tested in solving the problem of the multi-vehicle task assignment [24–26] . These intelligent methods find the
best task assignment solution by the objective function established on the total searching length and the heuris-
tic cost through iteration algorithms. In recent years, the self-organizing map (SOM), an NN-based algorithm,
was applied to the task assignment problem of a multi-vehicle system due to the competitiveness and self-
improving features of the neural network [27] . The SOM-based task assignment algorithm guarantees that each
vehicle in the multi-vehicle system can navigate along the shortest path to their target while maintaining the
shortest total navigation cost for the whole system, whose structure is shown in Figure 2. The target locations
serve as the inputs while the vehicle positions and paths are the outputs of the network, and the network is up-
dated by the weights between layers that are deduced based on distances between targets and vehicles [28] . The
turning direction angle and turning radius of the vehicle are then involved on the basis of the SOM method
due to the vehicle’s practical requirement of reducing the energy cost by reaching the target in a smooth curve
in the task assignment problem [29,30] .

However, the task assignment algorithms considering the underwater environment are still not thoroughly
investigated due to the complex environmental factors and the nonlinear UUV system. Considering the com-
plexity of the underwater environment such as the currents effect, Chow proposed an improved K-means
algorithm to simultaneously resolve the task assignment and path planning problems for the multi-UUV sys-
tem under the static ocean currents effect, where the vehicle successfully reached the target along smooth
curves on the basis of optimal task assignment [31] . Nevertheless, the method does not work well for mov-
ing targets, and it lacks the discussion of applications under the 3D static ocean currents effect as well as the
dynamic currents condition. Zhu et al. introduced SOM into the multi-UUV system and combined SOM
with a velocity synthesis algorithm; hence, the task assignment and path planning problem for the multi-UUV
system under time-varying ocean currents when chasing both static or dynamic targets could be addressed,
which resolved the issues that existed in Chow’s study. However, neither SOM-based methods could realize
satisfactory collision avoidance [32] .

Methods that have been applied to the task assignment of the multi-UUV system are listed in Table 1. Details
of various intelligent methods for task assignment of UUVs can be found in Section 2.1. Gaps are still left for
relative studies, which can be mainly concluded into two problems. The first problem is the difference among
heterogeneous UUVs. They have different model parameters, navigating velocities or safe distances such that
the assignment of parameters for every single UUV is not consistent in the practical application. The other
problem is the effect of the underwater environmental factors such as the obstacles and the fluid effect, which
may produce inevitable deviations or too many dynamic requirements for vehicles in the task assignment.