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performance of formation control relies highly on the low-level servo controller. The robustness property of
the system is not analyzed, which is important when facing uncertainties or disturbances. Therefore, further
improvements can be made based on these aforementioned points. A leader–follower formation control using
a bioinspired neurodynamics-based approach was proposed by Yi et al. [108] for resolving the impractical veloc-
ity jump problem of nonholonomic vehicles. Simulation results demonstrate the effectiveness of the proposed
control law.

[6]
In order to further improve the tracking performance, a non-time based controller was also proposed . The
path planner not only generated a desired path for the mobile robot, but also became part of the control
to adjust the actual path and desired path. Along with the bio-inspired backstepping tracking control, the
proposed method provided an overall better performance than a single backstepping control alone for multi-
robotic systems.

4.2.2. Surface robots
To fulfill the requirement of accomplishing complex tasks in the unpredictable marine environment, where the
ocean currents and the marine organism may affect the efficiency of the vehicle operation, formation control
on the system of multiple USVs has become a hot topic in recent decades [109] . Studies of combining the bio-
inspired model with the marine vehicle formation control have been proposed and the model is often used to
achieve the intelligent planning results of the multi-vehicle system [110] .

Regarding the bio-inspired model application on the USV formation control, a novel adaptive formation con-
trol scheme based on bio-inspired neurodynamics for waterjet USVs with the input and output constraints
was proposed [111] . However, the learning process of the adaptive neural network can reduce the real-time per-
formance, which is the superiority of the bio-inspired neural network. In addition, the robustness property of
the resulting closed-loop system is not analyzed when the undesired perturbation is injected into the system,
which is considered a critical problem in practical engineering.

For multi-robotic system operates in large and unknown environments, Ni et al. [26] used a dynamic bio-
inspired neural network for real-time formation control of multi-robotic systems in large and unknown en-
vironments. The proposed approach considered many uncertain situations. Figure 15 shows that the multi-
robotic systems still finish the formation task, when the leader USV was broken. However, the mathematical
analysis for the proposed algorithm is not provided, such as convergence analysis and robustness analysis.
Comparison with traditional approaches is not provided, thus it is not sufficient to demonstrate the efficiency
of the proposed method.

Intelligent formation control for a group of waterjet USVs considering formation tracking errors constraints
was proposed [112] . To guarantee line-of-sight range and angle tracking errors constraints, a time-varying
tan-type barrier Lyapunov function is employed. Besides, the bio-inspired neurodynamics was integrated
to address the traditional differential explosion problem, i.e., avoiding the differential operation of the virtual
control. However, the simulation example is much limited, thus the effectiveness and efficiency of the pro-
posed control scheme are not sufficiently verified, i.e., the lack of the comparison with another type of control
method.

4.2.3. Underwater robots
For underwater robots, the definition of formation control is similar to the surface vehicle but with additional
dimensions [113] . Formation control of the multi-UUV system considers both 2-D and 3-D, where the former
focuses on the lateral movement of the vehicle groups [114] .

A formation control on the multi-UUV system to realize the tracking of desired trajectory and obstacle avoid-