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Figure 14. Tracking trajectory comparison of the bio-inspired model based method and conventional backstepping method for the under-
water robots. A: curve tracking; B: helix tracking [105] .

and limited electric power of underwater robots, the speed jumps as well as the driving saturation problem
have to be considered. The bio-inspired backstepping controller was introduced in the control design to give
the resolution respectively [102] . Due to the characteristics of the shunting model, the outputs of the control are
bounded in a limited range with a smooth variation [103] .

The bio-inspired backstepping controller has been applied on different underwater robots under various con-
ditions by combining with a sliding mode control that controls the dynamic component of the vehicle, where
an adaptive term is used in the sliding mode control to estimate the non-linear uncertainties part and the
disturbance of the underwater vehicle dynamics [104] . For example, the driving saturation problem of a 7000m
manned submarine was resolved through this bio-inspired backstepping with the sliding mode control cas-
cade control [105] . The control contains a kinematic controller that used bio-inspired backstepping control to
eliminate the speed jump when the tracking error occurred at the initial state. Then, a sliding mode dynamic
controller was proposed to reduce the lumped uncertainty in the dynamics of the underwater robots, thus re-
alizing the robust trajectory tracking control without speed jumps for the underwater robots Figure 14. Jiang
et al. [106] accomplished the trajectory tracking of the autonomous underwater robots in marine environments
with a similar bio-inspired backstepping controller and the adaptive integral sliding mode controller. In the
sliding mode controller, the chattering problem was alleviated, which increased the practical feasibility of the
vehicle. However, more studies are needed to compare to prove the effectiveness of the proposed control
strategy, such as the tracking control based on the filtered backstepping method.

4.2. Formation control
The bio-inspired neurodynamics trajectory tracking control for a single nonholonomic mobile robot can be
extended to the formation control for multiple nonholonomic mobile robots, in which the follower can track
its real-time leader by the proposed kinematic controller. This section introduces leader-follower formation
control based on the bio-inspired neurodynamics tracking controller into three different robot platforms.

4.2.1. Mobile robots
The leader-follower formation control based on the bio-inspired neurodynamics tracking controller was stud-
ied by Peng et al. [107] . The asymptotic stability of the closed-loop system was guaranteed. The issue of imprac-
ticalvelocityjumparisingfromtheuseofthebacksteppingapproachwashandledbymeansofthebio-inspired
neurodynamics model. However, the control design was based on the level of the kinematics model so that the