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Li et al. Intell Robot 2021;1(1):58-83 I http://dx.doi.org/10.20517/ir.2021.08 Page 72

Figure 11. The block diagram of the bio-inspired tracking control for robots

4.1.1. Mobile robots
Real-time tracking control of a mobile robot is a challenging issue in mobile robotics. The main purpose of
the tracking control is to eliminate or reduce the effects of errors. However, the disturbance, noise, and sensor
errors will interfere with the output of the robotic system and produce errors. Many control algorithms of
the mobile robot have been studied for precisely tracking a desired trajectory. The conventional backstepping
control for mobile robots suffers from velocity jump issues, this problem is embedded in the design of the
controller. The linear velocity error term causes the velocity jump if the initial tracking error does not equal
zero. As seen this problem, the bio-inspired neural dynamics was brought into the design of the backstepping
control. For a nonholonomic mobile robot operates in a 2-D Cartesian work space, the main control variables
for its kinematic model are the linear velocity and angular velocity. Focusing on the design of solving the
velocity jump issue, the bio-inspired backstepping kinematic control for a mobile robot is defined as

= + cos (12)

(13)
= + 1 + 2 sin
= − + ( − ) [ ] − ( + ) [ ] − (14)
+

where is derived from neural dynamics equation regards to the error in driving direction for the mobile
robot, 1 and 2 arethedesignedparameters, and arerespectivelythedesiredlinearandangularvelocity
that are given at path planning stage, and are respectively the linear and angular velocity commands
that generated from the controller, and and are respectively the tracking error in driving and lateral
directions [14] . Compared to conventional design, the bio-inspired backstepping control takes the advantage
of the shunting model that provides bounded smooth output.

The bio-inspired backstepping controller resolved the problem of sharp speed jumps at the initial stage [24,88,89] .
The total design of the proposed control and path planning method were able to provide both real-time
collision-free path and provide smooth velocity tracking commands for a nonholonomic mobile robot. How-
ever, the generated angular velocity seemed to suffer from sharp changes, therefore, the validation of the pro-
posed control strategy is needed. In addition, the simulation environment is assumed as a simple environment
with no obstacles. Zheng et al. [90] proposed an adaptive robust finite-time bio-inspired neurodynamics con-
trol with unmeasurable angular velocity and multiple time-varying bounded disturbances. The outputs were
smooth and the sharp jumps of initial values were decreased.

In real-world applications, the model input of the mobile robot may have errors, therefore, to overcome the
problemofthisabruptchangeinthegeneratedvelocitiescausedbythemodelinputerrors,afuzzyneurodynamics-
based tracking controller, which incorporated fuzzy control to generate smooth velocities, was proposed [91] .
The proposed control considered the model input error that consequently have impacts on the tracking er-
ror, which was further reduced using fuzzy logic to incorporate with the bio-inspired backstepping control.