Feedback Linearization Techniques for Collaborative Nonholonomic Robots

Collaborative robots performing tasks together have significant advantages over a single
robot. Applications can be found in the fields of underwater robotics, air traffic control,
intelligent highways, mines and ores detection and tele-surgery. Collaborative wheeled
mobile robots can be modeled by a nonlinear system having nonholonomic constraints.
Due to these constraints, the collaborative robots arc not stabilizable at a point by
continuous time-invariant feedback control laws. Therefore, linear control is ineffective,
even locally, and innovative design techniques are needed. One possible design technique
is feedback control and the principal interest of this thesis is to evaluate the best feedback
control technique.
Feedback linearization is one of the possible feedback control techniques. Feedback
linearization is a method of transforming a nonlinear system into a linear system using
feedback transformation. It differs from conventional Taylor series linearization since it
is achieved using exact coordinates transformation rather than by linear approximations
of the system. Linearization of the collaborative robots system using Taylor series results
in a linear system which is uncontrollable and is thus unsuitable. On the other hand, the
feedback linearized control strategies result in a stable system. Feedback linearized
control strategies can he designed based on state or input, while both state and input
linearization can be achieved using static or dynamic feedback.
In this thesis, a kinematic model of the collaborative nonholonomic robots is derived,
based on the leader-follower formation. The objective of the kinematic model is to
facilitate the design of feedback control strategies that can stabilize the system and
Minimize the error between the desired and actual trajectory. The leader-follower
formation is used in this research since the collaborative robots are assumed to have
communication capabilities only.
The kinematic model for the leader-follower formation is simulated using
MATLAB/Simulink. A comparative assessment of various feedback control strategies is
evaluated. The leader robot model is tested using five feedback control strategies for
different trajectories. These feedback control strategies are derived using cascaded
system theory, stable tracking method based on linearization of corresponding error
model, approximation linearization, nonlinear control design and full state linearization
via dynamic feedback. For posture stabilization of the leader robot, time-varying and full
state dynamic feedback linearized control strategies are used. For the follower robots
using separation bearing and separation-separation formation, the feedback linearized
control strategies are derived using input-output via static feedback.
Based on the simulation results for the leader robot, it is found that the full state dynamic
feedback linearized control strategy improves system performance and minimizes the
mean of error more rapidly than the other four feedback control strategies. In addition to
stabilizing the system, the full state dynamic feedback linearized control strategy
achieves posture stabilization. For the follower robots, the input-output via static
feedback linearization control strategies minimize the error between the desired and
actual formation. Furthermore, the input-output linearized control strategies allow
dynamical change of the formation at run-time and minimize the disturbance of formation
change. Thus, for a given feasible trajectory, the full state feedback linearized strategy for
the leader robot and input-output feedback linearized strategies for the follower robots are
found to be more efficient in stabilizing the system.