  In this paper, a time-varying leader-follower formation control of
nonholonomic mobile robots based on a trajectory tracking control strategy is
considered. In the time-varying formation, the relative bearing and distance of
each follower are variable parameters, and therefore, the followers can carry
out various and complex behaviour even without changing the linear and angular
velocities of the leader robot. After proposing the kinematic model of the
time-varying leader-follower formation, the backstepping control method is
exploited to keep the structure of the defined formation. The global stability
of the formation is investigated using the Lyapunov theorem. Moreover, the
designed nonlinear controller suffers from the ineffectual large input commands
at the beginning of the formation. To rectify this problem, a fuzzy adaptive
algorithm is proposed to improve the backstepping controller and the global
stability of the resulting fuzzy adaptive backstepping controller is
guaranteed. Considering the rate change of relative distance and bearing in the
kinematic model of the leader-follower formation and controller design
procedure, makes the formation more practical in dynamic and clutter
environments, as well as capable of defining complicated behaviour for
followers, and provides crash and obstacle avoidance without switching between
different control strategies. Finally, the performance of the proposed
kinematics model and designed controllers are investigated through simulations
and experimental studies.
