  We present a novel concept for teach-and-repeat visual navigation. The
proposed concept is based on a mathematical model, which indicates that in
teach-and-repeat navigation scenarios, mobile robots do not need to perform
explicit localisation. Rather than that, a mobile robot which repeats a
previously taught path can simply `replay' the learned velocities, while using
its camera information only to correct its heading relative to the intended
path. To support our claim, we establish a position error model of a robot,
which traverses a taught path by only correcting its heading. Then, we outline
a mathematical proof which shows that this position error does not diverge over
time. Based on the insights from the model, we present a simple monocular
teach-and-repeat navigation method. The method is computationally efficient, it
does not require camera calibration, and it can learn and autonomously traverse
arbitrarily-shaped paths. In a series of experiments, we demonstrate that the
method can reliably guide mobile robots in realistic indoor and outdoor
conditions, and can cope with imperfect odometry, landmark deficiency,
illumination variations and naturally-occurring environment changes.
Furthermore, we provide the navigation system and the datasets gathered at
http://www.github.com/gestom/stroll_bearnav.
