  Micron-scale robots ($\mu$bots) have recently shown great promise for
emerging medical applications. Accurate controlling $\mu$bots, while critical
to their successful deployment, is challenging. In this work, we consider the
problem of tracking a reference trajectory using a $\mu$bot in the presence of
disturbances and uncertainty. The disturbances primarily come from Brownian
motion and other environmental phenomena, while the uncertainty originates from
errors in the model parameters. We model the $\mu$bot as an uncertain unicycle
that is controlled by a global magnetic field. To compensate for disturbances
and uncertainties, we develop a nonlinear mismatch controller. We define the
model mismatch error as the difference between our model's predicted velocity
and the actual velocity of the $\mu$bot. We employ a Gaussian Process to learn
the model mismatch error as a function of the applied control input. Then we
use a least-squares minimization to select a control action that minimizes the
difference between the actual velocity of the $\mu$bot and a reference
velocity. We demonstrate the online performance of our joint learning and
control algorithm in simulation, where our approach accurately learns the model
mismatch and improves tracking performance. We also validate our approach in an
experiment and show that certain error metrics are reduced by up to $40\%$.
