  This paper presents an approach towards guaranteed trajectory tracking for
nonlinear control-affine systems subject to external disturbances based on
robust control contraction metrics (CCM) that aims to minimize the $\mathcal
L_\infty$ gain from the disturbances to nominal-actual trajectory deviations.
The guarantee is in the form of invariant tubes, computed offline and valid for
any nominal trajectories, in which the actual states and inputs of the system
are guaranteed to stay despite disturbances. Under mild assumptions, we prove
that the proposed robust CCM (RCCM) approach yields tighter tubes than an
existing approach based on CCM and input-to-state stability analysis. We show
how the RCCM-based tracking controller together with tubes can be incorporated
into a feedback motion planning framework to plan safe trajectories for robotic
systems. Simulation results illustrate the effectiveness of the proposed method
and empirically demonstrate reduced conservatism compared to the CCM-based
approach.
