Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metrics

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