  Most real-world systems are affected by external disturbances, which may be
impossible or costly to measure. For instance, when autonomous robots move in
dusty environments, the perception of their sensors is disturbed. Moreover,
uneven terrains can cause ground robots to deviate from their planned
trajectories. Thus, learning the external disturbances and incorporating this
knowledge into the future predictions in decision-making can significantly
contribute to improved performance. Our core idea is to learn the external
disturbances that vary with the states of the system, and to incorporate this
knowledge into a novel formulation for robust tube model predictive control
(TMPC). Robust TMPC provides robustness to bounded disturbances considering the
known (fixed) upper bound of the disturbances, but it does not consider the
dynamics of the disturbances. This can lead to highly conservative solutions.
We propose a new dynamic version of robust TMPC (with proven robust stability),
called state-dependent dynamic TMPC (SDD-TMPC), which incorporates the dynamics
of the disturbances into the decision-making of TMPC. In order to learn the
dynamics of the disturbances as a function of the system states, a fuzzy model
is proposed. We compare the performance of SDD-TMPC, MPC, and TMPC via
simulations, in designed search-and-rescue scenarios. The results show that,
while remaining robust to bounded external disturbances, SDD-TMPC generates
less conservative solutions and remains feasible in more cases, compared to
TMPC.
