  In this paper we present a hierarchical multi-rate control architecture for
nonlinear autonomous systems operating in partially observable environments.
Control objectives are expressed using syntactically co-safe Linear Temporal
Logic (LTL) specifications and the nonlinear system is subject to state and
input constraints. At the highest level of abstraction, we model the
system-environment interaction using a discrete Mixed Observable Markov
Decision Problem (MOMDP), where the environment states are partially observed.
The high level control policy is used to update the constraint sets and cost
function of a Model Predictive Controller (MPC) which plans a reference
trajectory. Afterwards, the MPC planned trajectory is fed to a low-level
high-frequency tracking controller, which leverages Control Barrier Functions
(CBFs) to guarantee bounded tracking errors. Our strategy is based on model
abstractions of increasing complexity and layers running at different
frequencies. We show that the proposed hierarchical multi-rate control
architecture maximizes the probability of satisfying the high-level
specifications while guaranteeing state and input constraint satisfaction.
Finally, we tested the proposed strategy in simulations and experiments on
examples inspired by the Mars exploration mission, where only partial
environment observations are available.
