Model Predictive Control in Partially Observable Multi-Modal Discrete Environments

Autonomous systems operate in environments that can be observed only through noisy measurements. Thus, controllers should compute actions based on their beliefs about the surroundings. In these settings, we design a Model Predictive Controller (MPC) continuous-state Linear Time-Invariant (LTI) system model operating discrete-state environment described by Hidden Markov (HMM). Environment constraints are modeled as chance and observations asynchronous with state measurements controller updates. We show how to approximate solution of MPC problem defined over space feedback policies optimizing trajectory tree, where each branch is associated an measurement. The proposed approach guarantees constraint satisfaction recursive feasibility. Finally, test strategy navigation examples partially observable environments, satisfaction.