Model Predictive Control in Partially Observable Multi-Modal Discrete Environments

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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) based on a continuous-state Linear Time-Invariant (LTI) system model operating in a discrete-state environment described by a Hidden Markov Model (HMM). Environment constraints are modeled as chance constraints and environment observations can be asynchronous with system state measurements and controller updates. We show how to approximate the solution of the MPC problem defined over the space of feedback policies by optimizing over a trajectory tree, where each branch is associated with an environment measurement. The proposed approach guarantees chance constraint satisfaction and recursive feasibility. Finally, we test the proposed strategy on navigation examples in partially observable environments, where the proposed MPC guarantees chance constraint satisfaction.