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Hierarchical Finite State Machines for Efficient Optimal Planning in Large-scale Systems. (arXiv:2212.03724v2 [eess.SY] UPDATED)

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In this paper, we consider a planning problem for a hierarchical finite state
machine (HFSM) and develop an algorithm for efficiently computing optimal plans
between any two states. The algorithm consists of an offline and an online
step. In the offline step, one computes exit costs for each machine in the
HFSM. It needs to be done only once for a given HFSM, and it is shown to have
time complexity scaling linearly with the number of machines in the HFSM. In
the online step, one computes an optimal plan from an initial state to a goal
state, by first reducing the HFSM (using the exit costs), computing an optimal
trajectory for the reduced HFSM, and then expand this trajectory to an optimal
plan for the original HFSM. The time complexity is near-linearly with the depth
of the HFSM. It is argued that HFSMs arise naturally for large-scale control
systems, exemplified by an application where a robot moves between houses to
complete tasks. We compare our algorithm with Dijkstra's algorithm on HFSMs
consisting of up to 2 million states, where our algorithm outperforms the
latter, being several orders of magnitude faster.

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