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

Hierarchical Finite State Machines for Efficient Optimal Planning in Large-scale Systems