# Planning using hierarchical constrained Markov decision processes

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## Abstract

Constrained Markov decision processes offer a principled method to determine policies for sequential stochastic decision problems where multiple costs are concurrently considered. Although they could be very valuable in numerous robotic applications, to date their use has been quite limited. Among the reasons for their limited adoption is their computational complexity, since policy computation requires the solution of constrained linear programs with an extremely large number of variables. To overcome this limitation, we propose a hierarchical method to solve large problem instances. States are clustered into macro states and the parameters defining the dynamic behavior and the costs of the clustered model are determined using a Monte Carlo approach. We show that the algorithm we propose to create clustered states maintains valuable properties of the original model, like the existence of a solution for the problem. Our algorithm is validated in various planning problems in simulation and on a mobile robot platform, and we experimentally show that the clustered approach significantly outperforms the non-hierarchical solution while experiencing only moderate losses in terms of objective functions.

### Keywords

Constrained Markov decision processes Planning Uncertainty## Notes

### Acknowledgements

This paper extends preliminary results presented in Feyzabadi and Carpin (2015). This work is supported by the National Institute of Standards and Technology under cooperative agreement 70NANB12H143. Any opinions, findings, and conclusions or recommendations expressed in these materials are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the funding agencies of the U.S. Government.

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