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Charting the trade-off between design complexity and plan execution under probabilistic actions

Practical robot designs must strike a compromise between fabrication/manufacture cost and anticipated execution performance. Compared to parsimonious designs, more capable (and hence more expensive) robots generally achieve their ends with greater efficiency. This paper examines how the roboticist might explore the space of designs to gain an understanding of such trade-offs. We focus, specifically, on design choices that alter the set of actions available to the robot, and model those actions as involving uncertainty. We consider planning problems under the Markov Decision Process (MDP) model, which leads us to examine how to relate the cost of some design to the expected cost of an execution for the optimal policies feasible with that design. The complexity of this problem ─expressed via hardness in the fixed parameter tractability sense─depends on the number of actions to choose from. When that number is not negligible, we give a novel representation and an algorithm utilizing that structure that allows useful savings over naïve enumeration.