....¹

Functions such as $pre(p)$ are used for referential convenience throughout this paper. Here, $pre$ and $pre(p)$ are the same, and $pre(p)$ is read as ``the preconditions of $p$.''

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... conflict.²

Using universal quantification [WeldWeld1994] a single plan could have a $\forall agent, agent \not=$ productionManager $\rightarrow \neg using$(transport1, $agent$) condition that would exclude concurrent access to the transport. We could have also simply specified transport1 as a non-consumable resource with maximum capacity of one.

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... resource³

It is important not to confuse power with battery energy. A power source (e.g. battery, solar panels) makes a fixed amount of power in Watts available at any point in time. A battery's energy (in Watt-hours) is reduced by the integral of the total use of this power over time.

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... subinterval⁴

For summary resource usages of the last interval intersecting the child task, we replace $[0,0]$ with $[e,f]$ in the $persist$.

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... plans.⁵

In fact, it is NP-complete [ClementClement2002].

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....⁶

This is why Georgeff chose to cluster multiple operators into ``critical regions'' and synchronize the (fewer) regions since there would be many fewer interleavings to check georgeff:83. By exploiting the hierarchical structure of plans, we use the ``clusters'' predefined in the hierarchy to this kind of advantage without needing to cluster from the bottom up.

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... hierarchy.⁷

The analysis also applies to state constraints, but we restrict the discussion to resource usage constraints for simplicity.

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... problems.⁸

For other experiments, we used a decomposition rate of 20% since it seemed to work well.

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