Multi-agent coordination problems have many layers of complexity that make them interesting research problems. What uniquely separates multi-agent coordination problems from large single-agent planning and execution problems is that in multi-agent problems, different agents have different understandings of global state. The way that diverging beliefs are reconciled is through communication. My thesis builds a real-time executive that manages and reasons about communication between agents and provides the supplementing theory to prove that these algorithms are practical and efficient.

Simple Temporal Networks with Uncertainty (STNUs) provide a useful formalism with which to reason about events and the temporal constraints that apply to them. STNUs are in particular notable because they facilitate reasoning over stochastic, or uncontrollable, actions and their corresponding durations. To evaluate the feasibility of a set of constraints associated with an STNU, one checks the network's \textit{dynamic controllability}, which determines whether an adaptive schedule can be constructed on-the-fly. Our work improves the runtime of checking the dynamic controllability of STNUs with integer bounds to O(min(mn, m sqrt(n) log N) + km + k^2n + kn log n). Our approach pre-processes the STNU using an existing O(n^3) dynamic controllability checking algorithm and provides tighter bounds on its runtime. This makes our work easily adaptable to other algorithms that rely on checking variants of dynamic controllability.

In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal constraints is consistent. While many of the simpler models have been well-studied from a computational complexity perspective, the algorithms developed for advanced models which combine features have very loose complexity bounds. In this work, we provide tight completeness bounds for strong, weak, and dynamic controllability checking of temporal networks that have conditions, disjunctions, and temporal uncertainty. Our work exposes some of the subtle differences between these different structures and, remarkably, establishes a guarantee that all of these problems are computable in PSPACE.

In multi-agent temporal planning, individual agents cannot know a priori when other agents will execute their actions and so treat those actions as uncertain. Only when others communicate the results of their actions is that uncertainty resolved. If a full communication protocol is specified ahead of time, then delay controllability can be used to assess the feasibility of the temporal plan. However, agents often have flexibility in choosing when to communicate the results of their action. In this paper, we address the question of how to choose communication protocols that guarantee the feasibility of the original temporal plan subject to some cost associated with that communication. To do so, we introduce a means of extracting delay controllability conflicts and show how we can use these conflicts to more efficiently guide our search. We then present three conflict-directed search algorithms and explore the theoretical and empirical trade-offs between the different approaches.

In temporal planning, agents must schedule a set of events satisfying a set of predetermined constraints. These scheduling problems become more difficult when the duration of certain actions are outside the agent's control. Delay controllability is the generalized notion of whether a schedule can be constructed in the face of uncertainty if the agent eventually learns when events occur. Our work introduces the substantially more complex setting of determining variable-delay controllability, where an agent learns about events after some unknown but bounded amount of time has passed. We provide an efficient O(n^3) variable-delay controllability checker and show how to create an execution strategy for variable-delay controllability problems. To our knowledge, these essential capabilities are absent from existing controllability checking algorithms. We conclude by providing empirical evaluations of the quality of variable-delay controllability results as compared to approximations that use fixed delays to model the same problems.

In this paper, we focus on speeding up the temporal plan relaxation problem for dynamically controllable systems. We take a look at the current best-known algorithm for determining dynamic controllability and augment it to efficiently generate conflicts when the network is deemed uncontrollable. Our work preserves the O(n^3) runtime of the best available dynamic controllability checker and improves on the previous best runtime of O(n^4) for extracting dynamic controllability conflicts. We then turn our attention to temporal plan relaxation tasks and show how we can leverage our work on conflicts and the structure of the network to efficiently make incremental updates intended to restore dynamic controllability by relaxing constraints. Our new algorithm, RelaxIDC, has the same asymptotic runtime as previous algorithms but sees dramatic empirical improvements over the course of repeated dynamic controllability checks.