The formalism of Simple Temporal Networks (STNs) provides methods for evaluating the feasibility of temporal plans. The basic formalism deals with the consistency of quantitative temporal requirements on scheduled events. This implicitly assumes a single agent has full control over the timing of events. The extension of Simple Temporal Networks with Uncertainty (STNU) introduces uncertainty into the timing of some events. Two main approaches to the feasibility of STNUs involve (1) where a single schedule works irrespective of the duration outcomes, called Strong Controllability, and (2) whether a strategy exists to schedule future events based on the outcomes of past events, called Dynamic Controllability. Case (1) essentially assumes the timing of uncertain events cannot be observed by the agent while case (2) assumes full observability. The formalism of Partially Observable Simple Temporal Networks with Uncertainty (POSTNU) provides an intermediate stance between these two extremes, where a known subset of the uncertain events can be observed when they occur. A sound and complete polynomial algorithm to determining the Dynamic Controllability of POSTNUs has not previously been known; we present one in this paper. This answers an open problem that has been posed in the literature. The approach we take factors the problem into Strong Controllability micro-problems in an overall Dynamic Controllability macro-problem framework. It generalizes the notion of labeled distance graph from STNUs. The generalized labels are expressed as max/min expressions involving the observables. The paper introduces sound generalized reduction rules that act on the generalized labels. These incorporate tightenings based on observability that preserve dynamic viable strategies. It is shown that if the generalized reduction rules reach quiescence without exposing an inconsistency, then the POSTNU is Dynamically Controllable (DC). The paper also presents algorithms that apply the reduction rules in an organized way and reach quiescence in a polynomial number of steps if the POSTNU is Dynamically Controllable. Remarkably, the generalized perspective leads to a simpler and more uniform framework that applies also to the STNU special case. It helps illuminate the previous methods inasmuch as the max/min label representation is more semantically clear than the ad-hoc upper/lower case labels previously used.

Conditional simple temporal networks with uncertainty (CSTNUs) allow for the representation of temporal plans subject to both conditional constraints and uncertain durations. Dynamic controllability (DC) of CSTNUs ensures the existence of an execution strategy able to execute the network in real time (i.e., scheduling the time points under control) depending on how these two uncontrollable parts behave. However, CSTNUs do not deal with resources. In this paper, we define conditional simple temporal networks with uncertainty and resources (CSTNURs) by injecting resources and runtime resource constraints (RRCs) into the specification. Resources are mandatory for executing the time points and their availability is represented through temporal expressions, whereas RRCs restrict resource availability by further temporal constraints among resources. We provide a fully-automated encoding to translate any CSTNUR into an equivalent timed game automaton in polynomial time for a sound and complete DC-checking.

Dynamic Controllability (DC) of a Simple Temporal Problem with Uncertainty (STPU) uses a dynamic decision strategy, rather than a fixed schedule, to tackle temporal uncertainty. We extend this concept to the Controllable Conditional Temporal Problem with Uncertainty (CCTPU), which extends the STPU by conditioning temporal constraints on the assignment of controllable discrete variables. We define dynamic controllability of a CCTPU as the existence of a strategy that decides on both the values of discrete choice variables and the scheduling of controllable time points dynamically. This contrasts with previous work, which made a static assignment of choice variables and dynamic decisions over time points only. We propose an algorithm to find such a fully dynamic strategy. The algorithm computes the "envelope" of outcomes of temporal uncertainty in which a particular assignment of discrete variables is feasible, and aggregates these over all choices. When an aggregated envelope covers all uncertain situations of the CCTPU, the problem is dynamically controllable. However, the algorithm is complete only under certain assumptions. Experiments on an existing set of CCTPU benchmarks show that there are cases in which making both discrete and temporal decisions dynamically it is feasible to satisfy the problem constraints while assigning the discrete variables statically it is not.

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 paper, 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.

Dynamic Controllability (DC) of a Simple Temporal Problem with Uncertainty (STPU) uses a dynamic decision strategy, rather than a fixed schedule, to tackle temporal uncertainty. We extend this concept to the Controllable Conditional Temporal Problem with Uncertainty (CCTPU), which extends the STPU by conditioning temporal constraints on the assignment of controllable discrete variables. We define dynamic controllability of a CCTPU as the existence of a strategy that decides on both the values of discrete choice variables and the scheduling of controllable time points dynamically. This contrasts with previous work, which made a static assignment of choice variables and dynamic decisions over time points only. We propose an algorithm to find such a fully dynamic strategy. The algorithm computes the ''envelope'' of outcomes of temporal uncertainty in which a particular assignment of discrete variables is feasible, and aggregates these over all choices. When an aggregated envelope covers all uncertain situations of the CCTPU, the problem is dynamically controllable. However, the algorithm is not complete. Experiments on an existing set of CCTPU benchmarks show that there are cases in which making both discrete and temporal decisions dynamically it is feasible to satisfy the problem constraints, while assigning the discrete variables statically it is not.

The Temporal Network with Uncertainty (TNU) modeling framework is used to represent temporal knowledge in presence of qualitative temporal uncertainty. Dynamic Controllability (DC) is the problem of deciding the existence of a strategy for scheduling the controllable time points of the network observing past happenings only. In this paper, we address the DC problem for a very general class of TNU, namely Disjunctive Temporal Network with Uncertainty. We make the following contributions. First, we define strategies in the form of an executable language; second, we propose the first decision procedure to check whether a given strategy is a solution for the DC problem; third we present an efficient algorithm for strategy synthesis based on techniques derived from Timed Games and Satisfiability Modulo Theory. The experimental evaluation shows that the approach is superior to the state-of-the-art.

Flexibility in agent scheduling increases the resilience of temporal plans in the face of new constraints. However,current metrics of flexibility ignore domain knowledge about how such constraints might arise in practice, e.g., due to the uncertain duration of a robot’s transitiontime from one location to another. Probabilistic temporalplanning accounts for actions whose uncertain durations can be modeled with probability density functions. We introduce a new metric called robustness that measures the likelihood of success for probabilistic temporalplans. We show empirically that in multi-robot planning,robustness may be a better metric for assessing the quality of temporal plans than flexibility, thus reframing many popular scheduling optimization problems.

A Simple Temporal Network with Uncertainty (STNU) is a structure for representing and reasoning about temporal constraints in domains where some temporal durations are not controlled by the executor. The most important property of an STNU is whether it is dynamically controllable (DC) whether there exists a strategy for executing the controllable time-points that guarantees that all constraints will be satisfied no matter how the uncontrollable durations turn out. This paper provides a novel mapping from STNUs to Timed Game Automata (TGAs) that: (1) explicates the deep theoretical relationships between STNUs and TGAs; and (2) enables the memoryless strategies generated from the TGA to be transformed into equivalent STNU execution strategies that reduce the real-time computational burden for the executor. The paper formally proves that the STNU-to-TGA encoding properly captures the execution semantics of STNUs.

Recent attempts to automate business processes and medical-treatment processes have uncovered the need for a formal framework that can accommodate not only temporal constraints, but also observations and actions with uncontrollable durations. To meet this need, this paper defines a Conditional Simple Temporal Network with Uncertainty (CSTNU) that combines the simple temporal constraints from a Simple Temporal Network (STN) with the conditional nodes from a Conditional Simple Temporal Problem (CSTP) and the contingent links from a Simple Temporal Network with Uncertainty (STNU). A notion of dynamic controllability for a CSTNU is defined that generalizes the dynamic consistency of a CTP and the dynamic controllability of an STNU.