Dynamic Controllability Made Simple

Simple Temporal Networks with Uncertainty (STNUs) are a well-studied model for representing temporal constraints, where some intervals (contingent links) have an unknown but bounded duration, discovered only during execution. An STNU is dynamically controllable (DC) if there exists a strategy to execute its time-points satisfying all the constraints, regardless of the actual duration of contingent links revealed during execution. In this work we present a new system of constraint propagation rules for STNUs, which is sound-and-complete for DC checking. Our system comprises just three rules which, differently from the ones proposed in all previous works, only generate unconditioned constraints. In particular, after applying our sound rules, the network remains an STNU in all respects. Moreover, our completeness proof is short and non-algorithmic, based on the explicit construction of a valid execution strategy. This is a substantial simplification of the theory which underlies all the polynomial-time algorithms for DC-checking. Our analysis also shows: (1) the existence of late execution strategies for STNUs, (2) the equivalence of several variants of the notion of DC, (3) the existence of a fast algorithm for real-time execution of STNUs, which runs in O(KN) total time in a network with K contingent links and N time points, considerably improving the previous O(N^3)-time bound

Propagating Piecewise-Linear Weights in Temporal Networks

This paper presents a novel technique using piecewise-linear functions (PLFs) as weights on edges in the graphs of two kinds of temporal networks to solve several previously open problems. Generalizing constraint-propagation rules to accom- modate PLF weights requires implementing a small handful of functions. Most problems are solved by inserting one or more edges with an initial weight of \u3b4 (a variable), then using the modified rules to propagate the PLF weights. For one kind of network, a new set of propagation rules is introduced to avoid a non-termination issue that arises when propagating PLF weights. The paper also presents two new results for determining the tightest horizon that can be imposed while preserving a network\u2019s dynamic consistency/controllability

Sound-and-Complete Algorithms for Checking the Dynamic Controllability of Conditional Simple Temporal Networks with Uncertainty

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a data structure for representing and reasoning about time. CSTNUs incorporate observation time-points from Conditional Simple Temporal Networks (CSTNs) and contingent links from Simple Temporal Networks with Uncertainty (STNUs). A CSTNU is dynamically controllable (DC) if there exists a strategy for executing its time-points that guarantees the satisfaction of all relevant constraints no matter how the uncertainty associated with its observation time-points and contingent links is resolved in real time. This paper presents the first sound-and-complete DC-checking algorithms for CSTNUs that are based on the propagation of labeled constraints and demonstrates their practicality

A note on speeding up DC-checking for STNUs

A Simple Temporal Network with Uncertainty (STNU) includes real-valued variables, called time-points; binary difference constraints on those time-points; and contingent links that represent actions with uncertain durations. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC-checking algorithm for STNUs with the best worst-case time-complexity is the RUL$^-$ algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is $O(mn + k^2n + knlog n)$, where $n$ is the number of time-points, $m$ is the number of constraints (equivalently, the number of edges in the STNU graph), and $k$ is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new implementation of the algorithm that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation

Dynamic Controllability Checking for Conditional Simple Temporal Networks with Uncertainty: New Sound-and-Complete Algorithms based on Constraint Propagation

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a data structure for representing and reasoning about time. CSTNUs incorporate "observation time-points" from Conditional Simple Temporal Networks (CSTNs) and "contingent links" from Simple Temporal Networks with Uncertainty (STNUs). A CSTNU is "dynamically controllable" (DC) if there exists a strategy for executing its time-points that guarantees the satisfaction of all relevant constraints no matter how the uncertainty associated with its observation time-points and contingent links is resolved in real time. This paper presents the first sound-and-complete DC-checking algorithms for CSTNUs based on the propagation of labeled constraints and demonstrates their practicality

Speeding Up the RUL¯ Dynamic-Controllability-Checking Algorithm for Simple Temporal Networks with Uncertainty

A Simple Temporal Network with Uncertainty (STNU) in- cludes real-valued variables, called time-points; binary differ- ence constraints on those time-points; and contingent links that represent actions with uncertain durations. STNUs have been used for robot control, web-service composition, and business processes. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC- checking algorithm for STNUs with the best worst-case time- complexity is the RUL− algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is O(mn + k2n + kn log n), where n is the number of time-points, m is the number of constraints, and k is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new algorithm, called RUL2021, that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation

Solving dynamic controllability problem of multi-agent plans with uncertainty using mixed integer linear programming.

Executing multi-agent missions requires managing the uncertainty about uncontrollable events. When communications are intermittent, it additionally requires for each agent to act only based on its local view of the problem, that is independently of events which are controlled or observed by the other agents. In this paper, we propose a new framework for dealing with such contexts, with a focus on mission plans involving temporal constraints. This framework, called Multi-agent Simple Temporal Network with Uncertainty (MaSTNU), is a combination between Multi-agent Simple Temporal Network (MaSTN) and Simple Temporal Network with Uncertainty (STNU).We define the dynamic controllability property for MaSTNU, and a method for computing offline valid execution strategies which are then dispatched between agents. This method is based on a mixed-integer linear programming formulation and can also be used to optimize criteria such as the temporal flexibility of multi-agent plans.

A Structural Characterization of Temporal Dynamic Controllability

An important issue for temporal planners is the ability to handle temporal uncertainty. Recent papers have addressed the question of how to tell whether a temporal network is Dynamically Controllable, i.e., whether the temporal requirements are feasible in the light of uncertain durations of some processes. Previous work has presented an O(N5) algorithm for testing this property. Here, we introduce a new analysis of temporal cycles that leads to an O(N4) algorithm

Temporal and Resource Controllability of Workflows Under Uncertainty

Workflow technology has long been employed for the modeling, validation and execution of business processes. A workflow is a formal description of a business process in which single atomic work units (tasks), organized in a partial order, are assigned to processing entities (agents) in order to achieve some business goal(s). Workflows can also employ workflow paths (projections with respect to a total truth value assignment to the Boolean variables associated to the conditional split connectors) in order (not) to execute a subset of tasks. A workflow management system coordinates the execution of tasks that are part of workflow instances such that all relevant constraints are eventually satisfied. Temporal workflows specify business processes subject to temporal constraints such as controllable or uncontrollable durations, delays and deadlines. The choice of a workflow path may be controllable or not, considered either in isolation or in combination with uncontrollable durations. Access controlled workflows specify workflows in which users are authorized for task executions and authorization constraints say which users remain authorized to execute which tasks depending on who did what. Access controlled workflows may consider workflow paths too other than the uncertain availability of resources (users, throughout this thesis). When either a task duration or the choice of the workflow path to take or the availability of a user is out of control, we need to verify that the workflow can be executed by verifying all constraints for any possible combination of behaviors arising from the uncontrollable parts. Indeed, users might be absent before starting the execution (static resiliency), they can also become so during execution (decremental resiliency) or they can come and go throughout the execution (dynamic resiliency). Temporal access controlled workflows merge the two previous formalisms by considering several kinds of uncontrollable parts simultaneously. Authorization constraints may be extended to support conditional and temporal features. A few years ago some proposals addressed the temporal controllability of workflows by encoding them into temporal networks to exploit "off-the-shelf" controllability checking algorithms available for them. However, those proposals fail to address temporal controllability where the controllable and uncontrollable choices of workflow paths may mutually influence one another. Furthermore, to the best of my knowledge, controllability of access controlled workflows subject to uncontrollable workflow paths and algorithms to validate and execute dynamically resilient workflows remain unexplored. To overcome these limitations, this thesis goes for exact algorithms by addressing temporal and resource controllability of workflows under uncertainty. I provide several new classes of (temporal) constraint networks and corresponding algorithms to check their controllability. After that, I encode workflows into these new formalisms. I also provide an encoding into instantaneous timed games to model static, decremental and dynamic resiliency and synthesize memoryless execution strategies. I developed a few tools with which I carried out some initial experimental evaluations

Managing temporal uncertainty under limited communication : a formal model of tight and loose team coordination

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (leaves 155-157).In the future, groups of autonomous robots will cooperate in large networks in order to achieve a common goal. These multi-agent systems will need to be able to execute cooperative temporal plans in the presence of temporal uncertainty and communication limitations. The duration of many planned activities will not be under direct control of the robots. In addition, robots will often not be able to communicate during plan execution. In order for the robots to robustly execute a cooperative plan, they will need to guarantee that a successful execution strategy exists, and provide a means to reactively compensate for the uncertainty in real-time. This thesis presents a multi-agent executive that enables groups of distributed autonomous robots to dynamically schedule temporally flexible plans that contain both temporal uncertainty under communication limitations. Previous work has presented controllability algorithms that compile the simple temporal networks with uncertainty, STNUs, into a form suitable for execution. This thesis extends the previous controllability algorithms to operate on two-layer plans that specify group level coordination at the highest level and agent level coordination at a lower level. We introduce a Hierarchical Reformulation (HR) algorithm that reformulates the two-layer plan in order to enable agents to dynamically adapt to uncertainty within each group plan and use a static execution strategy between groups in order to compensate for communication limitations. Formally, the HR algorithm ensures that the two-layer plan is strongly controllable at the highest level and dynamically controllable at the lower level. Furthermore, we introduce a new fast dynamic controllability algorithm that has been empirically shown to run in O(N³)(cont.) The Hierarchical Reformulation algorithm has been validated on a set of hand coded examples. The speed of the new fast dynamic controllability algorithm has been tested using a set of randomly generated problems.by John L. Stedl.S.M