Guarding the perimeter of an area in order to detect potential intruders is an important task in a variety of security-related applications. This task can in many circumstances be performed by a set of camera-equipped unmanned aerial vehicles (UAVs). Such UAVs will occasionally require refueling or recharging, in which case they must temporarily be replaced by other UAVs in order to maintain complete surveillance of the perimeter. In this paper we consider the problem of scheduling such replacements. We present optimal replacement strategies and justify their optimality.

We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances. For the hop-constrained DSTP, we propose local search strategies aimed at improving any heuristically produced initial Steiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have recently developed ecient label correcting algorithms. The presented approach is applied to nding suitable 3D locations where unmanned aerial vehicles (UAVs) can be placed to relay information gathered in multi-target monitoring and surveillance. The eciency of our algorithms is illustrated by results of numerical experiments involving problem instances with up to 40 000 nodes and up to 20 million arcs.

The purpose of this article is to provide a uniform, lightweight language specification and tutorial for a class of temporal logics for reasoning about action and change that has been developed by our group during the period 1994-1998. The class of logics are collected under the name TAL, an acronym for Temporal Action Logics. TAL has its origins and inspiration in the work with Features and Fluents (FF) by Sandewall, but has diverged from the methodology and approach through the years. We first discuss distinctions and compatibility with FF, move on to the lightweight language specification, and then present a tutorial in terms of an excursion through the different parts of a relatively complex narrative defined using TAL. We conclude with an annotated list of published work from our group. The article tries to strike a reasonable balance between detail and readability, making a number of simplifications regarding narrative syntax and translation to a base logical language. Full details are available in numerous technical reports and articles which are listed in the final section of this article.

Recently, a great deal of progress has been made using nonmonotonic temporal logics to formalize reasoning about action and change. In particular, much focus has been placed on the proper representation of non-deterministic actions and the indirect effects of actions. One popular approach to representing the indirect effects of actions has been via the use of causal rules which in a more general sense can be viewed as fluent dependency constraints. Although fluent dependency constraints have been used primarily under a loose causal interpretation, we show that when interpreted in a broader sense they provide a flexible means for dealing with a number of other representational problems such as the qualification problem and the ramification constraints as qualification constraints problem, in addition to the standard ramification problem. More importantly, the use of fluent dependency constraints for different purposes does not involve additions to the base nonmonotonic temporal logic, TAL, used here, but simply the addition of several macro operators to an action language used to represent action scenarios or narratives. The payoff is that TAL has already been shown to offer a robust approach to representing action scenarios which permit incomplete specifications of both state and the timing of actions, non-deterministic actions, actions with duration, concurrent actions, use of both boolean and non-boolean fluents, and solutions to the frame and ramification problems for a wide class of action scenarios. In addition, all circumscribed action scenarios in these classes and the more general class involving qualification considered in this paper can be shown to be reducible to the first-order case. Finally, a restricted entailment method for this new class of scenarios is fully implemented. In the paper, we present a challenge example which incorporates all these features, propose a distinction between weak and strong qualification with a representation of both, and provide a visualization of the preferred entailments using a research tool VITAL for querying and visualizing action scenarios.