Institute of Fundamental Technological Research

We apply a non-classical four-valued logic in the process of reasoning regarding strategies for cops in a modified game of "Cops and Robber" played on a graph. We extend the game by introducing uncertainty in a form of random failures of detecting devices. This is realized by allowing that a robber can be detected in a node only with the given probability PA. Additionally, with the probability PF, cops can be given a false-positive, i.e., they are informed that the robber is located at some node, whereas it is located somewhere else. Consequently, non-zero PF introduces a measurement noise into the system. All the cops have access to information provided by the detectors and can communicate with each other, so they can coordinate the search. By adjusting the number of detectors, PA, and PF we can achieve a smooth transition between the two well-known variants of the game: "with fully visible robber" and "with invisible robber". We compare a simple probabilistic strategy for cops with the non-parametric strategy based on reasoning with a four-valued paraconsistent logic. It is shown that this novel approach leads to a good performance, as measured by the required mean catch-time. We conclude that this type of reasoning can be applied in real-world applications where there is no knowledge about the underlying source of errors which is particularly useful in robotics.

reasoning under uncertainty, non-classical logics, four-valued logic, paraconsistent reasoning, cops and robber game, multi-robotic systems

Niniejszy artykuł opisuje prace wykonane w celu przeprowadzenia eksperymentu weryfikującego działanie Planera zadania Search and Rescue na zespole trzech robotów kołowych w budynku użyteczności publicznej. Celem zadania jest przeszukanie obiektu przez grupę robotów, odnalezienie w nim poszkodowanych oraz wezwanie pomocy w odpowiednie miejsce. Punktem centralnym systemu jest Planer wykorzystujący język logiki czterowartosciowej 4QL, który został uprzednio przetestowany na symulacjach komputerowych. Jego działanie zostanie opisane pobieżnie, głównym tematem jest metodyka wdrożenia. Aby przeprowadzić eksperyment, należało zintegrować Planer z systemem wielorobotowym. Wedle autorów jest to zadanie nietrywialne, dlatego przy jego realizacji wykorzystano paradygmaty Test-driven development (TDD), zaadaptowane odpowiednio do realiów robotyki mobilnej. Finalny eksperyment został nagrany, a wideo udostępniono w Internecie.

logika wielowartościowa, search and rescue, systemy wielorobotowe

The paper reports initial results on modeling and simulating cooperation of rescue robots. Our aim is to investigate the efficiency of the “first simulate then act” paradigm for rescue operations undertaken by multiple mobile robots, assuming that information about the environment can be incomplete and partially inconsistent. To deal with ignorance and contradictions we adopt a non–standard logic in the inference engine. To demonstrate feasibility of our approach we present the architecture of the developed simulator and results of experiments done so far.

four-valued logic, search and rescue, multirobotic systems

The aim of this paper is to present application of non-standard logic in the process of reasoning regarding the state of environment in a multi-robotic system. We have investigated the possibility that the usage of four-valued logic can serve as an alternative to the traditional probabilistic approach when handling the uncertainties. As a proof of concept, we have considered a typical search-and-rescue scenario in which a group of n robots performs a search for k victims localized in random positions in an initially unknown building. The building is represented in the form of a graph while the uncertainties are modeled by parameters denoting probabilities of victim observation and random blocking of a robot transition between neighboring nodes (which precludes the possibility for the robot to know anything about the actual graph structure with full confidence). The simulation results show that the unique features of applied reasoning language give significant improvement over typical approaches based on the two-valued logic. The results have a preliminary character, in the sense that up to now, only numerical experiments have been performed—applying the idea in a real multi-robotic system is currently underway.

Search-and-rescue problem, Reasoning engine, Four-valued logic, 4QL, Simulation