860 research outputs found

    The astronaut and the banana peel: An EVA retriever scenario

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    To prepare for the problem of accidents in Space Station activities, the Extravehicular Activity Retriever (EVAR) robot is being constructed, whose purpose is to retrieve astronauts and tools that float free of the Space Station. Advanced Decision Systems is at the beginning of a project to develop research software capable of guiding EVAR through the retrieval process. This involves addressing problems in machine vision, dexterous manipulation, real time construction of programs via speech input, and reactive execution of plans despite the mishaps and unexpected conditions that arise in uncontrolled domains. The problem analysis phase of this work is presented. An EVAR scenario is used to elucidate major domain and technical problems. An overview of the technical approach to prototyping an EVAR system is also presented

    Static search games played over graphs and general metric spaces

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    We define a general game which forms a basis for modelling situations of static search and concealment over regions with spatial structure. The game involves two players, the searching player and the concealing player, and is played over a metric space. Each player simultaneously chooses to deploy at a point in the space; the searching player receiving a payoff of 1 if his opponent lies within a predetermined radius r of his position, the concealing player receiving a payoff of 1 otherwise. The concepts of dominance and equivalence of strategies are examined in the context of this game, before focusing on the more specific case of the game played over a graph. Methods are presented to simplify the analysis of such games, both by means of the iterated elimination of dominated strategies and through consideration of automorphisms of the graph. Lower and upper bounds on the value of the game are presented and optimal mixed strategies are calculated for games played over a particular family of graphs

    Search-and-rescue rendezvous

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    We consider a new type of asymmetric rendezvous search problem in which player II needs to give player I a ā€˜giftā€™ which can be in the form of information or material. The gift can either be transfered upon meeting, as in traditional rendezvous, or it can be dropped off by player II at a location he passes, in the hope it will be found by player I. The gift might be a water bottle for a traveller lost in the desert; a supply cache for Captain Scott in the Antarctic; or important information (left as a gift). The common aim of the two players is to minimize the time taken for I to either meet II or find the gift. We find optimal agent paths and drop off times when the search region is a line, the initial distance between the players is known and one or both of the players can leave gifts. A novel and important technique introduced in this paper is the use of families of linear programs to solve this and previous rendezvous problems. Previously, the approach was to guess the answer and then prove it was optimal. Our work has applications to other forms of rendezvous on the line: we can solve the symmetric version (players must use the same strategy) with two gifts and we show that there are no asymmetric solutions to this two gifts problem. We also solve the GiftStart problem, where the gift or gifts must be dropped at the start of the game. Furthermore, we can solve the Minmax version of the game where the objective function is to minimize the maximum rendezvous time. This problem admits variations where players have 0, 1 or 2 gifts at disposal. In particular, we show that the classical Wait For Mommy strategy is optimal for this setting

    Searching a variable speed network

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    A point lies on a network according to some unknown probability distribution. Starting at a specified root of the network, a Searcher moves to find this point at speeds that depend on his location and direction. He seeks the randomized search algorithm that minimizes the expected search time. This is equivalent to modeling the problem as a zero-sum hide-and-seek game whose value is called the search value of the network. We make a new and direct derivation of an explicit formula for the search value of a tree, proving that it is equal to half the sum of the minimum tour time of the tree and a quantity called its incline. The incline of a tree is an average over the leaf nodes of the difference between the time taken to travel from the root to a leaf node and the time taken to travel from a leaf node to the root. This difference can be interpreted as height of a leaf node, assuming uphill is slower than downhill. We then apply this formula to obtain numerous results for general networks. We also introduce a new general method of comparing the search value of networks that differ in a single arc. Some simple networks have very complicated optimal strategies that require mixing of a continuum of pure strategies. Many of our results generalize analogous ones obtained for constant velocity (in both directions) by S. Gal, but not all of those results can be extended

    The Modular Clock Algorithm for Blind Rendezvous

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    This thesis examines the problem in initializing communications whereby cognitive radios need to find common spectrum with other cognitive radios, a process known as frequency rendezvous. It examines the rendezvous problem as it exists in a dynamic spectrum access cognitive network. Specifically, it addresses the problem of rendezvous in an infrastructureless environment. A new algorithm, the modular clock algorithm, is developed and analyzed as a solution for the simple rendezvous environment model, coupled with a modified version for environment models with less information. The thesis includes a taxonomy of commonly used environment models, and analysis of previous efforts to solve the rendezvous problem. Mathematical models and solutions used in applied statistics are analyzed for use in cognitive networking. A symmetric rendezvous pursuit-evasion game is developed and analyzed. Analysis and simulation results show that the modular clock algorithm performs better than random under a simple rendezvous environment model, while a modified version of the modular clock algorithm performs better than random in more difficult environment models

    Contributions To Pursuit-Evasion Game Theory.

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    This dissertation studies adversarial conflicts among a group of agents moving in the plane, possibly among obstacles, where some agents are pursuers and others are evaders. The goal of the pursuers is to capture the evaders, where capture requires a pursuer to be either co-located with an evader, or in close proximity. The goal of the evaders is to avoid capture. These scenarios, where different groups compete to accomplish conflicting goals, are referred to as pursuit-evasion games, and the agents are called players. Games featuring one pursuer and one evader are analyzed using dominance, where a point in the plane is said to be dominated by a player if that player is able to reach the point before the opposing players, regardless of the opposing players' actions. Two generalizations of the Apollonius circle are provided. One solves games with environments containing obstacles, and the other provides an alternative solution method for the Homicidal Chauffeur game. Optimal pursuit and evasion strategies based on dominance are provided. One benefit of dominance analysis is that it extends to games with many players. Two foundational games are studied; one features multiple pursuers against a single evader, and the other features a single pursuer against multiple evaders. Both are solved using dominance through a reduction to single pursuer, single evader games. Another game featuring competing teams of pursuers is introduced, where an evader cooperates with friendly pursuers to rendezvous before being captured by adversaries. Next, the assumption of complete and perfect information is relaxed, and uncertainties in player speeds, player positions, obstacle locations, and cost functions are studied. The sensitivity of the dominance boundary to perturbations in parameters is provided, and probabilistic dominance is introduced. The effect of information is studied by comparing solutions of games with perfect information to games with uncertainty. Finally, a pursuit law is developed that requires minimal information and highlights a limitation of dominance regions. These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120650/1/dwoyler_1.pd
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