Abstract-Area coverage is an important task for mobile robots, with many real-world applications. Motivated by potential efficiency and robustness improvements, there is growing interest in the use of multiple robots in coverage. Previous investigations of multi-robot coverage focuses on completeness and eliminating redundancy, but does not formally address robustness, nor examine the impact of the initial positions of robots on the coverage time. Indeed, a common assumption is that non-redundancy leads to improved coverage time. We address robustness and efficiency in a family of multi-robot coverage algorithms, based on spanning-tree coverage of approximate cell decomposition. We analytically show that the algorithms are robust, in that as long as a single robot is able to move, the coverage will be completed. We also show that non-redundant (non-backtracking) versions of the algorithms have a worst-case coverage time virtually identical to that of a single robotthus no performance gain is guaranteed in non-redundant coverage. Moreover, this worst-case is in fact common in realworld applications. Surprisingly, however, redundant coverage algorithms lead to guaranteed performance which halves the coverage time even in the worst case.
Area coverage is an important task for mobile robots, with many real-world applications. In many cases, the coverage has to be completed without the use of a map or any apriori knowledge about the area, a process referred-to as on-line coverage. Previous investigations of multi-robot on-line coverage focused on the improved efficiency gained from the use of multiple robots, but did not formally addressed the potential for greater robustness. We present a novel multi-robot on-line coverage algorithm, based on approximate cell decomposition. We analytically show that the algorithm is complete and robust, in that as long as a single robot is able to move, the coverage will be completed. We analyze the assumptions underlying the algorithm requirements and present a number of techniques for executing it in real robots. We show empirical coverage-time results of running the algorithm in two different environments and several group sizes.
We investigate the extent to which it is possible to evaluate the probability of a particular candidate winning an election, given imperfect information about the preferences of the electorate. We assume that for each voter, we have a probability distribution over a set of preference orderings. Thus, for each voter, we have a number of possible preference orderings -we do not know which of these orderings actually represents the voter's preferences, but we know for each one the probability that it does. We give a polynomial algorithm to solve the problem of computing the probability that a given candidate will win when the number of candidates is a constant. However, when the number of candidates is not bounded, we prove that the problem becomes #P-Hard for the Plurality, Borda, and Copeland voting protocols. We further show that even evaluating if a candidate has any chance to be a winner is NP-Complete for the Plurality voting protocol, in the weighted voters case. We give a polynomial algorithm for this problem when the voters weights are equal.
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