Suppose there is an area to survey. If we deploy one robot it takes time T to sweep the area. Now if we deploy 2 robots, we would expect it to take time T/2. However in reality, because we are sending two robots, we would have to implement additional coordination planning routines and obstacle avoidance routines so that they do not collide with each other. These overhead computational costs add up and we will actually see the area being surveyed in time T/2+X. Now could you suggest papers where they talk about the estimation of X? It does not have to be in the context of area surveying. It can be any other multi-robot task also.
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1$\begingroup$ I'm not sure it's enough for an answer, and I can't find a free copy online, but you might find the paper Design and implementation of an efficient path planning algorithm for networked robots of use. $\endgroup$– sempaiscubaCommented Mar 26, 2019 at 21:44
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3 Answers
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I came across one paper that had a good description of this issue from Kristina Lerman and Aram Galstyan at University of Southern California entitled "Mathematical Model of Foraging in a Group of Robots: Effect of Interference"
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I think the question relies too much on variable factors so that there is no definitive answer. In a worst case scenario, you want to map a tunnel system and all of your robots start at the single entrance to the system. All of your robots will have to drive together to the first intersection where they can spread. More robots will could decrease the performance of your fleet. In a best case, you have some swimming robots with sonars (so with limited sensor range) that should map the sea floor. If you don't have too many robots, the fleet performance will scale linearly as the boats are able to move immediately to unscanned areas.
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Perhaps, the following related work can be somehow enlighting or provide useful insights, as per your request:
answered Mar 27, 2019 at 11:25
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$\begingroup$ In the paper a teleoperation strategy was explained which is using a human in the loop. I like this approach (see my own answer) but it wasn't mentioned in the answer. So the paper is reasonable well but the answer is too short. $\endgroup$ Commented Mar 27, 2019 at 22:55
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$\begingroup$ Well, it's true there're humans in the loop, exactly as other aspects that differ from the context described by the OP, like here the task itself. However, the OP asked for references related to the topic of estimating the overhead X but not necessarily linked to surveillance for example. I just dropped a pointer to a work that tries to approach this estimation from a scientific standpoint, thus providing a handful of interconnections to other pertinent studies. For this, it'd turn out to be a very good reading anyway. $\endgroup$ Commented Mar 28, 2019 at 7:32