Abstract
We consider the problem of satisfying communication demands in a multi-agent system where several robots cooperate on a task and a fixed subset of the agents act as mobile routers. Our goal is to position the team of robotic routers to provide communication coverage to the remaining client robots. We allow for dynamic environments and variable client demands, thus necessitating an adaptive solution. We present an innovative method that calculates a mapping between a robot’s current position and the signal strength that it receives along each spatial direction, for its wireless links to every other robot. We show that this information can be used to design a simple positional controller that retains a quadratic structure, while capturing the behavior of wireless signals in real-world environments. Notably, our approach does not necessitate stochastic sampling along directions that are counter-productive to the overall coordination goal, nor does it require exact client positions, or a known map of the environment.
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Notes
- 1.
Note that all quantities in this section are time-dependent; we omit this dependency for simplicity.
- 2.
We choose to work with ESNR values rather than rates since the rates supported on a link are discretized (non-continuous).
- 3.
In this paper we mainly consider \(d=2\) although all concepts are extensible to \(d=3\).
- 4.
For simplicity, we denote \(f_{ij}(\theta )\) as \(f(\theta )\) as we consider only the single link between robotic router i and client j for the rest of this section.
- 5.
Of course, the resolution at which \(\theta \) is available depends on the number of channel measurements.
- 6.
In practice, the router and client transmit back-to-back packets with a small gap \(\delta \approx 200 \,\upmu \)s to obtain \(\hat{h}^r(t+\delta )\) and \(\hat{h}(t)\), respectively. The router collects these values and approximates \(\hat{h}(t) \hat{h}^r(t)\) as \(\hat{h}(t) \hat{h}^r(t+\delta ) e^{-j2\varDelta _{f}\delta }\). The router computes this 10 times per second (an overhead of just 0.1Â %).
- 7.
Mathematically, \(\sigma _{ij} = \sum _\theta {[(\theta -\theta _\mathrm{max})^2f_{ij}(\theta )]}/\sum _\theta {[(\theta -\theta _\mathrm{max})^2\text {mean}\{f_{ij}(\theta )\}]} \).
- 8.
Note that the data-rate is capped by 60 Mb/s causing the plot to appear flat at times unlike ESNR.
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Acknowledgments
We thank Dan Feldman and Brian Julian for experimental and theoretical contributions to this work. The authors acknowledge MIT Lincoln Laboratory and MAST project under ARL Grant W911NF-08-2-0004 for their support.
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Gil, S., Kumar, S., Katabi, D., Rus, D. (2016). Adaptive Communication in Multi-robot Systems Using Directionality of Signal Strength. In: Inaba, M., Corke, P. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-28872-7_4
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