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In this paper, we consider the problem of robotic router formation, where two nodes need to maintain their connectivity over a large area by using a number of mobile routers. We are interested in the robust operation of such networks in realistic communication environments that naturally experience path loss, shadowing, and multipath fading. We propose a probabilistic router formation and motion-planning approach by integrating our previously proposed stochastic channel learning framework with robotic router optimization. We furthermore consider power constraints of the network, including both communication and motion costs, and characterize the underlying tradeoffs. Instead of taking the common approach of formation optimization through maximization of the Fiedler eigenvalue, we take a different approach and use the end-to-end bit error rate (BER) as our performance metric. We show that the proposed framework results in a different robotic configuration, with a considerably better performance, as compared with only considering disk models for communication and/or maximizing the Fielder eigenvalue. Finally, we show the performance with a simple preliminary experiment, with an emphasis on the impact of localization errors. Along this line, we show interesting interplays between the localization quality and the channel correlation/learning quality.