First passage distance to connectivity for mobile robots
Arjun Muralidharan, Yasamin Mostofi · 2017
We consider a robot that needs to establish connectivity with a remote human operator (or with another robot) as it moves along a path. We are interested in answering the following question: how long would the robot move before it finds a connected spot? More specifically, we are interested in mathematically characterizing the PDF of the distance traveled before the robot gets connected, as a function of the underlying wireless channel parameters. We start with the case where multipath fading is negligible, and utilize the stochastic differential equation literature to derive the PDF of the distance traveled before connectivity, considering shadowing and path loss components of the channel. We then include the effect of multipath and carry out the analysis using stochastic dynamic programming. Finally, we confirm our theoretical derivations by running several simulations with real channel parameters and highlight interesting trends of the distance to connectivity.