A Probabilistic Trajectory and Dispersion Study of Martian Tumbleweed Rover Swarms in Global Dust Storm Conditions

Global Dust Storms (GDSs) dominate the Martian climate, yet the mechanisms of dust lifting, transport, and deposition remain poorly constrained because in situ observations are limited: landers are stationary, and their Radioisotope Thermoelectric Generators (RTGs) contaminate local measurements. Our solution is a swarm of lightweight, wind-propelled spherical rovers -- Dust Rovers (DRs) -- that follow natural wind patterns to collect high-spatial-resolution in situ dust data during storms. Here, we quantify the dispersion and communication connectivity of this robotic architecture. Using 625 wind states calculated using the Mars Climate Database (MCD) for the MY34 storm at the Curiosity site, we build a bivariate-normal model of the near-surface wind velocity and characterise its diurnal structure. Rover trajectories and swarm dispersion are propagated with three integrators: the Euler and fourth-order Runge-Kutta schemes for the deterministic dynamics, and a stochastic Ornstein-Uhlenbeck formulation that simulates turbulent gust forcing. Dispersion is controlled by the unmeasured gust correlation time: with a static rolling threshold enforced, the white-gust case (tau g = Delta t = 1 s) provides a two-rover separation below 1 m over an hour (0.44 km over a sol), whereas correlation times of 10-60 s yield 6-25 m over an hour (1.4-3.3 km over a sol). We demonstrate that a 20-rover swarm needs only a 1.6-4.1 km per-rover range to remain connected over a sol, and stays connected across the plausible envelope -- for gust amplitudes up to twice the nominal value with tau g <= 60 s, and at the nominal amplitude up to tau g 150 s.