In this work, we analyze the decentralized formation control problem for a class of multi-robotic systems evolving on slippery surfaces. Grounded on experimental data of robots moving on a gravel surface inducing slippery, we show that a deterministic model cannot capture the uncertainties resulting from the kinematics of the robots while, instead, a model incorporating stochastic noise is capable of emulating such perturbations on wheel driving speed and turn rate. To account for these uncertainties, we consider a second order non-holonomic unicycle model to capture the full dynamics of individual vehicles where both actuation force and torque are subject to stochastic disturbances. Upon reducing the input-output dynamics of individual robot to a stochastic double integrator, we investigate the effects of these perturbations on the control input using concepts from stochastic stability theory and through numerical simulations. We demonstrated the applicability of the proposed scheme for formation control notably by providing sufficient conditions for exponential mean square convergence and we numerically determined the range of noise intensities for which team of robots can achieve formation stabilization. The promising findings from this work are expected to aid the design of robust control schemes for formation control of non-holonomic robots on off-road or un-paved surfaces.

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