Wheeled Mobile Robots on Rough Terrains as Stochastic Nonholonomic Systems

In this paper, we investigate the motion of wheeled mobile robots on rough terrains modeled as noisy nonholonomic constraints. Such constraints are the natural extension of ideal nonholonomic constraints when the Stratonovich process is directly introduced in the constraint equations. The resulting stochastic model can capture motion on rough surfaces, random deformation in the wheel-ground contact, or stochastic loss/gain of traction. We study a differential robot with ideal noisy and affine noisy constraints, where each case models a certain aspect of motion on rough terrains. We then investigate their corresponding stochastic dynamics and the propagation of mean and covariance through Monte-Carlo simulations. The proposed model for roving rough terrains has the potential to serve as the stochastic model employed in model-based motion planning, pose estimation, and control of rover systems. The main challenge will be dealing with the nonlinear appearance of the noise and its feedback in the equations of motion.