Traditional approaches to motion modeling for skid-steer robots struggle to capture nonlinear tire-terrain dynamics, especially during high-speed maneuvers. In this paper, we tackle such nonlinearities by enhancing a dynamic unicycle model with Gaussian Process (GP) regression outputs. This enables us to develop an adaptive, uncertainty-informed navigation formulation. We solve the resultant stochastic optimal control problem using a chance-constrained Model Predictive Path Integral (MPPI) control method. This approach formulates obstacle avoidance and path-following as chance constraints, accounting for residual uncertainties from the GP to ensure safety and reliability in control. Leveraging GPU acceleration, we efficiently manage the non-convex nature of the problem, ensuring real-time performance. Our approach unifies path-following and obstacle avoidance across different terrains, unlike prior works which typically focus on one or the other. We compare our GP-MPPI method against unicycle and data-driven kinematic models within the MPPI framework. In simulations, our approach shows superior tracking accuracy and obstacle avoidance. We further validate our approach through hardware experiments on a skid-steer robot platform, demonstrating its effectiveness in high-speed navigation. The GPU implementation of the proposed method and supplementary video footage are available at https://stochasticmppi.github.io.

Skid-Steer Wheeled Mobile Robots (SSWMRs) are increasingly being used for off-road autonomy applications. When turning at high speeds, these robots tend to undergo significant skidding and slipping. In this work, using Gaussian Process Regression (GPR) and Sigma-Point Transforms, we estimate the non-linear effects of tire-terrain interaction on robot velocities in a probabilistic fashion. Using the mean estimates from GPR, we propose a data-driven dynamic motion model that is more accurate at predicting future robot poses than conventional kinematic motion models. By efficiently solving a convex optimization problem based on the history of past robot motion, the GPR augmented motion model generalizes to previously unseen terrain conditions. The output distribution from the proposed motion model can be used for local motion planning approaches, such as stochastic model predictive control, leveraging model uncertainty to make safe decisions. We validate our work on a benchmark real-world multi-terrain SSWMR dataset. Our results show that the model generalizes to three different terrains while significantly reducing errors in linear and angular motion predictions. As shown in the attached video, we perform a separate set of experiments on a physical robot to demonstrate the robustness of the proposed algorithm.