Multi-scale modeling of wheel–terrain interactions for planetary rovers

Assessing the mobility and stability of off-road vehicles poses fundamental challenges, particularly in extraterrestrial environments. Current research relies primarily on experimental data and empirical models, while high-fidelity numerical simulations are hindered by the complexity of wheel–terrain interactions. These involve multiple length scales due to heterogeneous terrain materials such as sand, gravel, and rock. This paper presents a multiscale computational framework for wheel–terrain interaction that consistently captures coupled behavior across scales. Interactions involving wheel–rock, wheel–sand, and rock–sand are modeled using a nonlinear contact formulation that supports arbitrary geometries for both wheels and terrain constituents. The internal dynamics of the coupled system are resolved using the Discrete Element Method (DEM) and the Material Point Method (MPM), linked through a contact-coupling interface that enables accurate two-way transfer between discrete granular flow and large-deformation continuum response. A highly parallel computational strategy significantly improves scalability across DEM- or MPM-dominated contact regimes in high-resolution simulations. The framework is validated against analytical benchmarks, including head-on sphere collisions, wheel-drop tests, and rolling tests, to assess its quantitative predictive robustness. It is then applied to simulate two NASA Mars rover incidents: the permanent entrapment of Spirit and the excessive slip experienced by Curiosity . The framework demonstrates strong potential for realistic off-road applications, including mobility prediction, stability assessment, and post-incident analysis. In particular, for the Spirit case, material properties matched to observations are compiled to reproduce, as closely as possible, the normalized sinkage-slip trend and to compare it with published single-wheel measurements, thereby providing a partial quantitative analysis at field scale.