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This paper presents a computational framework for the physics-based simulation of light vehicles operating on discrete terrain. The focus is on characterizing through simulation the mobility of vehicles that weigh 1000 pounds or less, such as a reconnaissance robot. The terrain is considered to be deformable and is represented as a collection of bodies of spherical shape. The modeling stage relies on a novel formulation of the frictional contact problem that requires at each time step of the numerical simulation the solution of an optimization problem. The proposed computational framework, when run on ubiquitous Graphics Processing Unit (GPU) cards, allows the simulation of systems in which the terrain is represented by more than 0.5 million bodies leading to problems with more than one million degrees of freedom.