MEMNet: Learning Vehicle Motion Equivalency Mapping from Planar to Complex Terrains

<title>Abstract</title> <p> Accurate off-road vehicle modeling remains challenging due to complex terrain geometry and nonlinear tire-terrain interactions. Traditional physics-based models require terrain- and vehicle-specific reformulation, limiting scalability and real-time applicability. Moreover, field testing is costly, difficult to reproduce, and logistically complex. While mixed-reality (MR) testing has shown promise for structured driving environments, extending it to off-road scenarios requires learning a dynamics-level mapping between vehicle motion on flat and complex terrains under identical control inputs. This work introduces Motion Equivalency Mapping (MEM), a mapping of vehicle motion from planar to complex terrains. To learn this mapping, we propose MEMNet, a recurrent neural network that predicts vehicle state on uneven terrains using control inputs, corresponding flat-terrain states and uneven terrain information. A synthetic dataset of 25,228 trajectories spanning six terrain classes: upward/downward ramp, upward/downward step, convex/concave bump, with varying geometries and command profiles was generated. In addition to training MEMNet with dataset of all terrain classes, seperate models for each terrain class were also trained. Terrain-class specific (TS) models preserve terrain-induced geometric features and produce physically consistent trajectory rollouts, while the single all-terrain (AT) MEMNet model captures generalized dynamic trends with reduced fidelity on certain terrain classes. Our all AT MEMNet model achieved R ² =0.9984 for position, R ² =0.9857 for velocity, and R ² = 0.9614 for acceleration. But, altitude reconstruction remains a clear limitation of the AT model. These results demonstrate the feasibility of learning a motion equivalency map from planar to complex terrains, providing an alternative to terrain-specific reformulation of vehicle models while also identifying the limitations of the AT MEMNet model. </p>