  While autonomous navigation of mobile robots on rigid terrain is a
well-explored problem, navigating on deformable terrain such as tall grass or
bushes remains a challenge. To address it, we introduce an explainable,
physics-aware and end-to-end differentiable model which predicts the outcome of
robot-terrain interaction from camera images, both on rigid and non-rigid
terrain. The proposed MonoForce model consists of a black-box module which
predicts robot-terrain interaction forces from onboard cameras, followed by a
white-box module, which transforms these forces and a control signals into
predicted trajectories, using only the laws of classical mechanics. The
differentiable white-box module allows backpropagating the predicted trajectory
errors into the black-box module, serving as a self-supervised loss that
measures consistency between the predicted forces and ground-truth trajectories
of the robot. Experimental evaluation on a public dataset and our data has
shown that while the prediction capabilities are comparable to state-of-the-art
algorithms on rigid terrain, MonoForce shows superior accuracy on non-rigid
terrain such as tall grass or bushes. To facilitate the reproducibility of our
results, we release both the code and datasets.
