# MonoForce: Self-supervised Learning of Physics-informed Model for Predicting Robot-terrain Interaction

arXiv: https://arxiv.org/abs/2309.09007 · HTML: https://mlsanity.com/paper/2309.09007/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2023.

## Built on by (most cited first, 2 of 2)

- [FusionForce: End-to-end Differentiable Neural-Symbolic Layer for Trajectory Prediction](https://mlsanity.com/paper/2502.10156/) (2025)
- [ProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling](https://mlsanity.com/paper/2510.19364/) (2025)

## Abstract (arXiv)

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.