# Learning the Contact Manifold for Accurate Pose Estimation During Peg-in-Hole Insertion of Complex Geometries

arXiv: https://arxiv.org/abs/2505.19215 · HTML: https://mlsanity.com/paper/2505.19215/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2025.

## Built on by (most cited first, 1 of 1)

- [Learning Contact Dynamics through Touching: Action-conditional Graph Neural Networks for Robotic Peg Insertion](https://mlsanity.com/paper/2509.12151/) (2025)

## Abstract (arXiv)

Contact-rich assembly of complex, non-convex parts with tight tolerances remains a formidable challenge. Purely model-based methods struggle with discontinuous contact dynamics, while model-free methods require vast data and often lack precision. In this work, we introduce a hybrid framework that uses only contact-state information between a complex peg and its mating hole to recover the full SE(3) pose during assembly. In under 10 seconds of online execution, a sequence of primitive probing motions constructs a local contact submanifold, which is then aligned to a precomputed offline contact manifold to yield sub-mm and sub-degree pose estimates. To eliminate costly k-NN searches, we train a lightweight network that projects sparse contact observations onto the contact manifold and is 95x faster and 18% more accurate. Our method, evaluated on three industrially relevant geometries with clearances of 0.1-1.0 mm, achieves a success rate of 93.3%, a 4.1x improvement compared to primitive-only strategies without state estimation.