# Differentiable Contact Dynamics for Legged Locomotion: Policy Learning and Contact-Implicit Trajectory Optimization

- Source: arXiv cs.RO
- Published: 2026-10-27T04:00:00.000Z
- RoboHot: https://robohot.news/en/items/lxrggxlnjgtzpuavxdo7df00c
- Original: https://arxiv.org/abs/2610.35852

## Summary

This paper proposes a smooth analytic gradient for frictional contact that replaces the exact contact sensitivity only in the backward pass, leaving the forward hard-contact solve and the hardware-feasible trajectory unchanged. A policy trained on 100,000 samples in under 2 minutes on a desktop PC transfers to hardware without fine-tuning; under a trotting policy the robot withstands pushes and traverses gravel and slippery ground. In trajectory optimization, the gradient finds contact-rich solutions that the exact gradient and the Signorini relaxation gradient miss.