# Nonsmooth optimal value and policy functions in mechanical systems subject to unilateral constraints

arXiv: https://arxiv.org/abs/1710.06745 · HTML: https://mlsanity.com/paper/1710.06745/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2017.

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

- [Physics-informed Value Learner for Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2509.06782/) (2025)

## Abstract (arXiv)

State-of-the-art approaches to optimal control use smooth approximations of value and policy functions and gradient-based algorithms for improving approximator parameters. Unfortunately, we show that value and policy functions that arise in optimal control of mechanical systems subject to unilateral constraints -- i.e. the contact-rich dynamics of robot locomotion and manipulation -- are generally nonsmooth due to the underlying dynamics exhibiting discontinuous or piecewise-differentiable trajectory outcomes. Simple mechanical systems are used to illustrate this result and the implications for optimal control of contact-rich robot dynamics.