Bundled Gradients through Contact via Randomized Smoothing

TL;DR

This paper introduces a stochastic approach using randomized smoothing to improve gradient-based optimization in contact-rich dynamics, leading to better convergence in manipulation planning.

Contribution

It formalizes the gradient bundle concept and demonstrates its effectiveness in mitigating non-smooth contact dynamics for optimal control.

Findings

Gradient bundle reduces sensitivity to non-smooth contact dynamics.

The proposed method improves convergence in iLQR-based contact planning.

Combining with convex implicit time-stepping enables tractable manipulation planning.

Abstract

The empirical success of derivative-free methods in reinforcement learning for planning through contact seems at odds with the perceived fragility of classical gradient-based optimization methods in these domains. What is causing this gap, and how might we use the answer to improve gradient-based methods? We believe a stochastic formulation of dynamics is one crucial ingredient. We use tools from randomized smoothing to analyze sampling-based approximations of the gradient, and formalize such approximations through the gradient bundle. We show that using the gradient bundle in lieu of the gradient mitigates fast-changing gradients of non-smooth contact dynamics modeled by the implicit time-stepping, or the penalty method. Finally, we apply the gradient bundle to optimal control using iLQR, introducing a novel algorithm which improves convergence over using exact gradients. Combining our algorithm with a convex implicit time-stepping formulation of contact, we show that we can tractably tackle planning-through-contact problems in manipulation.