Bundled Gradients through Contact via Randomized Smoothing
This work addresses the problem of improving gradient-based methods for planning through contact in robotics, offering a solution that is incremental but enhances convergence in specific domains like manipulation.
The paper tackles the challenge of using gradient-based optimization for planning through contact in reinforcement learning by introducing a stochastic formulation of dynamics and the gradient bundle concept. It shows that this approach mitigates issues with non-smooth contact dynamics and improves convergence in optimal control, as demonstrated with a novel algorithm applied to manipulation tasks.
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.