An Optimization Approach to Certified Manipulation

Abstract

The goal of this thesis is to explore the problem of contact-rich robotic manipulation from an optimization perspective. We plan to study the interplay between contact mechanics, geometry, and machine learning to synthesize manipulation plans with varying theoretical properties. More specifically, we propose a quasi-dynamic mechanics model for contact-trajectory optimization and apply it to solve long-horizon manipulation problems in conjunction with randomized planning. We also discuss a machine learning pipeline to solve this problem from video demonstrations, leveraging novel tools from differentiable optimization and learning. Finally, we aim to explore the issue of certification for planar manipulation tasks in the frictionless plane. We propose a theory of certification that enables us to generate long-horizon manipulation plans that are robust to bounded pose uncertainty. The desired outcome of these techniques is to validate them over a wide range of standard manipulation tasks in 2D environments. Our current results demonstrate the ability of model-based approaches at synthesizing high-quality manipulation plans with varying properties, such as optimality, convergence, robustness, and computation speed.