Accelerating Numerical Methods for Optimal Control

Many modern control methods, such as model-predictive control, rely heavily on solving optimization problems in real time. In particular, the ability to efficiently solve optimal control problems has enabled many of the recent breakthroughs in achieving highly dynamic behaviors for complex robotic systems. The high computational requirements of these algorithms demand novel algorithms tailor-suited to meeting the tight requirements on runtime performance, memory usage, reliability, and flexibility. This thesis introduces a state-of-the-art algorithm for trajectory optimization that leverages the problem structure while being applicable across a wide variety of problem requirements, including those involving conic constraints and non-Euclidean state vectors such as 3D rotations. Additionally, algorithms for exposing parallelization in both the temporal and spatial domains are proposed. While optimal control algorithms—such as those developed in this thesis—work well for many systems, their performance is generally limited by the provided analytical model. To address this limitation, this thesis also proposes a sample-efficient method for updating controller performance through the combination of information from an approximate model with data from the true system dynamics.