Model Predictive PseudoSpectral Optimal Control with Semi-Parametric Dynamics

Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of model knowledge can be overcome with machine learning techniques by utilizing measurements to build a dynamical model from the data. This paper aims to take the middle ground between these two approaches by introducing a semi-parametric representation of the underlying system dynamics. Our goal is to leverage the considerable information contained in a traditional physics based model and combine it with a data-driven, non-parametric regression technique known as a Gaussian Process. Integrating this semi-parametric model with PseudoSpectral Optimal Control (PSOC), we demonstrate model learning in an episodic and receding horizon fashion. In order to manage parametric uncertainty, we introduce an algorithm that utilizes Sparse Spectrum Gaussian Processes (SSGP) for incremental learning after each rollout. The goal of this paper is to motivate and demonstrate the constrained optimization techniques with semi-parametric models for online learning.