# Pseudospectral Model Predictive Control under Partially Learned Dynamics

## TL;DR

This paper introduces a semi-parametric model predictive control method that combines physics-based models with Gaussian Processes for improved trajectory optimization under uncertain dynamics, demonstrated on robotics simulations.

## Contribution

It presents a novel semi-parametric modeling approach integrated with pseudospectral control and online learning using Sparse Spectrum Gaussian Processes for robotic systems.

## Key findings

- Effective handling of unmodeled damping and parametric errors
- Successful online learning and obstacle avoidance in simulations
- Improved trajectory optimization with semi-parametric models

## Abstract

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, 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 model predictive pseudospectral control, we demonstrate this technique on both a cart pole and quadrotor simulation with unmodeled damping and parametric error. In order to manage parametric uncertainty, we introduce an algorithm that utilizes Sparse Spectrum Gaussian Processes (SSGP) for online learning after each rollout. We implement this online learning technique on a cart pole and quadrator, then demonstrate the use of online learning and obstacle avoidance for the dubin vehicle dynamics.