Gaussian process for dynamic systems

Abstract

State estimation is a fundamental problem for agents which operate in the real world. An agent must have knowledge of its state and the environment within which it operates. However, this knowledge of the world is available only through noisy and imperfect sensors. The key to this problem is the interpretation of this data in a probabilistically sound manner. One of the most successful approaches for state estimation is through the use of Bayesian filtering techniques including Kalman and particle filters. These filters commonly rely on parametric models of the system. However, these models are difficult to develop and often require simplifying assumptions which do not address the full complexity of the system. In this thesis, we introduce a non-parametric method for building these system models. Specifically, we use Gaussian processes to learn both the dynamics and observation models. These models are more accurate than their parametric counterparts and are flexible enough to capture all aspects of the system. The basic technique requires ground truth training data, and we show how it can be extended to learn models without this data. We again extend this framework to allow for control of systems given expert demonstrations. We test the effectiveness of our methods using a variety of robotic platforms.