PhD Comprehensive Exam | Yating Yuan, Planning and Control as Probabilistic Inference on Factor Graphs

MS Teams: Please email amgrad@uwaterloo.ca for the meeting link

Candidate

Yating Yuan | Applied Mathematics, University of Waterloo

Title

Planning and Control as Probabilistic Inference on Factor Graphs

Abstract

Planning and optimal control under uncertainty are central problems in the field of autonomous robotics. While planning methods or optimal control algorithms as probabilistic inferences have been separately developed over the past decades, the main purpose of this proposal is to present a unified framework for planning collision-free trajectories and finding the optimal controls together via probabilistic inference. In this framework, Gaussian Processes (GPs) will be used to represent discrete-time trajectories, the signed distance field is employed to represent the environment information for obstacle cost, then the optimal problem can be defined as a distribution over trajectories and controls and be treated as a Maximum A Posterior (MAP) estimation problem. Moreover, with Bayes’ law and factor graphs, the MAP can be factorized and transformed into a nonlinear least squares problem that can be solved by numerical tools, such as QR decomposition and Cholesky factorization. On the other hand, the control policy is inferred by variable elimination. Finally, we conduct comparison experiments to show the feasibility of the proposed framework.