Title: Motion Primitive Path Planning for Parametrically Uncertain Systems via the Koopman Operator

Geordan Gutow

Robotics Ph.D. Candidate

Georgia Institute of Technology

Email: ggutow3@gatech.edu

Date: Tuesday April 26th, 2022

Time: 11:00AM to 1:00PM EDT

Location: Montgomery Knight Building, 317

Meeting Link: https://gatech.zoom.us/j/95861438816

Committee

1. Dr. Jonathan Rogers (Primary Advisor) – School of Aerospace Engineering, Georgia Institute of Technology
2. Dr. Seth Hutchinson – School of Interactive Computing, Georgia Institute of Technology
3. Dr. Anirban Mazumdar – School of Mechanical Engineering, Georgia Institute of Technology
4. Dr. Charles Pippen – Georgia Tech Research Institute
5. Dr. Panagiotis Tsiotras – School of Aerospace Engineering, Georgia Institute of Technology

Abstract:

Kinodynamic motion planning addresses the problem of finding the control inputs to a dynamical system such that that system's trajectory satisfies constraints such as obstacle avoidance or entering a goal set. Motion primitives are a popular tool for kinodynamic motion planning as they allow constructing trajectories that are guaranteed to satisfy the system dynamics without requiring on-demand simulation. This work provides a generalization of motion primitives to systems subject to parametric uncertainty. Quantities of interest in optimal motion planning, including integrated cost terms and constraint indicator functions, are cast as expectations of functions of the terminal state of a motion primitive. Explicit uncertainty quantification via the Koopman operator is used to obtain sample-efficient schemes for evaluating these expectations. The sampling scheme permits casting the planning problem as a Chance-Constrained Markov Decision Process with a finite set of actions, for which a policy can be obtained by forward search on an And/Or graph. Techniques for efficient solution of this search problem are presented. The key bottleneck is identified as the expected value calculation, which is a high dimensional integral. One way to accelerate such calculations is through the use of a "sparse" numerical integration scheme. A method is described for obtaining maximally sparse numerical integration schemes for use with hypergraph search algorithms. The approach formulates a mixed-integer linear program that is tailored to the specific structure of the hypergraph on which chance-constrained motion primitive planning problems are solved. Finally, the effectiveness of Monte Carlo Tree Search and Lazy constraint enforcement is investigated.