Applied Math Colloquium: Christian Parkinson
Mathematics/Psychology : 106
Date & Time
February 1, 2023, 12:00 pm – 1:00 pm
Title: The Hamilton-Jacobi Formulation of Optimal Path Planning for Autonomous Vehicles
Speaker: Christian Parkinson (University of Arizona)
Abstract: We present a partial-differential-equation-based optimal path planning framework for simple self-driving cars. This formulation relies on optimal control theory, dynamic programming, and a Hamilton-Jacobi-Bellman equation, and thus provides an interpretable alternative to black-box machine learning algorithms. We design grid-based numerical methods used to resolve the solution to the Hamilton-Jacobi-Bellman equation and generate optimal trajectories. We then describe how efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations can be developed to solve similar problems in higher dimensions and in nearly real-time. We demonstrate our methods with several examples.