Mathematics Colloquium
Christian Parkinson
University of Arizona
Title: Optimal Path Planning in the Hamilton-Jacobi Formulation
Date: Monday, January 8, 2024
Place and Time: Love 101, 3:05-3:55 pm
Abstract. We present a partial-differential-equation-based optimal path planning framework. This formulation relies on optimal control theory, dynamic programming, and Hamilton-Jacobi-Bellman equations, and thus provides an interpretable alternative to black-box machine learning algorithms. We briefly discuss grid-based numerical methods used to resolve the solution to the Hamilton-Jacobi-Bellman equation and generate optimal trajectories, and then describe how efficient and scalable algorithms for solutions of high dimensional Hamilton-Jacobi equations can be used to solve similar problems in higher dimensions and in nearly real-time. We demonstrate all of our methods with several examples.