17 citations · 22 across the 9 of their papers we have counts for
11 papers
Efficient and Scalable Path-Planning Algorithms for Curvature Constrained Motion in the Hamilton-Jacobi Formulation
Christian Parkinson, Isabelle Boyle
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This…
Analysis of a Reaction-Diffusion SIR Epidemic Model with Noncompliant Behavior
Christian Parkinson, Weinan Wang
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differentia…
Time-Optimal Paths for Simple Cars with Moving Obstacles in the Hamilton-Jacobi Formulation
Christian Parkinson, Madeline Ceccia
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles…
A Multilayer Network Model of the Coevolution of the Spread of a Disease and Competing Opinions
Kaiyan Peng, Zheng Lu, Vanessa Lin +5
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phen…
A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles
Christian Parkinson, Andrea L. Bertozzi, Stanley Osher
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global…
A Model for Optimal Human Navigation with Stochastic Effects
Christian Parkinson, David Arnold, Andrea L. Bertozzi +1
We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous…
A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations
Christian Parkinson
We present a fast sweeping method for a class of Hamilton-Jacobi equations that arise from time-independent problems in optimal control theory. The basic method in two dimensions u…
Matrix Completion With Selective Sampling
Christian Parkinson, Kevin Huynh, Deanna Needell
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors hav…
Modeling Environmental Crime in Protected Areas Using the Level Set Method
David J. Arnold, Dayne Fernandez, Ruizhe Jia +5
National parks often serve as hotspots for environmental crime such as illegal deforestation and animal poaching. Previous attempts to model environmental crime were either discret…
Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach
Christian Parkinson, David Arnold, Andrea L. Bertozzi +2
We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a cont…
Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity
Stephen Pankavich, Christian Parkinson
We consider a spatially-heterogeneous generalization of a well-established model for the dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The mo…