William Sharpless

Hello,

I am a Mechanical and Aerospace PhD candidate in Sylvia Herbert's Safety and Autonomous Systems group at UC San Diego.

My work involves differential games (HJB-PDE's), control and learning, and my thesis concentrates on feasible methods for safe, high-dimensional autonomy. I am an HHMI/NIH Interfaces fellow, and I am also supported by the ONR and the Society of Hellman.

Before, I did my undergraduate degree in applied mathematics at UC Berkeley where I worked with Claire Tomlin, Adam Arkin and Jay Keasling.

willsharpless [at] ucsd [dot] edu  /  CV  /  Google Scholar  /  Github  /  Linkedin

Here, we derive novel HJB forms for dual-objective problems (multi-reward or reward & cost) and solve the corresponding Bellman eqns. We use these to design a novel on-policy algorithm (DO-HJ-PPO) which outerperforms STL-RL and CMDP (C-PPO) algorithms for a variety of safe-arrival and multi-achievment tasks.

[RSS workshop paper] (full paper coming soon)

In this work, we explore learning smooth, tunable CBF's via the HJB PINN approach, dubbed Reachability Barrier Networks (RBNs). Due to the structure of the problem and uniqueness of the solution, we found RBNs to be more readily learned than neural CBFs, yielding safer appxs. with 5.5x less collisions in multi-agent scenario.

[paper]

Here, we show that to learn a nonlinear HJ-PDE for autonomy, one may introduce the linear solution for ~25x increase in accuracy and ~20x acceleration in training for problems up to 50-dimensions.

[paper]

Here, we propose a novel, lifted differential game that is guaranteed to be conservative, is solved rapidly, and allows the use of lifting functions such as neural nets, polynomials and radial basis functions to reduce linear error.

[paper]

Here, we demonstrate how the error between a nonlinear system of interest and a linearization of it may transformed into an antagonistic player, yielding a conservative linear game that may be solved rapidly in high-dimensions.

[paper]

In this work, we propose and demonstrate the use of Koopman linearizations to allow the use of the Hopf formula for linear differential games to yield a performant algorithm for high-dimensional, nonlinear autonomy.

[paper]

Julia software for accelerated non-smooth, convex optimization of the Hopf objective for solving high-dimensional differential games.

A fast, interactive level set solver for HJB flows made in GLSL.

Website template by Jon Barron (source code).
How the mighty have fallen.