The Python LevelSet Toolbox (LevelSetPy)

TL;DR

The Python LevelSet Toolbox (LevelSetPy) is an open-source library that provides efficient, GPU-accelerated solutions for hyperbolic Hamilton-Jacobi equations, facilitating applications in robotics, control, and reinforcement learning.

Contribution

It introduces a fast, GPU-accelerated Python library for solving Hamilton-Jacobi equations with detailed implementation and comparison to existing tools.

Findings

GPU acceleration significantly speeds up computations.

Python implementation outperforms existing alternatives.

Library supports applications in robotics and control systems.

Abstract

This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces; dynamics evolution with levelsets; spatial derivatives; total variation diminishing Runge-Kutta integration schemes; and their applications to the theory of reachable sets. They are increasingly finding applications in multiple research domains such as reinforcement learning, robotics, control engineering and automation. We describe the library components, illustrate usage with an example, and provide comparisons with existing implementations. This GPU-accelerated package allows for easy portability to many modern libraries for the numerical analyses of the HJ equations. We also provide a CPU implementation in python that is significantly faster than existing alternatives.