Safe Control for Pursuit-Evasion with Density Functions

TL;DR

This paper introduces a scalable, density function-based safe control framework for pursuit-evasion problems, avoiding complex PDEs and enabling efficient safety guarantees through convex optimization.

Contribution

It extends safety analysis to dynamic unsafe sets using density functions, reformulating pursuit-evasion as a convex sum-of-squares program for improved computational efficiency.

Findings

Successfully avoids Hamilton-Jacobi-Isaacs PDE complexity

Demonstrates scalable safety guarantees in pursuit-evasion scenarios

Numerical simulations confirm effectiveness of the approach

Abstract

This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust safe control problem. Using density functions and semi-algebraic set definitions, we derive sufficient conditions for weak eventuality and evasion, reformulating the problem into a convex sum-of-squares program solvable via standard semidefinite programming solvers. This approach avoids the computational complexity of solving the Hamilton-Jacobi-Isaacs partial differential equation, offering a scalable and efficient framework. Numerical simulations demonstrate the efficacy of the proposed method.