Computation of avoidance regions for driver assistance systems by using a Hamilton-Jacobi approach

TL;DR

This paper develops a Hamilton-Jacobi-based method to compute safety regions for car collision avoidance, accommodating complex obstacle dynamics and vehicle geometries, with efficient PDE solving and comparison to control approaches.

Contribution

It introduces a new level set formulation for obstacle avoidance and provides conditions for safety over time, applicable to various road and obstacle scenarios.

Findings

Successfully computed nonconvex safety regions for complex scenarios

Demonstrated efficiency of the PDE solver in high-dimensional problems

Compared Hamilton-Jacobi approach with direct optimal control, showing advantages

Abstract

We consider the problem of computing safety regions, modeled as nonconvex backward reachable sets, for a nonlinear car collision avoidance model with time-dependent obstacles. The Hamilton-Jacobi-Bellman framework is used. A new formulation of level set functions for obstacle avoidance is given and sufficient conditions for granting the obstacle avoidance on the whole time interval are obtained, even though the conditions are checked only at discrete times. Different scenarios including various road configurations, different geometry of vehicle and obstacles, as well as fixed or moving obstacles, are then studied and computed. Computations involve solving nonlinear partial differential equations of up to five space dimensions plus time with nonsmooth obstacle representations, and an efficient solver is used to this end. A comparison with a direct optimal control approach is also done for one of the examples.