Reachability-based Safe Planning for Multi-Vehicle Systems withMultiple Targets

TL;DR

This paper introduces a scalable reachability-based safety planning method for multi-vehicle systems with multiple targets, capable of guaranteeing safety for any number of vehicles by clustering and control strategies.

Contribution

It presents a novel approach that extends safety guarantees to large vehicle groups, overcoming the curse of dimensionality in reachability analysis.

Findings

Successfully demonstrated safety guarantees for 15 vehicles in simulation.

Developed an efficient clustering method for large vehicle groups.

Generalized the 3-vehicle collision avoidance solution to any number of vehicles.

Abstract

Recently there have been a lot of interests in introducing UAVs for a wide range of applications, making ensuring safety of multi-vehicle systems a highly crucial problem. Hamilton-Jacobi (HJ) reachability is a promising tool for analyzing safety of vehicles for low-dimensional systems. However, reachability suffers from the curse of dimensionality, making its direct application to more than two vehicles intractable. Recent works have made it tractable to guarantee safety for 3 and 4 vehicles with reachability. However, the number of vehicles safety can be guaranteed for remains small. In this paper, we propose a novel reachability-based approach that guarantees safety for any number of vehicles while vehicles complete their objectives of visiting multiple targets efficiently, given any K-vehicle collision avoidance algorithm where K can in general be a small number. We achieve this by developing an approach to group vehicles into clusters efficiently and a control strategy that guarantees safety for any in-cluster and cross-cluster pair of vehicles for all time. Our proposed method is scalable to large number of vehicles with little computation overhead. We demonstrate our proposed approach with a simulation on 15 vehicles. In addition, we contribute a more general solution to the 3-vehicle collision avoidance problem from a past recent work, show that the prior work is a special case of our proposed generalization, and prove its validity.