Provably Safe and Scalable Multivehicle Trajectory Planning

Abstract

The Hamilton–Jacobi (HJ) reachability is a promising tool for guaranteeing goal satisfaction and safety for multivehicle systems. However, a direct application of HJ reachability in most cases becomes intractable due to its exponentially scaling computational complexity with respect to the number of vehicles. In the work by Chen <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2018), the sequential trajectory planning (STP) method was proposed, which allows safe, multiple-vehicle trajectory planning to be done with a computation complexity that scales linearly with the number of vehicles. However, the STP computation is still not tractable for large-scale systems using the currently available tools. In this work, we introduce BEACLS, a C++-based reachability toolbox, that can leverage GPU parallelization to improve the computation speed of HJ reachability by nearly 100 times compared with the existing MATLAB implementations. We then combine BEACLS with STP for the safe, large-scale multiple-unmanned aerial vehicle (UAV) planning in a city environment and a multicity environment. We show that intuitive multilane structures naturally emerge, and the size of disturbances and the vehicle density are the primary factors determining the number and width of lanes. We also extend the STP method to safely account for an adversarial intruder during trajectory planning. In the proposed formulation, the number of vehicles that need to replan is a design parameter that can be chosen based on the computational resources available during run time. The proposed formulation along with BEACLS provides both an algorithm and an efficient computational tool for resilient, large-scale multiple-vehicle trajectory planning.