# Guaranteed Safe Reachability-based Trajectory Design for a High-Fidelity Model of an Autonomous Passenger Vehicle

## TL;DR

This paper extends the Reachability-based Trajectory Design (RTD) algorithm to a high-fidelity autonomous passenger vehicle, demonstrating real-time safe trajectory planning in complex driving scenarios with obstacles.

## Contribution

It applies RTD to a full-scale passenger vehicle with detailed dynamics, showing its effectiveness and safety in real-world driving conditions.

## Key findings

- RTD successfully plans safe trajectories at speeds up to 15 m/s.
- RTD outperforms NMPC and RRT in real-time safety guarantees.
- The approach handles obstacles detected within sensor range effectively.

## Abstract

Trajectory planning is challenging for autonomous cars since they operate in unpredictable environments with limited sensor horizons. To incorporate new information as it is sensed, planning is done in a loop, with the next plan being computed as the previous plan is executed. The recent Reachability-based Trajectory Design (RTD) is a provably safe, real-time algorithm for trajectory planning. RTD consists of an offline component, where a Forward Reachable Set (FRS) is computed for the vehicle tracking parameterized trajectories; and an online part, where the FRS is used to map obstacles to constraints for trajectory optimization in a provably-safe way. In the literature, RTD has only been applied to small mobile robots. The contribution of this work is applying RTD to a passenger vehicle in CarSim, with a full powertrain model, chassis and tire dynamics. RTD produces safe trajectory plans with the vehicle traveling up to 15 m/s on a two-lane road, with randomly-placed obstacles only known to the vehicle when detected within its sensor horizon. RTD is compared with a Nonlinear Model-Predictive Control (NMPC) and a Rapidly-exploring Random Tree (RRT) approach. The experiment demonstrates RTD's ability to plan safe trajectories in real time, in contrast to the existing state-of-the-art approaches.