# Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments

## TL;DR

This paper presents a safety-guaranteed trajectory planning method for autonomous vehicles that accounts for model mismatch by using a conservative reachable set, enabling real-time obstacle avoidance in unforeseen environments.

## Contribution

It introduces a novel approach combining low-fidelity planning with high-fidelity safety guarantees through conservative reachable sets and real-time obstacle intersection analysis.

## Key findings

- Successfully demonstrated in simulation with Dubin's car and unicycle models.
- Proves safety guarantees based on bounded computation time and sensing horizon.
- Provides a framework for real-time safe trajectory synthesis in complex environments.

## Abstract

Path planning for autonomous vehicles in arbitrary environments requires a guarantee of safety, but this can be impractical to ensure in real-time when the vehicle is described with a high-fidelity model. To address this problem, this paper develops a method to perform trajectory design by considering a low-fidelity model that accounts for model mismatch. The presented method begins by computing a conservative Forward Reachable Set (FRS) of a high-fidelity model's trajectories produced when tracking trajectories of a low-fidelity model over a finite time horizon. At runtime, the vehicle intersects this FRS with obstacles in the environment to eliminate trajectories that can lead to a collision, then selects an optimal plan from the remaining safe set. By bounding the time for this set intersection and subsequent path selection, this paper proves a lower bound for the FRS time horizon and sensing horizon to guarantee safety. This method is demonstrated in simulation using a kinematic Dubin's car as the low-fidelity model and a dynamic unicycle as the high-fidelity model.