A constant-time algorithm for checking reachability of arrival times and arrival velocities of autonomous vehicles

Abstract

A fast algorithm for checking whether an autonomous vehicle can arrive at a position at a given arrival time and velocity is the key to Autonomous Intersection Management (AIM). This paper presents a complete set of closed form equations that fully describes the set of all reachable arrival configurations in longitudinal motion planning if the vehicle's controller is a double integrator with bounded acceleration. This result improves the running time of the algorithm for checking the reachability of an arrival configuration from logarithmic time to constant time. We also apply the result to check the reachability in a segmented road and discuss how the algorithm can be applied to real vehicles.