Motion Planning for Arrival Time and Velocity Requirements on Non-homogeneous Terrains

The control of autonomous vehicles can be far more precise than the control of any vehicles operated by human drivers. Without planning, however, traditional feedback control is, by itself, insufficient to control a vehicle to run for a long distance while providing guarantees of timing and velocity at a destination. Previous work on motion planning of autonomous vehicles for a given arrival time and velocity assumed a homogeneous driving condition—i.e., environmental factors such as road friction, gravity and speed limits remain the same along the path to the destination. But this assumption is invalid in many real world situations. This paper considers a longitudinal motion planning problem in which a vehicle aims to arrive at a given position at a specific time and at a specific velocity on a road segmented based on the variance in driving conditions. Our contributions include 1) a sound and complete planning algorithm for roads with two road segments only; and 2) a sampling-based algorithm with heuristics for roads with multiple road segments. Our experimental results showed that our sampling-based algorithm has a high probability of success even when there are a large number of road segments