Partitioning of the Free Space-Time for On-Road Navigation of Autonomous Ground Vehicles

TL;DR

This paper introduces a systematic method for partitioning free space-time for autonomous ground vehicle navigation, transforming complex trajectory planning into a graph search problem that accounts for obstacles and robustness.

Contribution

It presents a novel partitioning approach that simplifies the NP-hard trajectory planning problem into a graph search with efficient optimization, incorporating robustness considerations.

Findings

Partitioning enables polynomial-time trajectory optimization.

Graph-based approach effectively handles static and moving obstacles.

Robustness criteria can be integrated during graph exploration.

Abstract

In this article, we consider the problem of trajectory planning and control for on-road driving of an autonomous ground vehicle (AGV) in presence of static or moving obstacles. We propose a systematic approach to partition the collision-free portion of the space-time into convex sub-regions that can be interpreted in terms of relative positions with respect to a set of fixed or mobile obstacles. We show that this partitioning allows decomposing the NP-hard problem of computing an optimal collision-free trajectory, as a path-finding problem in a well-designed graph followed by a simple (polynomial time) optimization phase for any quadratic convex cost function. Moreover, robustness criteria such as margin of error while executing the trajectory can easily be taken into account at the graph-exploration phase, thus reducing the number of paths to explore.