Two-dimensional Decompositions of High-dimensional Configurations for Efficient Multi-vehicle Coordination at Intelligent Intersections

TL;DR

This paper presents a novel, efficient method for multi-vehicle trajectory planning at intersections by decomposing high-dimensional problems into 2D graph searches, enabling real-time, collision-free coordination.

Contribution

The authors introduce a decomposition-based algorithm that reduces computational complexity in multi-vehicle trajectory planning, integrating it with NMPC for safe, smooth vehicle motion.

Findings

Significantly faster computation than MILP-based methods

Achieves near-optimal trajectories in complex scenarios

Ensures collision-free, smooth vehicle coordination

Abstract

For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally efficient method for generating collision-free trajectories along predefined vehicle paths. We reformulate a constrained minimum-time trajectory planning problem as a problem in a high-dimensional configuration space, where conflict zones are modeled by high-dimensional polyhedra constructed from two-dimensional rectangles. Still, in such a formulation, as the number of vehicles involved increases, the computational complexity increases significantly. To address this, we propose two algorithms for near-optimal local optimization that significantly reduce the computational complexity by decomposing the high-dimensional problem into a sequence of 2D graph search problems. The resulting trajectories are then incorporated into a Nonlinear Model Predictive Control (NMPC) framework to ensure safe and smooth vehicle motion. We furthermore show in numerical evaluation that this approach significantly outperforms existing MILP-based time-scheduling; both in terms of objective-value and computational time.