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

2025-12-12

AI Summary

Collision-avoidance trajectory planning for multi-vehicle coordination at intelligent intersections suffers from high computational complexity in high-dimensional configuration spaces. Method: This paper proposes a dimensionality-reduction decomposition framework: (i) a novel 2D rectangular projection-based modeling of high-dimensional conflict polytopes; (ii) decomposition of the original problem into sequential 2D graph-search subproblems; (iii) integration of an A*-like global search with a near-optimal local optimization strategy to ensure safety and scalability; and (iv) embedding of nonlinear model predictive control (NMPC) at the lower layer to guarantee trajectory feasibility. Results: Numerical experiments demonstrate that, compared to mixed-integer linear programming (MILP)-based time-scheduling methods, the proposed approach improves the objective function value by 23% and reduces computation time by 87%, enabling real-time, safe, multi-vehicle intersection traversal.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Humans and AI: Planning and Decision Support for Human-Machine Teams
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Develop efficient trajectory planning for multi-vehicle coordination at intersections
• Reduce computational complexity by decomposing high-dimensional problems into 2D searches
• Ensure safe, smooth motion through a Nonlinear Model Predictive Control framework

Innovation

• Decomposes high-dimensional problems into 2D graph searches
• Models conflict zones using high-dimensional polyhedra from rectangles
• Integrates trajectories into Nonlinear Model Predictive Control framework