通过二维分解提升智能交叉口多车协同的计算效率
Two-dimensional Decompositions of High-dimensional Configurations for Efficient Multi-vehicle Coordination at Intelligent Intersections
- 将高维轨迹规划问题分解为一系列二维图搜索，降低复杂度
- 在保证无碰撞的前提下，求解速度比传统方法快数倍
- 适合需要实时协同控制的智能交通系统应用
针对智能交叉口等共享空间中的多车复杂交通场景，安全协调与轨迹规划因计算复杂性而面临挑战。本文提出一种计算高效的碰撞避免轨迹生成方法，将约束最小时间轨迹规划问题重构为高维配置空间中的优化问题，冲突区域由二维矩形构建的高维多面体表示。随着车辆数量增加，该方法的计算复杂度仍显著上升。为此，我们设计两种近似最优的局部优化算法，通过将高维问题分解为一系列二维图搜索问题，大幅降低计算开销。所得轨迹被集成至非线性模型预测控制（NMPC）框架中，确保车辆运动的安全与平滑。数值实验表明，该方法在目标值和计算时间上均显著优于现有的基于MILP的时间调度方案。
原文摘要 · Abstract (English)
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.
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