结合PCA与K-Means降维的Fast-MPC无人驾驶实时轨迹跟踪

Fast-MPC with PCA and K-Means Dimensionality Reduction for Real-Time Trajectory Tracking in Autonomous Vehicles

摘要: 本文提出了一种基于快速模型预测控制(Fast-MPC)的方法，旨在解决无人驾驶车辆在全速域轨迹跟踪中的二次规划(QP)问题。传统的模型预测控制(MPC)方法在高维不等式约束下的计算效率较低，尤其在无人驾驶车辆的高速轨迹跟踪任务中，难以满足实时性要求。尽管Fast-MPC显著加快了求解速度，但在处理高维不等式约束时表现出敏感性，导致计算效率下降。为了解决这一问题，本文应用了一种基于主成分分析(PCA)和K-means聚类的不等式降维方法。在PCA的基础上，本文进一步引入K-means聚类算法对降维后的数据进行聚类，从而在降低问题维度的同时，保留了不同约束类群中的关键信息。从而降低了QP问题的复杂度。该算法在Simulink和CarSim联合仿真平台上进行了双移线场景测试。实验结果表明，结合PCA的Fast-MPC方法不仅有效提高了求解速度，最大减少了约束维度的60%，并在高速轨迹跟踪中有效避免了振荡现象。同时，车辆在高动态环境中的轨迹跟踪精度得到了显著改善，尤其是在横向控制方面的表现更加稳定可靠。该方法为无人驾驶车辆的实时轨迹跟踪提供了高效且稳定的解决方案。

Abstract: This study proposes a fast model predictive control (Fast-MPC)-based method with dimensionality reduction to address quadratic programming (QP) challenges in real-time trajectory tracking for autonomous vehicles. Traditional model predictive control (MPC) suffers from low computational efficiency under high-dimensional inequality constraints, making it difficult to meet real-time requirements, especially in high-speed trajectory tracking tasks. Although Fast-MPC significantly accelerates the optimization process, its sensitivity to high-dimensional inequality constraints may cause computational efficiency degradation and solution instability. To overcome these limitations, this paper introduces an inequality dimension-reduction method that integrates principal component analysis (PCA) and k-means clustering algorithm (K-means). By employing dynamic grouping and an optimized constraint retention strategy, the proposed approach effectively reduces QP complexity while significantly enhancing computational efficiency. Compared to conventional dimension-reduction techniques, the proposed algorithm achieves a 60% dimensionality reduction in constraint space and avoids trajectory oscillations through more accurate feature preservation. Comprehensive co-simulations using Simulink/CarSim platforms under double-lane-change scenarios validate that the algorithm notably improves trajectory tracking accuracy, particularly showcasing stable and reliable performance in high-dynamic lateral stabilization. Further analysis reveals that this method exhibits strong adaptability, making it extendable to dynamic obstacle avoidance and real-time trajectory tracking in complex urban environments. This work provides an efficient and robust solution for autonomous vehicle trajectory tracking, demonstrating strong potential for deployment in complex driving scenarios with dynamic obstacles.