主办：陕西省汽车工程学会
ISSN 1671-7988  CN 61-1394/TH
创刊：1976年
汽车实用技术

汽车实用技术 ›› 2026, Vol. 51 ›› Issue (3): 15-22.DOI: 10.16638/j.cnki.1671-7988.2026.003.003

• 智能驾驶与车辆控制技术 • 上一篇    

融合时变权重 LQR 与五次多项式的 轨迹规划方法

尹力，赵明欣   

  1. 内蒙古交通职业技术学院
  • 发布日期:2026-02-04
  • 通讯作者: 尹力
  • 作者简介:尹力（1985－），男，副教授，研究方向为智能网联技术

Trajectory Planning Method Utilizing Time-Varying Weighted LQR and Quintic Polynomial

YIN Li, ZHAO Mingxin   

  1. Inner Mongolia Vocational and Technical College of Transportation
  • Published:2026-02-04
  • Contact: YIN Li

PDF

摘要： 针对智能汽车紧急横向避障场景下传统固定权重线性二次调节器（LQR）在避障后段 对横向位移误差抑制不足、难以平衡全程跟踪性能的问题，文章提出了一种融合五次多项式 轨迹规划与时变权重 LQR 控制的协同方法。首先，基于笛卡尔坐标系，利用五次多项式生成 满足起终点位移、速度、加速度连续性的平滑避障参考轨迹，有效避免了曲率突变并约束了 侧向加速度峰值（<0.1g）。其次，设计了一种时变权重 LQR 跟踪控制器：在避障前期（t<2 s）， 赋予横向位移误差较低权重，侧重响应速度与控制平顺性；在避障后期（t≥2 s），则显著增大 其权重，强制控制器优先抑制累积性横向误差，提升跟踪精度。在 MATLAB/Simulink/CarSim 联合仿真平台上构建典型行人避障场景进行验证。结果表明，相较于固定权重 LQR，所提方 法将横向位移误差峰值由大于 0.5 m 显著降低至小于 0.2 m（降幅大于 60%），并有效抑制了 误差在避障后期的累积漂移趋势；横摆角误差峰值由大于 0.05 rad 降低至小于 0.02 rad（降幅 大于 60%）；侧向加速度峰值稳定维持在 0.1g 以内。该方法通过轨迹平滑性保障与控制器权 重动态调节的协同，显著提升了紧急避障过程的安全性（确保安全距离）与舒适性（平顺控 制），为智能汽车动态避障控制提供了有效解决方案。

关键词: 智能汽车；横向避障；时变权重；五次多项式曲线；线性二次调节器

Abstract: This study addresses the limitations of traditional fixed-weight linear quadratic regulator (LQR) controllers in intelligent vehicle lateral emergency obstacle avoidance, notably the insufficient suppression of lateral displacement error in the post-avoidance phase and the difficulty in balancing tracking performance throughout the maneuver. A synergistic approach integrating quintic polynomial trajectory planning with a time-varying weighted LQR controller is proposed. Firstly, smooth obstacle-avoidance reference trajectories are generated in the Cartesian frame using quintic polynomials, satisfying continuity constraints on position, velocity, and acceleration at both start and end points. This effectively avoids curvature discontinuity and constrains the peak lateral acceleration (<0.1g). Secondly, a time-varying weighted LQR tracking controller is designed: a lower weight is assigned to lateral displacement error during the initial avoidance phase (t<2 s) to prioritize responsiveness and control smoothness, while a significantly higher weight is applied to lateral displacement error in the later phase (t≥2 s) to force the controller to prioritize suppressing cumulative lateral errors and enhance tracking precision. Validation is conducted on a MATLAB/ Simulink/CarSim co-simulation platform under a typical pedestrian avoidance scenario. Results demonstrate significant improvements over the fixed-weight LQR: The proposed method reduces the peak lateral displacement error from>0.5 m to<0.2 m (reduction>60%) and effectively suppresses the drift trend of ey accumulation in the later stage; The peak yaw angle error is reduced from>0.05 rad to<0.02 rad (reduction>60%); The peak lateral acceleration remains stably below 0.1g. The synergy between smooth trajectory generation and dynamic controller weighting adjustment significantly enhances both safety (ensuring safe distance) and comfort (smooth control) during emergency obstacle avoidance, providing an effective solution for intelligent vehicle dynamic obstacle avoidance control.

Key words: intelligent vehicle; lateral collision avoidance; time-varying weights; quintic polynomial curve; linear quadratic regulator