用分段二次贝塞尔曲线实现带安全距离的平滑路径规划
Smooth path planning with safety margins using Piece-Wise Bezier curves
- 用分段二次贝塞尔曲线构建连续可微路径，提升平滑性
- 相比传统折线路径，轨迹偏差更小，鲁棒性显著提升
- 适合嵌入式系统实时应用，对自动驾驶有实用价值
本文提出一种计算高效的二次规划（QP）方法，利用分段二次贝塞尔（PWB）曲线为移动机器人生成平滑的$C^1$连续路径。方法在结构化优化框架中显式引入安全裕度，平衡轨迹平滑性与鲁棒性，同时保持可管理的数值复杂度，适用于实时和嵌入式应用场景。对比仿真显示，该方法在典型场景下优于传统的分段线性（PWL）路径规划，表现出更小的轨迹偏差、更强的鲁棒性和更高的整体路径质量。通过纯追踪（Pure-Pursuit）控制器验证了其实际有效性与可扩展性。
原文摘要 · Abstract (English)
In this paper, we propose a computationally efficient quadratic programming (QP) approach for generating smooth, $C^1$ continuous paths for mobile robots using piece-wise quadratic Bezier (PWB) curves. Our method explicitly incorporates safety margins within a structured optimization framework, balancing trajectory smoothness and robustness with manageable numerical complexity suitable for real-time and embedded applications. Comparative simulations demonstrate clear advantages over traditional piece-wise linear (PWL) path planning methods, showing reduced trajectory deviations, enhanced robustness, and improved overall path quality. These benefits are validated through simulations using a Pure-Pursuit controller in representative scenarios, highlighting the practical effectiveness and scalability of our approach for safe navigation.
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