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.
翻译：本文提出了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。该方法在结构化优化框架中显式地融入了安全裕度，在轨迹平滑性与鲁棒性之间取得平衡，同时保持适用于实时及嵌入式应用的可管理数值复杂度。对比仿真结果表明，相较于传统的分段线性（PWL）路径规划方法，本方法在轨迹偏差减小、鲁棒性增强及整体路径质量提升方面具有明显优势。通过采用纯追踪控制器在典型场景中进行仿真验证，进一步证实了该方法在安全导航中的实际有效性和可扩展性。
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