用B样条与四元数融合生成平滑轨迹，提升五轴加工机器人精度与效率
Smooth trajectory generation and hybrid B-splines-Quaternions based tool path interpolation for a 3T1R parallel kinematic milling robot
- 分步优化任务空间与关节空间轨迹，采用最小加速度准则
- 通过贝塞尔曲线拟合路径长度与姿态关系，实现位置与姿态同步
- 四元数避免万向节锁，低功耗微控制器实现实时运行
本文提出一种针对四自由度并联铣削机器人的平滑轨迹生成方法。该方法结合B样条与四元数插值技术，分别处理解耦的位置与姿态数据点。通过拟合光滑的分段贝塞尔曲线，建立路径长度与刀具姿态之间的非线性关系，并利用序列二次规划求解，实现位置与姿态在弧长参数化下的同步。借助贝塞尔曲线的凸包性质，确保多智能体轨迹生成中的时空分离约束。姿态插值采用单位四元数表示，有效避免万向节锁，实现平滑连续旋转。位置插值使用修正多项式。时间轨迹在任务空间与关节空间分两阶段优化，采用最小加加速度（minimum jerk）和时间最优分段贝塞尔曲线，在低成本微控制器上实现。实验结果表明，相比传统方法，本方法显著提升精度、降低速度波动并提高计算效率。
原文摘要 · Abstract (English)
This paper presents a smooth trajectory generation method for a four-degree-of-freedom parallel kinematic milling robot. The proposed approach integrates B-spline and Quaternion interpolation techniques to manage decoupled position and orientation data points. The synchronization of orientation and arc-length-parameterized position data is achieved through the fitting of smooth piece-wise Bezier curves, which describe the non-linear relationship between path length and tool orientation, solved via sequential quadratic programming. By leveraging the convex hull properties of Bezier curves, the method ensures spatial and temporal separation constraints for multi-agent trajectory generation. Unit quaternions are employed for orientation interpolation, providing a robust and efficient representation that avoids gimbal lock and facilitates smooth, continuous rotation. Modifier polynomials are used for position interpolation. Temporal trajectories are optimized using minimum jerk, time-optimal piece-wise Bezier curves in two stages: task space followed by joint space, implemented on a low-cost microcontroller. Experimental results demonstrate that the proposed method offers enhanced accuracy, reduced velocity fluctuations, and computational efficiency compared to conventional interpolation methods.
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