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.

翻译：本文提出了一种面向四自由度并联运动铣削机器人的平滑轨迹生成方法。所提出的方法整合了B样条与四元数插补技术，以处理解耦的位置与姿态数据点。姿态与弧长参数化位置数据的同步是通过拟合平滑分段贝塞尔曲线实现的，这些曲线描述了路径长度与刀具姿态之间的非线性关系，并通过序列二次规划求解。利用贝塞尔曲线的凸包性质，该方法确保了多智能体轨迹生成的空间与时间分离约束。单位四元数被用于姿态插补，提供了一种鲁棒且高效的表示方式，避免了万向节锁问题并促进了平滑、连续的旋转。修正多项式被用于位置插补。时间轨迹通过最小化加加速度、时间最优的分段贝塞尔曲线在两个阶段进行优化：任务空间优化后接关节空间优化，并在低成本微控制器上实现。实验结果表明，与传统插补方法相比，所提出的方法在精度、速度波动抑制和计算效率方面均有提升。