The linear-format path is widely adopted to approximate the continuous contour in robot controllers. The tangential discontinuity of the linear paths usually causes the discontinuity of the joint velocity. To comply with the joint kinematics limits, the robots have to stop at each corner point, resulting in a great loss of efficiency. To achieve a smooth motion, this paper presents an analytical decoupled C³ continuous local path smoothing method for industrial robots. The tool position path is smoothed in the reference frame while the tool orientation is smoothed in the rotation parametric space based on the exponential coordinates of rotations. The quintic B-splines are inserted at the corners of the linear segments to achieve the G³ continuity of the tool position path and tool orientation path. The orientation smoothing error is constrained analytically. By reparameterization of the remaining linear segments using specially constructed B-splines, the C³ continuity of the tool position path and tool orientation path is achieved. Then, the synchronization of the tool orientation path and tool position path can be guaranteed by sharing the same curve parameter. Besides, to improve the smoothness of the angular motion on the remaining linear segments during parameter synchronization, the transition lengths of the inserted B-splines are optimized. The proposed local smoothing method guarantees that the generated smooth orientation path in the rotation space is invariant with the selection of the reference frame and the orientation of the tool frame, and ensures the jerk-continuous motion with a smoother angular motion on the remaining linear segments, which could improve the motion smoothness of the tool path and tracking accuracy. The effectiveness of the proposed method is validated through simulation and experiments.

线性格式路径被广泛采用来近似机器人控制器中的连续轮廓。线性路径的切向不连续性通常会导致关节速度的不连续性。为了遵守关节运动学限制，机器人必须在每个角点停止，从而导致效率的极大损失。为了实现平滑运动，本文提出了一种用于工业机器人的解析解耦C ³连续局部路径平滑方法。刀具位置路径在参考系中平滑，而刀具方向在旋转参数空间中基于旋转的指数坐标进行平滑。将五次 B 样条插入线性段的拐角处以获得 G ³刀具位置路径和刀具定向路径的连续性。方向平滑误差受到解析约束。通过使用特殊构造的 B 样条重新参数化剩余的线性段，C ³实现了刀具位置路径和刀具定向路径的连续性。这样，通过共享相同的曲线参数，可以保证刀具定向路径和刀具位置路径的同步。此外，为了提高参数同步过程中剩余线性段上角运动的平滑度，优化了插入B样条的过渡长度。所提出的局部平滑方法保证了旋转空间中生成的平滑定向路径与参考坐标系的选择和工具坐标系的定向保持不变，并确保在剩余的线性段上以更平滑的角运动进行加加速度连续运动，可以提高刀具路径的运动平滑度和跟踪精度。