A five-axis coordinated laser surface scanning path smoothing method using Bezier curves and quaternions (<italic>invited</italic>)

ObjectiveIn the five-axis coordinated laser engraving process, it is necessary to simultaneously and precisely control the three-dimensional scanning path and the two-dimensional beam orientation. The existing linear interpolation method using small line segments only possesses low-order continuity. This limitation easily leads to sudden velocity changes, which induces machine tool vibration and seriously affects the machining quality. To address these issues, this paper proposes a path smoothing method that decouples position and orientation.MethodsThe proposed method separately considers geometric smoothing of the laser path and smoothing of the laser beam orientation. For position smoothing, cubic Bezier curves are employed to smooth the laser scanning path. By constructing auxiliary points based on tangent vectors, the first-order continuity of the trajectory is guaranteed. For orientation smoothing, to overcome the defects of traditional Euler angles such as gimbal lock and low computational efficiency, quaternions are introduced to smooth the laser direction vector. A quadratic quaternion spherical interpolation algorithm is constructed to achieve continuous angular velocity at the path nodes. This theoretically eliminates the "soft impact" during the motion. The method is validated through simulation and machining experiments by comparing it with the traditional linear interpolation method.Results and DiscussionsThe simulation and experimental results demonstrate the effectiveness of the proposed algorithm. In terms of position smoothing, the cubic Bezier interpolation reduces the average position error from 0.0657 mm to 0.0221 mm, a decrease of approximately two-thirds compared to linear interpolation. The variance of velocity change is reduced from 0.0047 mm2·s−2 to 0.0018 mm2·s−2, also decreasing by about two-thirds. In terms of orientation smoothing, the quadratic quaternion spherical interpolation reduces the average direction vector error from 1.1449° to 0.3829°, which is about one-third of the error observed in linear interpolation. Furthermore, the variance of angular velocity change decreases from 4.79×10−4 (°)/s2 to 2.34×10−4 (°)/s2, representing a reduction of more than half.ConclusionsThe proposed smoothing method significantly improves the position and orientation accuracy of the laser beam during the machining process compared to traditional linear interpolation. It effectively avoids sudden velocity changes during movement and ensures smoother machine operation. This study provides a trajectory planning method with engineering application value for realizing high-stability and high-precision complex surface machining in five-axis laser engraving systems.