Quaternion-based placement orientation trajectory smoothing method under the Domain of Admissible Orientation

In automated fiber placement (AFP), the abrupt variations of orientations affect layup quality and kinematic performance. This paper proposes a quaternion-based orientation smoothing method constrained by the Domain of Admissible Orientation (DAO) to solve this problem. The DAO is the orientation domain attached to each orientation and defined by the interference avoidance and layup process constraints. All the placement orientations are interpolated into a quaternion curve, and the quaternion curve is smoothed by minimizing its energy function. The energy function is presented in three-dimensional (3D) space, so to facilitate this minimization, the DAO is also transformed into 3D space to constrain the orientation. Then, a spline shortcut generation (SPSG) algorithm is proposed to geometric smooth the curve by generating a spline passing through all DAOs. After that, a Resampling method nonlinearly optimizes the energy function by sampling the curve parameters to redefine the layup orientation within the DAO. Experiments show that the method effectively smooths the orientation trajectory under layup constraints and improves the kinematic performance of APF machines. Graphical Abstract