Time-optimal path parameterization planning for automatic fiber placement based on reachability quadratic analysis

Automated fiber placement technology can be used to improve the rigidity and load-bearing capacity of hyperbolic surface components in industrial fields such as automobiles, ships, and aviation. However, because multiple layers of fibers need to be continuously placed to meet usage requirements, the production efficiency of fiber placement is low. To achieve time-optimal path parameterization (TOPP), this study optimizes the path discrete point quantity and time parameters of TOPP in order to maximize time optimization. Firstly, in order to ensure the accuracy of surface fiber placement, a trajectory error calculation method based on third-order conical spiral approximation is introduced to constrain trajectory accuracy. Additionally, the fiber placement path normal change that may affect the stability of fiber placement force is also constrained. The maximum trajectory error and maximum surface normal change are used as constraints for the maximum step length of the path discrete points to reduce redundant points. Secondly, in response to the non-optimization problem of time parameters in TOPP, a new TOPP approach based on reachability quadratic analysis is proposed. Through coarse searching for discrete points, time parameters that better fulfill the characteristics of time optimization are solved and fitted by a polynomial. Finally, the grid points are densified for velocity planning. This study conducted simulation experiments on hyperbolic surface placement with a 6-RUS as the experimental object. The results show that under the same placement path, the traditional method Path1 takes a total of 2.05 s, while Path2 takes a total of 2.29 s. The proposed method in this study takes Path1 1.55 s and Path2 1.76 s, respectively, reducing the time by 0.5 and 0.53 s compared to the traditional method.