Synchronization-aware continuous trajectory planning for nozzle-based printing

In nozzle-based printing (NBP), precise synchronization between nozzle motion and auxiliary process behaviors is essential for deposition quality. This requirement becomes particularly challenging under short-segment trajectories, where geometric continuity, dynamic constraints, and motion-process synchronization are tightly coupled. Conventional trajectory planning methods typically treat motion and auxiliary process commands separately, which may cause motion interruptions, velocity fluctuations, and synchronization errors. Moreover, abrupt curvature transitions at trajectory corners can induce excessive centripetal acceleration and jerk, compromising motion smoothness and process stability. This study proposes a synchronization-aware trajectory planning framework for NBP based on unified constraint propagation. Rather than being treated independently, geometric continuity, curvature-constrained dynamics, and synchronization constraints are incorporated into the proposed planning framework. Geometry-continuous trajectory reconstruction, feasible velocity propagation, and synchronization-consistent process scheduling are jointly formulated to maintain propagation consistency and reliable motion-process coordination across short-segment trajectories. Simulations show that acceleration and jerk violations are effectively suppressed while maintaining stable velocity propagation. On an STM32F765 controller operating at 216 MHz, planning throughput averaged approximately 933 commands/s with a look-ahead window size of 10, indicating sufficient average planning capacity for the test trajectory. Pneumatic extrusion and inkjet printing experiments further demonstrate reliable synchronization under diverse deposition conditions. Material accumulation is mitigated, while position-synchronized triggering reduces the coefficient of variation and root-mean-square error of inter-droplet spacing by 93.1% and 86.9%, respectively.