Trajectory planning is pivotal in intelligent robotic calligraphy, impacting both the process and presentation quality of calligraphic works. Existing methods predominantly focus on two-dimensional trajectories, which inadequately capture the nuances of brush calligraphy. How to obtain the three-dimensional spatial writing trajectories according to the writing rules of brush calligraphy as well as the trajectory state, velocity and acceleration, has become an urgent issue to be addressed. This paper introduces a three-dimensional spatial trajectory planning model tailored to brush calligraphy rules. By designing a spatial trajectory planning algorithm and modeling stroke trajectory states, we account for variations in velocity and acceleration. Experimental results demonstrate certain performance, with smooth position, continuous velocity, and stable acceleration of each stage ensuring seamless writing operations by the robotic end-effector. Compared to other methods, our approach significantly enhances the fidelity of calligraphic reproduction especially in basic strokes. Moreover, our proposed model can conform to brush stroke dynamics.
Guo et al. (2026) studied this question.