A Novel Inverse Kinematics Solution of Calligraphy Writing Robot Based on Quaternion

In robot calligraphy writing, the accuracy requirement for adjusting the writing brush’s posture is extremely high, especially when reproducing complex calligraphy characters. However, due to the complex solution of inverse kinematics and the existence of multiple solutions for pose and position, the robustness of the robot is compromised, resulting in suboptimal copying performance. In this study, quaternions are employed to represent the robot’s pose, and an improved particle swarm optimization algorithm (I-PSO) is proposed. Through the error analysis experiments, it is proved that the convergence speed, statistics, p-value, and convergence accuracy of I-PSO algorithm are maximally improved by 80.70%, 60.00%, 58.33%, and 34.56% compared with genetic algorithm (GA), simulated annealing algorithm (SA), and F-PSO algorithm. Furthermore, comparative experimental analysis on Wang Xizhi’s Chinese character shows that the balance degree ( \({I}_{b}\) ), local structure ratio similarity ( \({I}_{{S}_{1}}\) ) and relative structure ratio similarity ( \({I}_{{S}_{2}}\) ) achieved by the I-PSO algorithm are superior to those of traditional algorithms, reaching 0.81, 0.79 and 0.81 respectively. The results indicate that the inverse kinematics solution method proposed in this study enhances the ability of the writing robot to adjust its posture efficiently and accurately, enabling precise reproduction of complex Chinese characters, especially those involving turning strokes.