Numerical Method Using Homotopic Iterative Functions Based on the via Point for the Joint-Space Trajectory Generation

In recent years, many methods have been developed to calculate the trajectory of a robotic arm in the joint-space. These methods have many advantages, such as a soft motion and infinite jerk avoidance. Nevertheless, these methods present other problems that must be avoided, such as an unnatural motion while generating the trajectory and producing unsafe planning. In this sense, this work presents a numerical method named iterative optimal solution trajectory via (zeta)(v)-homotopy former (IOSTV (zeta)(v)-HF). It is proposed to reduce and avoid oscillation while obtaining trajectories with different shapes to perform better, reliable, smooth, and long-life robotic systems. The algorithm with the proposed method is described, and examples of the trajectories obtained with different parameters are presented. In addition, these were mapped and a trajectory with a continuous velocity and a reduced oscillation and another trajectory with the same restrictions but with a continuous acceleration and zero oscillations were shown; the method is versatile since it allows for choosing and finding the most optimal solutions according to the application. Finally, the article ends with a critical discussion of the experimental results.