A novel Fibonacci sequence-based motion profile

In contrast to polynomial smooth S-curves and typical sine curves, this article presents a revolutionary curve design technique based on the Fibonacci sequence. This technique removes discontinuities that arise during the transition between acceleration segments by adding several fixed-form smooth transition segments into the original curve while maintaining the piecewise structure of the traditional S-curve. The proposed motion profile aims to improve control stability, positioning accuracy, and current performance, while maintaining the performance advantages of a multisegment S-curve design. This article elaborates on the design principles of the modified motion profile and derives its analytical models for acceleration, jerk, velocity, and displacement. Furthermore, it provides complete mathematical formulas for possible profile variants under different parameter settings, as well as profile type selection criteria based on hardware parameters. To evaluate the feasibility of the proposed approach on real control systems and its advantages in accuracy and current behavior, simulations are conducted. This article uses the proposed modified motion profile and the traditional S-curve as motion commands, comparing the speed and acceleration responses under motor models with different damping ratios to verify its feasibility and performance advantages. Furthermore, we conducted experiments on a brushless DC motor and recorded data through the motor's built-in feedback. The results show that, compared to the traditional S-curve, the proposed modified motion profile improves positioning accuracy and current stability.