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A novel Fibonacci sequence-based motion profile.

Wu-Sung Yao1, Yu-Chuan Tseng1, Jun-Hao Hu1

  • 1Department of Mechatronics Engineering, National Kaohsiung University of Science and Technology, Kaohsiung City, Taiwan.

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|March 7, 2026
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Summary
This summary is machine-generated.

This study introduces a novel Fibonacci sequence-based motion profile that enhances control stability and positioning accuracy. The new design eliminates discontinuities in acceleration, improving performance over traditional S-curves for robotic systems.

Keywords:
Fibonacci sequenceS-curvejerk-continuous planningjerk-limited motionmotion control

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Area of Science:

  • Robotics and Control Systems
  • Applied Mathematics
  • Mechanical Engineering

Background:

  • Traditional S-curves and sine curves often exhibit discontinuities during acceleration transitions.
  • These discontinuities can negatively impact control stability, positioning accuracy, and current performance in motion control systems.
  • Existing motion profiles may not fully leverage mathematical sequences for optimized smooth transitions.

Purpose of the Study:

  • To present a novel motion profile design based on the Fibonacci sequence.
  • To eliminate discontinuities in acceleration segments while preserving the piecewise structure of S-curves.
  • To enhance control stability, positioning accuracy, and current performance in motion control applications.

Main Methods:

  • Developed a modified motion profile by incorporating Fibonacci sequence-based smooth transition segments.
  • Derived analytical models for acceleration, jerk, velocity, and displacement of the proposed profile.
  • Conducted simulations comparing the modified profile with traditional S-curves using motor models with varying damping ratios.
  • Performed experimental validation on a brushless DC motor system.

Main Results:

  • The Fibonacci-based motion profile effectively removes discontinuities between acceleration segments.
  • Simulations and experiments demonstrated improved positioning accuracy compared to traditional S-curves.
  • The proposed profile showed enhanced current stability and overall performance in motion control tasks.
  • Analytical models and selection criteria for profile variants were established.

Conclusions:

  • The Fibonacci sequence-based motion profile offers a significant improvement over traditional S-curves.
  • This novel approach enhances precision and stability in motion control systems, particularly for applications requiring high accuracy.
  • The method is validated through simulations and experimental results on a brushless DC motor.