Document Type : Research Paper

Authors

• Hadiseh Babazadeh ¹
• Parisa Nabati ²
• Hadi Pirmohamad ²

¹ Department of Electrical Engineering, Urmia University of Technology, Urmia, Iran

² Department of Science, Urmia University of Technology, Urmia, Iran

Abstract

This paper presents a numerical stochastic kinematic analysis of the velocity response of a six-degree-of-freedom PUMA560 robotic manipulator under white/colored noise. Stochastic disturbances are injected directly into the joint motion functions, and the resulting linear/angular velocities of the end effector are computed using the manipulator Jacobian. White noise is modeled as the derivative of Brownian motion, while colored noise is represented by Ornstein–Uhlenbeck processes. Numerical simulations are conducted using first-, third-, and fifth-order polynomial joint trajectories, and noise effects are quantitatively evaluated using the Root-Mean-Square-Error (RMSE). The results demonstrate that higher-order joint trajectories amplify noise-induced deviations in end-effector velocity. Comparative analysis shows that the manipulator exhibits greater robustness to colored noise than to white noise. Additionally, variations in link lengths indicate that linear velocity sensitivity increases with link length, whereas angular velocity remains largely unaffected. These findings provide insights for improving manipulator design and velocity accuracy under stochastic disturbances.

Keywords

• Jacobian
• kinematics
• differential equations
• angular velocity
• noise