Trajectory planning of a 5 DOF collaborative robot using numerical methods with quaternions

Abstract

This work presents a quaternion-based methodology for trajectory control of a 5-degree-of-freedom (DOF) collaborative robot. The mathematical representation of quaternions and their application in trajectory interpolation are addressed, avoiding issues such as singularities and discontinuities found in other representations like Euler angles and rotation matrices. The interpolation method with a 4-1-4 parabolic blend is implemented, prioritizing position and velocity continuity while maintaining minimal acceleration variation. The method is validated through simulations in MATLAB/Simulink, comparing the results obtained using homogeneous transformation matrices and quaternions. The results show that using quaternions reduces trajectory tracking errors and optimizes the system's computational performance. Finally, the numerical computation results of both methods are discussed.