Open AccessA combined polar and Cartesian piecewise trajectory generation and analysis of a robotic arm
Author(s) -
Dupac Mihai
Publication year - 2019
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1049
Subject(s) - frenet–serret formulas , cartesian coordinate system , trajectory , piecewise , kinematics , polar coordinate system , robotic arm , mathematics , mathematical analysis , geometry , physics , computer science , classical mechanics , artificial intelligence , curvature , astronomy
In this paper, a combined polar‐Cartesian approach to generate a smooth trajectory of a robotic arm along priori defined via‐points is presented. Due to the characteristics/geometry of the robotic arm, cylindrical coordinates are associated with the trajectory of motion. Possible trajectories representing the system dynamics are generated by mix‐matching higher order polar piecewise polynomials used to devise the radial trajectory and Cartesian piecewise polynomials used to calculate the related height in a normal plane unfolded along the radial trajectory of the motion. To describe the kinematic properties of the end effector, a moving noninertial orthonormal Frenet frame is considered. Using the Frenet frame, the components of the velocity and acceleration along the frame unit vectors are calculated. Numerical simulations are performed for two different configurations in order to validate the approach.