Offset Trajectory Planning of Robot End Effector and its Jerk with Curvature Theory

Abstract

Some situations that change the parameters of the kinematic structure may cause the robot end effector to deviate [Merlet [2005] Parallel Robots, Vol. 128 (Springer Science & Business Media, Germany)] from the desired trajectory. This effect is called the robustness of the robot by Merlet. One of the ways to correct the robustness is by updating the robot trajectory. The jerk vector of the robot end effector is the third-order positional variation of the TCP and defined as thus the time derivative of the acceleration vector. If there is a high curvature on the transition curve trajectory of robot, then there is a tangential jerk along the trajectory. In this study, the geometrically offset trajectory of the robot end effector from the current trajectory was obtained by using the curvature theory. The angular velocity and angular acceleration of the offset trajectory were calculated. An example of the main trajectory of robot end effector and its offset is given. Also, the jerk of the robot end effector of the offset trajectory was calculated according to the curvature of the trajectory surface in case of a jerk problem caused by a high curvature in the transition curve along the offset trajectory curve.

Surface family interpolating a common spherical indicatrix curve

“…When we look at the studies in the literature, we can see the curvature theory in robot trajectory motion. Some of these papers are [25][26][27][28][29][30].…”

The Quasi Parallel Curve of a Space Curve

“…In [5,6], the authors are define the Mannheim offsets and the involute-evolute offsets of ruled surfaces. Offset surfaces are also seen in other subjects, [7,8]. Parallel curves are important, for example, in numerically controlled machining, where a two-axis machine defines the shape of the cut made with a circular cutting tool.…”