Research on Attitude Interpolation and Tracking Control Based on Improved Orientation Vector SLERP Method

Abstract

SummaryIn order to make the end of the three-axis platform follow the control command and achieve stable control of the end attitude, an improved orientation vector spherical linear interpolation (SLERP) method is proposed for the requirements, which specifically handles the position of the gimbal lock, so that the platform can move smoothly around the gimbal lock position. A three-axis platform with a camera at the end is set up for the validity of the proposed algorithm. At first, an adaptive speed measurement method based on incremental encoder is introduced, which can automatically adapt to high and low speed, and estimate the ultra-low speed to realize the speed measurement of large dynamic range, and this is used for the motion control of the three-axis platform. Then, the SLERP method for the quaternion interpolation on the starting and ending attitudes represented in quaternion is introduced in detail, and it is continuously improved in response to its existing problems for the platform. Finally, an orientation vector SLERP method is proposed, which uses viscosity factor and rejection factor to adjust the algorithm near the platform’s gimbal lock position. A tracking experiment was designed using the red ball as the following target detected by the designed target tracking algorithm using the camera, which verified the effectiveness of the attitude tracking control based on the proposed improved orientation vector SLERP.

Algorithm to Generate Trajectories in a Robotic Arm Using an LCD Touch Screen to Help Physically Disabled People

“…The guide shows the results of position, velocity, and acceleration which are in the next tables, with velocity and acceleration graphs. With the coordinates x p , y p , the degrees of the second and third articulation are calculated with the function ( 9) and (10), and the degrees of the first articulation is calculated depending on the four conditions where the coordinate x p , y p are located. Secondly, the degrees are switched (q 2 , q 3 , α) in the closed interval (0, 1) or (−1, 0), and finally, the trajectory is calculated, with the current position encrypted and calculating the parameter ζ.…”

“…This topic has been improved throughout time, and nowadays, some related works with robotic assistance arms have been developed [6][7][8] to help people with physical disabilities to become more independent in daily life. According to the works in [9,10], the most commonly used methods to calculate trajectories in robotic arms are cubic polynomials [11], trapezoidal trajectory [12], and the Euler angles [10]. With these methods, it is possible to obtain smooth motions in the joint space, and these movements are predictable in the task space.…”

“…Finally, another method that is very popular to calculate the trajectory of a robotic arm is Euler angles. According to [10] which can cause malfunction of robots with systematic errors and lead to undesirable results because of the nonlinearity of the three Euler angles.…”

Collision-free trajectory planning for multi-robot simultaneous motion in preforms weaving

“…To obtain the joint coordinates of the robot by inverse kinematics, the orientation of each position needs to be interpolated after the positions of the collision-free path at the robot end are obtained by the AGG-RRT algorithm. There are three primary representations of the robot end orientation, namely, the Euler angle method, the rotation matrix method, and the quaternion method [25]. Among them, orientation interpolation based on the quaternion method is widely used because it has the advantages of avoiding the gimbal locking problem, simple operation, high efficiency, and smooth interpolation path [26].…”