Estimation of Cartesian Space Robot Trajectories Using Unit Quaternion Space

Smooth orientation planning has an important influence on the working quality and service life as for industrial robot. Based on the logarithmic quaternion, a compact method to map a spline curve from Cartesian space to quaternion space is proposed, and consequently the multi-orientation smooth interpolation of quaternion is realized. Combining with the relevant example case, the detailed method and steps of multi-orientation interpolation are introduced for mapping Hermite spline curve into quaternion space, and the validity of the principle is verified by using the example case. The present multi-orientation smooth interpolation of quaternion has the characteristics of simple construction, easy implementation and intuitive understanding. The method is not only applicable to multi-orientation interpolation of quaternion with Hermite spline curve, but also can extended to the spline curves such as Bezier spline and B-spline.

Download Full-text

Generalization of orientational motion in unit quaternion space

2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids) ◽

10.1109/humanoids.2016.7803366 ◽

2016 ◽

Cited By ~ 1

Author(s):

Aljaz Kramberger ◽

Andrej Gams ◽

Bojan Nemec ◽

Ales Ude

Keyword(s):

Unit Quaternion ◽

Quaternion Space ◽

Orientational Motion

Download Full-text

Second-Order Geometric Sliding Mode Attitude Observer with Application to Quadrotor on a Test Bench

Mathematical Problems in Engineering ◽

10.1155/2013/328974 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

Honglei An ◽

Jie Li ◽

Jian Wang ◽

Jianwen Wang ◽

Hongxu Ma

Keyword(s):

Angular Velocity ◽

Sliding Mode ◽

Experimental Studies ◽

Second Order ◽

Velocity Estimation ◽

Sliding Mode Observer ◽

Group Method ◽

Test Bed ◽

Unit Quaternion ◽

Quaternion Space

A sliding mode observer design framework is proposed based on the Lie group method of numerical integration on manifolds, and a Second-Order Geometric Sliding Mode Attitude Observer (SOGSMAO) is designed for angular velocity estimation of quadrotor attitude. The algorithm constructs feedback in the angular velocity space and the space of equivalent Lie algebra of unit quaternion space, respectively. It avoids not only the complexity of constructing feedback in unit quaternion space but also the process of mandatory rescaling which is seen to deteriorate the accuracy of the angular velocity estimates during sliding. The performance of SOGSMAO is compared with traditional quaternion based sliding mode observer in which multiplicative quaternion correction is used and the results show that SOGSMAO gains better tracking performance. Then SOGSMAO is realized on a test bed and the effectiveness of the observer algorithm is verified by experimental studies.

Download Full-text