Robust kinematic control of manipulator robots using dual quaternion representation

In this paper, we study the problem of rational motion interpolation under kinematic constraints of spatial SS open chains. The objective is to synthesize a smooth rational motion that interpolates a given set of end effector positions and satisfies the kinematic constraints imposed by spatial SS open chains. The kinematic constraints under consideration define a constraint manifold representing all the positions available to the end effector. By choosing dual quaternion representation for the displacement of the end effector, the problem is reduced to designing a smooth curve in the space of dual quaternions that is constrained to lie inside the constraint manifold of the spatial SS open chain. An iterative numerical algorithm is presented that solves this problem effectively. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational planar and spherical motions for open and closed chains under kinematic constraints.

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Automatic Fairing of Two-Parameter Rational B-Spline Motion

Journal of Mechanical Design ◽

10.1115/1.2803253 ◽

2007 ◽

Vol 130 (1) ◽

Cited By ~ 5

Author(s):

Anurag Purwar ◽

Xiaoyi Chi ◽

Qiaode Jeffrey Ge

Keyword(s):

Tool Path ◽

Fine Tuning ◽

Camera Motion ◽

Dual Quaternion ◽

B Spline ◽

Computer Aided ◽

Spatial Displacements ◽

Five Axis ◽

Quaternion Representation ◽

Two Parameter

This paper deals with the problem of automatic fairing (or fine-tuning) of two-parameter rational B-spline spherical and spatial motions. The results presented in this paper extend the previous results on fine-tuning of one-parameter rational B-spline motions. A dual quaternion representation of spatial displacements is employed and the problem of fairing two-parameter motions is studied as a surface fairing problem in the space of dual quaternions. By combining surface fairing techniques from the field of computer aided geometric design with the computer aided synthesis of freeform rational motions, smoother (C3 continuous) two-parameter rational B-spline motions are generated. Several examples are presented to illustrate the effectiveness of the proposed method. Techniques for motion smoothing have important applications in the Cartesian motion planning, camera motion synthesis, and spatial navigation in virtual reality systems. In particular, smoother two-parameter freeform motions have applications in the development of a kinematic based approach to geometric shape design and in five-axis NC tool path planning.

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Automatic Fairing of Two-Parameter Rational B-Spline Motion

Volume 2: 31st Design Automation Conference, Parts A and B ◽

10.1115/detc2005-85458 ◽

2005 ◽

Author(s):

Anurag Purwar ◽

Xiaoyi Chi ◽

Qiaode Jeffrey Ge

Keyword(s):

Spatial Navigation ◽

Fine Tuning ◽

Camera Motion ◽

Dual Quaternion ◽

Computer Aided Geometric Design ◽

B Spline ◽

Computer Aided ◽

Spatial Displacements ◽

Quaternion Representation ◽

Two Parameter

This paper deals with the problem of automatic fairing of two-parameter B-Spline spherical and spatial motions. The concept of two-parameter freeform motions brings together the notion of the analytically determined two-parameter motions in Theoretical Kinematics and the concept of freeform surfaces in the field of Computer Aided Geometric Design (CAGD). A dual quaternion representation of spatial displacements is used and the problem of fairing two-parameter motions is studied as a surface fairing problem in the space of dual quaternions. By combining the latest results in surface fairing from the field of CAGD and computer aided synthesis of freeform rational motions, smoother (C3 continuous) two-parameter rational B-Spline motions are generated. The results presented in this paper are extensions of previous results on fine-tuning of one-parameter B-spline motions. The problem of motion smoothing has important applications in the Cartesian motion planning, camera motion synthesis, spatial navigation in visualization, and virtual reality systems. Several examples are presented to illustrate the effectiveness of the proposed method.

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