Abstract
Smooth orientation planning is beneficial for the working performance and service life of industrial robots, keeping robots from violent impacts and shocks caused by discontinuous orientation planning. Nevertheless, the popular used quaternion interpolations can hardly guarantee C2 continuity for multiorientation interpolation. Aiming at the problem, an efficient quaternion interpolation methodology based on logarithmic quaternion was proposed. Quaternions of more than two key orientations were expressed in the exponential forms of quaternion. These four-dimensional quaternions in space S3, when logarithms were taken for them, could be converted to three-dimensional points in space R3 so that B-spline interpolation could be applied freely to interpolate. The core formulas that B-spline interpolated points were mapped to quaternion were founded since B-spline interpolated point vectors were decomposed to the product of unitized forms and exponents were taken for them. The proposed methodology made B-spline curve applicable to quaternion interpolation through dimension reduction and the high-order continuity of the B-spline curve remained when B-spline interpolated points were mapped to quaternions. The function for reversely finding control points of B-spline curve with zero curvature at endpoints was derived, which helped interpolation curve become smoother and sleeker. The validity and rationality of the principle were verified by the study case. For comparison, the study case was also analyzed by the popular quaternion interpolations, Spherical Linear Interpolation (SLERP) and Spherical and Quadrangle (SQUAD). The comparison results demonstrated the proposed methodology had higher smoothness than SLERP and SQUAD and thus would provide better protection for robot end-effector from violent impacts led by unreasonable multiorientation interpolation. It should be noted that the proposed methodology can be extended to multiorientation quaternion interpolation with higher continuity than the second order.
Highlights
Trajectory planning of industrial robot end-effector in workspace is a fundamental and important task
In order to compare with the proposed quaternion interpolation methodology, the most commonly used quaternion interpolation methods Spherical Linear Interpolation (SLERP) and Spherical and Quadrangle (SQUAD) described in the previous section are applied for the same case study above as well. e results of the research and analysis below reflect there are more or less deficiencies for these two methods to be used in multiorientation quaternion interpolation. e comparison and analysis mainly focus on these items: quaternion interpolation curve, rotation angle routing, angular velocity routing, angular acceleration routing, and rotating axis trajectory. e detailed comparison and analysis process are as follows
High-order continuous orientation planning is beneficial to working performance and service life of robot end-effector
Summary
Trajectory planning of industrial robot end-effector in workspace is a fundamental and important task. E trajectory planning of industrial robots is divided into position planning and orientation planning, while the valid and reasonable orientation planning is one of the foundational cores to ensure perfect working completion for the robot mechanical arm. Quaternion used to describe orientation has the following advantages: (1) avoid the phenomenon of locking universal joints when rotating; (2) higher calculation efficiency; (3) easy to provide smooth interpolation. At is, high-order interpolation methods in Cartesian space cannot be directly used for multiorientation interpolation of quaternion. Ough many scholars have been proposing kinds of quaternion orientation interpolations, the existing research for quaternion interpolation still needs to be developed further especially for smooth higher-order continuous interpolation between multiple orientations The algorithms of the three-dimensional vector in Cartesian space are not Mathematical Problems in Engineering suitable for quaternion directly [8], and interpolating theories in the three-dimensional vector space cannot be directly applied to quaternion orientation interpolation. at is, high-order interpolation methods in Cartesian space cannot be directly used for multiorientation interpolation of quaternion. ough many scholars have been proposing kinds of quaternion orientation interpolations, the existing research for quaternion interpolation still needs to be developed further especially for smooth higher-order continuous interpolation between multiple orientations
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
