Rotation (mathematics)
Related papers: 20
About
Rotation in mathematics refers to the transformation that moves points in a space around a fixed axis or origin while preserving distances and orientation. In robotics and AI, rotation is fundamental to representing and computing the orientation of rigid bodies, coordinate frames, robot joints, and end-effectors in three-dimensional space. It is expressed through multiple mathematical formalisms—including rotation matrices, Euler angles, quaternions, and axis-angle representations—each offering different trade-offs in computational efficiency, singularity avoidance, and interpolation smoothness. Rotation underpins virtually every aspect of robotic systems: solving hand-eye calibration, estimating 6D object pose for manipulation, designing parallel and concentric-tube manipulators, planning humanoid locomotion, and performing SLAM-based navigation. Algorithms for place recognition, image matching, and motion control all depend on accurate rotation estimation and comparison. Metrics for measuring distances between rotations guide optimization in pose graph SLAM and dynamic movement primitives for orientation. Understanding rotation mathematically matters because errors in orientation representation cascade into failures in grasping, navigation, and physical interaction. Choosing the right rotation parameterization—and computing it efficiently and robustly—is therefore a critical engineering decision across nearly all robotics and autonomous systems applications.
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Closed-form solution of absolute orientation using unit quaternions
Berthold K. P. Horn
Citations: 4109 • 1987
PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes
Xiang Yu, Tanner Schmidt, Venkatraman Narayanan, Dieter Fox
Citations: 2088 • 2018
Closed-form solution of absolute orientation using orthonormal matrices
Berthold K. P. Horn, Hugh M. Hilden, S. Negahdaripour
Citations: 1147 • 1988
Design and Control of Concentric-Tube Robots
Pierre E. Dupont, Jesse Lock, Brandon Itkowitz, Evan J. Butler
Citations: 733 • 2010
Metrics for 3D Rotations: Comparison and Analysis
Du Q. Huynh
Citations: 693 • 2009
Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB
Y.C. Shiu, S. Ahmad
Citations: 606 • 1989
Hand-Eye Calibration
Radu Horaud, Fadi Dornaika
Citations: 578 • 1995
Postural Stability of Biped Robots and the Foot-Rotation Indicator (FRI) Point
Ambarish Goswami
Citations: 567 • 1999
On the Parametrization of the Three-Dimensional Rotation Group
John Stuelpnagel
Citations: 479 • 1964
Evaluation of robotic training forces that either enhance or reduce error in chronic hemiparetic stroke survivors
James L. Patton, Mary Ellen Stoykov, Mark Kovic, Ferdinando A. Mussa-Ivaldi
Citations: 470 • 2005
Estimation of self-motion by optic flow processing in single visual interneurons
Holger G. Krapp, R Hengstenberg
Citations: 411 • 1996
Development of a new humanoid robot WABIAN-2
Yu Ogura, Hiroyuki Aikawa, K. Shimomura, Hideki Kondō, Akitoshi Morishima, Hun‐ok Lim, Atsuo Takanishi
Citations: 369 • 2006
Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications
Marko B. Popović, Ambarish Goswami, Hugh Herr
Citations: 324 • 2005
Catchment areas of panoramic snapshots in outdoor scenes
Jochen Zeil, Martin I. Hofmann, Javaan Chahl
Citations: 311 • 2003
Image Matching Using SIFT, SURF, BRIEF and ORB: Performance Comparison for Distorted Images
Ebrahim Karami, Siva Prasad, Mohamed Shehata
Citations: 304 • 2017
Neurons responding to whole-body motion in the primate hippocampus
Shane M. O’Mara, Edmund T. Rolls, Alain Berthoz, R.P. Kesner
Citations: 299 • 1994
Video Compass
Jana Košecká, Wei Zhang
Citations: 296 • 2002
Scan Context++: Structural Place Recognition Robust to Rotation and Lateral Variations in Urban Environments
Giseop Kim, Sun‐Wook Choi, Ayoung Kim
Citations: 288 • 2021
Innovative design for wheeled locomotion in rough terrain
Roland Siegwart, Pierre Lamon, T. Estier, Michel Lauria, R. Piguet
Citations: 276 • 2002
Aeromechanics of passive rotation in flapping flight
John P. Whitney, Robert J. Wood
Citations: 269 • 2010