Conformal rotation vector

The conformal rotation vector, whose coordinates are also known as modified Rodrigues parameters or Wiener–Milenkovic parameters, is a three-dimensional vector representing a three-dimensional rotation or orientation. It is the stereographic projection of a versor (unit quaternion) onto the pure-imaginary hyperplane. It was first described by Thomas Wiener (1962),^[1] called the conformal rotation vector by Veljko Milenkovic (1982),^[2] and named the modified Rodrigues vector by Malcolm Shuster (1993).^[3] It is related to the Rodrigues vector first described by Olinde Rodrigues (1840) and called by Josiah Gibbs (1884) the vector semitangent of version.

• Milenkovic, Veljko (1982), "Coordinates Suitable for Angular Motion Synthesis in Robots", Robots VI: Conference Proceedings, Robots VI, Detroit, Michigan, 2-4 March 1982, Society of Manufacturing Engineers, pp. 407–420
• Shuster, Malcolm D. (1993), "A Survey of Attitude Representations" (PDF), The Journal of the Astronautical Sciences, 41 (4): 439–517
• Wiener, Thomas Freud (1962), Theoretical Analysis of Gimballess Inertial Reference Equipment Using Delta-Modulated Instruments (Ph.D. thesis), Massachusetts Institute of Technology, hdl:1721.1/14454

• Bauchau, Olivier A.; Trainelli, Lorenzo (2003), "The Vectorial Parameterization of Rotation" (PDF), Nonlinear Dynamics, 32: 71–92, doi:10.1023/A:1024265401576
• Bruccoleri, Christian; Mortari, Daniele (2006), "MRAD: Modified Rodrigues Vector Attitude Determination", The Journal of the Astronautical Sciences, 54 (3): 383–390, doi:10.1007/BF03256496
• Chung, Soon-Jo; Ahsun, Umair; Slotine, Jean-Jacques E. (2009), "Application of synchronization to formation flying spacecraft: Lagrangian approach", Journal of Guidance, Control, and Dynamics, 32 (2): 512–526, doi:10.2514/1.37261
• Crassidis, John L.; Markley, Francis Landis (1996), "Attitude estimation using modified Rodrigues parameters", Flight Mechanics/Estimation Theory Symposium, Greenbelt, Maryland, May 14-16, 1996
• Hurtado, John E. (2009), "Interior Parameters, Exterior Parameters, and a Cayley-Like Transform" (PDF), Journal of Guidance, Control, and Dynamics, 32 (2): 653–657, doi:10.2514/1.39624
• Karlgaard, Christopher D.; Schaub, Hanspeter (2010), "Nonsingular attitude filtering using modified Rodrigues parameters" (PDF), The Journal of the Astronautical Sciences, 57 (4): 777–791, doi:10.1007/BF03321529
• Marandi, S.R.; Modi, Vinod J. (1987), "A Preferred Coordinate System and the Associated Orientation Representation in Attitude Dynamics", Acta Astronautica, 15 (11): 833–843, doi:10.1016/0094-5765(87)90038-5
• Markley, Francis Landis; Crassidis, John L. (2014), Fundamentals of Spacecraft Attitude Determination and Control, Springer, doi:10.1007/978-1-4939-0802-8
• Schaub, Hanspeter; Junkins, John L. (1996), "Stereographic Orientation Parameters for Attitude Dynamics: A Generalization of the Rodrigues Parameters" (PDF), Journal of the Astronautical Sciences, 44 (1): 1–19
• Shoham, M.; Jen, F.-H. (1993), "On rotations and translations with application to robot manipulators", Advanced Robotics, 8 (2): 203–229, doi:10.1163/156855394x00464
• Terzakis, George; Lourakis, Manolis; Ait-Boudaoud, Djamel (2018), "Modified Rodrigues Parameters: An Efficient Representation of Orientation in 3D Vision and Graphics" (PDF), Journal of Mathematical Imaging and Vision, 60 (3): 422–442, doi:10.1007/s10851-017-0765-x
• Tsiotras, Panagiotis; Longuski, James M. (1995), "A New Parameterization of the Attitude Kinematics" (PDF), Journal of the Astronautical Sciences, 43 (3): 243–262

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