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, whose coordinates are called Rodrigues parameters or Euler–Rodrigues parameters.

Notes

1. Wiener 1962.
2. Milenkovic 1982.
3. Shuster 1993.

References

• 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

Further reading

• 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