The cross-motion invariant group and its application to kinematics

Bruno Vilhena Adorno, Philippe Fraisse

Research output: Contribution to journalArticlepeer-review


This article presents the cross-motion invariant group—CMI(3)—whose group operation is defined over unit dual quaternions such that rigid motions are cross-motion invariant; that is, the resultant translation does not depend on rotation and vice-versa. We present the main properties of CMI(3) and the differences between this group and the standard group Spin(3)⋉ℝ3 of unit dual quaternions, as well as the kinematic equations under a sequence of CMI(3) operations. Two numerical examples are presented in order to illustrate the main characteristics of CMI(3).
Original languageEnglish
Pages (from-to)1359-1378
Number of pages20
JournalIMA Journal of Mathematical Control and Information
Issue number4
Early online date11 Jul 2016
Publication statusPublished - 1 Dec 2017


  • cross-motion invariance
  • kinematics
  • rigid motion
  • unit dual quaternion


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