Quaternion Based Free-Floating Space Manipulator Dynamics Modeling Using the Dynamically Equivalent Manipulator Approach El¨ zbieta Jarz˛ ebowska and Marcin Klak Abstract The paper presents a dynamics modeling method dedicated to free- floating spacecraft, e.g. manipulators, based on a modified Dynamically Equivalent Manipulator (DEM) method. DEM enables dynamics modeling of space manip- ulators by their suitable substitution by ground fixed manipulator models. This provides attractive modeling and control design tools. It enables carrying tests and experiments for space manipulators in Earth labs multiple times what contributes to mission cost and failure reductions. Originally, DEM is developed in Euler angles. The paper contribution is the modification of DEM to present space manipulators dynamics in quaternion parameterization. Quaternions do not share Euler angles’ drawbacks and they are computationally more efficient, but their implementation reveals challenges due to nonlinear relations for space manipulator angular velocities and a constraint equation they add to its dynamics. The motivation for DEM modification is to make dynamic models suitable for description of arbitrary space manipulator maneuvers and missions like debris removal, servicing, space mining and on-orbit docking and assemblies. The development of DEM in quaternion parameterization is illustrated by an example of space manipulator attitude dynamics and reorientation control. Keywords Dynamically equivalent manipulator · Quaternion-based dynamics · Space robot attitude · Free-floating maneuvers E. Jarz˛ ebowska () Warsaw University of Technology, Warsaw, Poland e-mail: elajarz@meil.pw.edu.pl M. Klak Warsaw University of Technology, Warsaw, Poland GMV Innovating Solutions, Warsaw, Poland © Springer Nature Switzerland AG 2021 J. Awrejcewicz (ed.), Perspectives in Dynamical Systems III: Control and Stability, Springer Proceedings in Mathematics & Statistics 364, https://doi.org/10.1007/978-3-030-77314-4_6 71