A Singularity Free Formulation of the Dynamically Equivalent Manipulator Mapping of Space Manipulators

This paper presents the singularity-free dynamic equations of the dynamically equivalent manipulator (DEM) of spacecraft-manipulator systems. The DEM is a fixed-base manipulator with the same dynamic properties as the corresponding free-floating spacecraftmanipulator system. The DEM consists of a spherical joint, representing the spacecraft and a robotic arm with the same joint types as the space manipulator. The spherical joint is normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spherical joint is non-Euclidean. We obtain a computationally efficient and singularity-free formulation of the DEM dynamics with the same complexity as the conventional Lagrangian approach. The dynamics are presented so that this can be implemented for simulation and control without extensive knowledge of the mathematical background.