Quaternion and Euler-angle based approaches to the dynamical modeling, position control, and tracking control of a space robot

Space robots are vehicles that regularly undergo large-angle three-dimensional rotations. Euler-angle parameterizations of three-dimensional rotations contain singular points in the coordinate space that can cause failure of both dynamical models and controllers. These singularities are not present if the three-dimensional rotations are parameterized in terms of quaternions. This dissertation discusses the dynamical modeling and control of a space robot when using both Euler-angles and quaternions. The dynamical models are formulated from Lagrange's analytical theory of mechanics. One model is described in terms of generalized coordinates in which Euler-angles are utilized as rotational parameters and the other model is described in terms of non-generalized coordinates and utilizes quaternions as rotational parameters. Model-based position controller designs in terms of both generalized coordinates and non-generalized coordinates are then presented along with the stability analysis of the closed-loop systems and simulations. The trajectory tracking problem is also discussed. Techniques for interpolating a space robot's trajectory between a set of waypoints are included. Trajectory tracking control laws are further examined and simulations of the space robot tracking interpolated trajectories are presented.