Figure 1: A spacecraft with three thrusters aligned with the principal axes but offset from the center of mass. These three thrusters are sufficient to make the spacecraft locally kinematically controllable on SE(3), with decoupling velocities being translation along the x-axis and rotation about axes aligned with y and z but offset from the center of mass.
Figure 2: Any configuration in obstacle-free SE(3) can be reached by
a sequence of two rotations (to point the spacecraft at the goal), a
translation, and three rotations (ZYZ Euler angles) to achieve the desired
final orientation.
Figure 3: The kinematic path can then be time-scaled to yield a time-optimal
trajectory along the path. For thruster limits of 100 N, the time-optimal
trajectory takes 19.16 seconds and the thruster actuations are shown in the
figure.