  The Underactuated Lightweight Tensegrity Robotic Assistive Spine (ULTRA
Spine) project is an ongoing effort to develop a flexible, actuated backbone
for quadruped robots. In this work, model-predictive control is used to track a
trajectory in the robot's state space, in simulation. The state trajectory used
here corresponds to a bending motion of the spine, with translations and
rotations of the moving vertebrae. Two different controllers are presented in
this work: one that does not use a reference input but includes smoothing
constrants, and a second one that uses a reference input without smoothing. For
the smoothing controller, without reference inputs, the error converges to
zero, while the simpler-to-tune controller with an input reference shows small
errors but not complete convergence. It is expected that this controller will
converge as it is improved further.
