  Despite their abundance in robotics and nature, underactuated systems remain
a challenge for control engineering. Trajectory optimization provides a
generally applicable solution, however its efficiency strongly depends on the
skill of the engineer to frame the problem in an optimizer-friendly way. This
paper proposes a procedure that automates such problem reformulation for a
class of tasks in which the desired trajectory is specified by a sequence of
waypoints. The approach is based on introducing auxiliary optimization
variables that represent waypoint activations. To validate the proposed method,
a letter drawing task is set up where shapes traced by the tip of a rotary
inverted pendulum are visualized using long exposure photography.
