Underactuated Waypoint Trajectory Optimization for Light Painting Photography
This work addresses control engineering difficulties for underactuated systems, but it is incremental as it focuses on automating problem reformulation for a specific class of tasks.
The paper tackles the challenge of automating trajectory optimization for underactuated systems by proposing a method that reformulates waypoint-based tasks using auxiliary variables, validated through a letter drawing experiment with a rotary inverted pendulum.
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.