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Underactuated waypoint trajectory optimization for light painting photography

Christian Eilers; Jonas Eschmann; Robin Menzenbach; Boris Belousov; Fabio Muratore; Jan Peters
In: International Conference on Robotics and Automation. IEEE International Conference on Robotics and Automation (ICRA-2020), May 31 - August 31, Virtual, Pages 1505-1510, IEEE, 2020.


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.

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