Underactuated Trajectory-Tracking Control for Long-Exposure Photography

Controlling underactuated system is still a challenge because of their chaotic behavior. In this report, we apply optimal control techniques to a rotary inverted pendulum, also known as Furuta pendulum. The goal is to track optimized trajectories in order to do light-painting with the tip of the pendulum using long exposure photography. Therefore, we compare trajectory optimization using the collocation and single shooting method. By formulating the loss function with time dependent RBF activations, we were able to overcome limitations of naive loss functions. To compensate for modeling errors, the optimized trajectories are tracked on the real system through linear quadratic control.