Optimal Control of a Magnetically Suspended Under Actuated Robot for Swing-Up Motion

This paper describes the analysis, design, and implementation of an under-actuated robot control system for swing up motion. The robot, called the “Mag-Foot” robot, uses permanent magnets to adhere to steel surfaces. This robot uses a novel tilting foot design for locomotion and can swing over small obstacles using an underactuated swinging motion. Since the robot can only adhere to the surface using limited (and relatively small) magnetic forces, it may fall down due to the reaction forces caused by the swing-up motion. To prevent failure, an optimal swing up trajectory is designed so that the maximum reaction force during the trajectory is minimized. The trajectories are parameterized using sigmoids and are determined by solving the dynamic equations as a 2 point boundary value problem. Finally, experiments are performed to evaluate the validity of this approach. The results of these experiments are promising and illustrate the validity of our approach.