Trajectory tracking wireless control of an asymmetric state constrained robotic pendulum based on electromagnetic actuators

This study shows the development of an automatic controller for a virtual robotic pendulum, designed in a computer assisted design software, with electromagnetic motion based on the application of a Barrier Lyapunov Function controller that considers asymmetric state restrictions in the device motion. The selected robotic device includes a magnetic pendulum that is composed by a spherical permanent magnet as its bob, which is prone to reaching a fixed state when it gets actuated by a set of two electromagnetic actuators placed at distal lateral positions. The proposed controller is aimed at preventing the pendulum from reaching positions where it can get stuck by considering physical state restrictions. An approximate model describes the relationship between the force that is generated between the permanent magnet and the electromagnets, which is used to define the level of actuation on the pendulum. The performance of the controller is evaluated in terms of its capacity to track the desired trajectories, along with its theoretical property of avoiding the system to reach the state restrictions. The proposed controller enforces the angular motion of the pendulum to track a smooth reference trajectory with errors smaller than 0.5 degrees after 7 seconds of numerical evaluation. The controller robustness forced the angular motion to stay over the reference thereafter.