Optimal Trajectory Tracking for a Magnetically Driven Microswimmer

Remotely actuated micro-scale swimming robots have received considerable research attention in recent years due to their promising potential for biomedical applications such as minimally invasive drug delivery. An important requirement for such applications is the ability of the robot to track a reference trajectory. In this work, a micro-robot driven by a torque induced through an applied magnetic field is considered. The spatial and rotational dynamics are formulated in terms of the body-frame torque, which is directly related to the magnetic field in the spatial frame. Controllability of the nonlinear system is then proven using the Lie algebra rank condition. Finally, an iterative linear quadratic tracking algorithm is presented and demonstrated on the system that can track arbitrary paths with both steady and time-varying velocities.