Singularity-Free Approximate Waypoint Tracking Controller for Underactuated Magnetic Robots

Abstract

Magnetic robots use external magnetic fields to draw energy, generating steering capabilities crucial for minimally invasive surgeries and enabling next generation untethered surgical tool miniaturization. However, accurate control is challenging due to configuration-dependent singularities in the manipulation Jacobian, which can cause unsafe behavior with standard controls. We analyze the nonlinear nature of magnetic fields to understand singularity-free control limits without adding more magnetic actuators, which increases bulk and cost. Using Chow’s Theorem, we study the motion feasibility of a single magnetic robot moving in a plane, powered by stationary electromagnets. We determine the degree of nonholonomy for an underactuated case and show that any desired motion in the state-space can be approximated with more complex controls. We deploy an approximate-tracking controller to steer a magnetic robot between any two points in the state-space, avoiding singularities. Simulations show a 0.82 mm RMS positional tracking error for an 8 mm long cylindrical magnetic tool using our method.