Magnetic actuation systems that utilize external electromagnetic coils present a promising approach for controlling untethered small-scale robots, notably in medical applications. However, these systems frequently experience actuation singularities at which robotic control over the agent is lost or severely diminished. Such singularities may lead to excessively large current or rapid current changes that significantly affect the robots’ stability in specific areas of the workspace. In order to effectively mitigate these actuation singularities, this paper introduces a closed-loop control method using a novel nested electromagnetic coil system, leveraging finite element analysis-based magnetic field data and a novel controller combining a singularity solver and optimal current control method. The electromagnetic system has 12 coils nested in four coil units, each having three concentric coils with different outer radius, surrounding a central workspace. We call the 12-coil system Variable Outer Radius Individually Addressable Coil Stacks (VORIACS). Here, we experimentally evaluate the method for closed-loop trajectory tracking of a soft magnetic capsule endoscope (PillCam™) and a permanent magnet robot inside the VORIACS system at different magnetic field orientations. The results demonstrate that the VORIACS system with a singularity solver reduces root mean square (RMS) position tracking errors of the PillCam™by 46% to 50% and orientation tracking errors by 41% to 42% compared to a standard 4-coil system. Moreover, the system can achieve a notable 60.73% reduction in RMS position error, with sub-millimeter precision control when controlling the permanent magnet robot. We further manipulate the PillCam™for tracking a medical application-inspired complex trajectory, showcasing the system’s potential in precise control of magnetic devices for medical use.
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