Magnetic Trap Control in Electromagnetic Actuation: 3D Limits and 2D Realization

Magnetic microrobots (MMRs), driven by electromagnetic actuation systems, offer promise for biomedical uses such as targeted drug delivery and minimally invasive therapy, but their motion control is hindered by environmental and system constraints. We propose a magnetic trap strategy to guide MMRs. Earnshaw’s theorem confirms that stable 3D magnetic traps are impossible, so we constrain the Z-axis to form 2D traps in the X–Y plane. Experiments achieved control with errors below 2 mm at 1,024 of 1,331 test points, demonstrating feasibility under constraints. This work provides theoretical insight and practical, robust guidance for controlling MMRs with an electromagnetic actuation system in biomedical scenarios.