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Abstract—This work demonstrates a novel approach to steering a magnetic swimming robot in two dimensions with a single pair of Maxwell coils. By leveraging the curvature of the magnetic field gradient, we achieve motion along two axes. This method allows us to control medical magnetic robots using only existing MRI technology, without requiring additional hard- ware or posing any additional risk to the patient. We implement a switching time optimization algorithm which generates a schedule of control inputs that direct the swimming robot to a goal location in the workspace. By alternating the direction of the magnetic field gradient produced by the single pair of coils per this schedule, we are able to move the swimmer to desired points in two dimensions. Finally, we demonstrate the feasibility of our approach with an experimental implementation on the millimeter scale and discuss future opportunities to expand this work to the microscale, as well as other control problems and real-world applications. 

Abstract—This work demonstrates a novel approach to steering a magnetic swimming robot in two dimensions with a single pair of Maxwell coils. By leveraging the curvature of the magnetic field gradient, we achieve motion along two axes. This method allows us to control medical magnetic robots using only existing MRI technology, without requiring additional hard- ware or posing any additional risk to the patient. We implement a switching time optimization algorithm which generates a schedule of control inputs that direct the swimming robot to a goal location in the workspace. By alternating the direction of the magnetic field gradient produced by the single pair of coils per this schedule, we are able to move the swimmer to desired points in two dimensions. Finally, we demonstrate the feasibility of our approach with an experimental implementation on the millimeter scale and discuss future opportunities to expand this work to the microscale, as well as other control problems and real-world applications.