Balancing a 3D Inverted Pendulum using Remote Magnetic Manipulation

Jasan Zughaibi, Bradley J. Nelson, Michael Muehlebach

Abstract: Magnetic navigation offers wireless control over magnetic objects, which has important medical applications, such as targeted drug delivery and minimally invasive surgery. Magnetic navigation systems are categorized into systems using permanent magnets and systems based on electromagnets. Electromagnetic Navigation Systems (eMNSs) are believed to have a superior actuation bandwidth, facilitating trajectory tracking and disturbance rejection. This greatly expands the range of potential medical applications and includes even dynamic environments as encountered in cardiovascular interventions. To showcase the dynamic capabilities of eMNSs, we successfully stabilize a (non-magnetic) inverted pendulum on the tip of a magnetically driven arm. Our approach employs a model-based framework that leverages Lagrangian mechanics to capture the interaction between the mechanical dynamics and the magnetic field. Using system identification, we estimate unknown parameters, the actuation bandwidth, and characterize the system's nonlinearity. To explore the limits of electromagnetic navigation and evaluate its scalability, we characterize the electrical system dynamics and perform reference measurements on a clinical-scale eMNS, affirming that the proposed dynamic control methodologies effectively translate to larger coil configurations. A state-feedback controller stabilizes the inherently unstable pendulum, and an iterative learning control scheme enables accurate tracking of non-equilibrium trajectories. Furthermore, to understand structural limitations of our control strategy, we analyze the influence of magnetic field gradients on the motion of the system. To our knowledge, this is the first demonstration to stabilize a 3D inverted pendulum through electromagnetic navigation.