Pitch Angle Control of a Magnetically Actuated Capsule Robot with Nonlinear FEA-based MPC and EKF Multisensory Fusion

TL;DR

This work addresses pitch regulation for magnetically actuated ingestible capsule robots navigating inclined gastric surfaces. It couples finite-element magnetostatic maps with a nonlinear, constrained model predictive controller and an EKF-based multisensory estimator to achieve robust pitch control using a four-coil actuation system. The approach yields a 3–5× reduction in settling time and stable closed-loop regulation under intermittent imaging (1 Hz camera updates) when fused with onboard IMU data, demonstrating scalability for docking and multi-DOF locomotion. The practical impact lies in enabling stable, contact-rich interactions in the GI tract with reduced imaging requirements, paving the way for advanced diagnostic and therapeutic ultrasound-like tasks inside the stomach.

Abstract

Magnetically actuated capsule robots promise minimally invasive diagnosis and therapy in the gastrointestinal (GI) tract, but existing systems largely neglect control of capsule pitch, a degree of freedom critical for contact-rich interaction with inclined gastric walls. This paper presents a nonlinear, model-based framework for magnetic pitch control of an ingestible capsule robot actuated by a four-coil electromagnetic array. Angle-dependent magnetic forces and torques acting on embedded permanent magnets are characterized using three-dimensional finite-element simulations and embedded as lookup tables in a control-oriented rigid-body pitching model with rolling contact and actuator dynamics. A constrained model predictive controller (MPC) is designed to regulate pitch while respecting hardware-imposed current and slew-rate limits. Experiments on a compliant stomach-inspired surface demonstrate robust pitch reorientation from both horizontal and upright configurations, achieving about three to five times faster settling and reduced oscillatory motion than on-off control. Furthermore, an extended Kalman filter (EKF) fusing inertial sensing with intermittent visual measurements enables stable closed-loop control when the camera update rate is reduced from 30 Hz to 1 Hz, emulating clinically realistic imaging constraints. These results establish finite-element-informed MPC with sensor fusion as a scalable strategy for pitch regulation, controlled docking, and future multi-degree-of-freedom capsule locomotion.

Figures (9)

• Figure 1: System overview of magnetically actuated pitch control for an ingestible capsule robot. (a) Four external electromagnetic coils generate controlled magnetic fields that interact with internal permanent magnets. (b) The magnetic field produce torques that regulate capsule pitch as it rolls on a soft stomach phantom to enable docking on inclined gastric walls. (c) State estimation through fusion of onboard inertial sensing and downsampled camera-based angle measurements, which emulates low-rate X-ray.
• Figure 2: Combined hardware geometry of the capsule robot and electromagnetic coil assembly. (a): Capsule dimensions and internal magnet placement, including colored fiducial rings used for vision-based pitch estimation. (b): Geometry of a single electromagnetic coil with conical iron core. (c) Front-view of the four-coil arrangement defining the operating workspace.
• Figure 3: Embedded electronics and inertial sensing architecture. (a) Block diagram of the internal electronics, including the BLE-enabled microcontroller, IMU, level shifter, regulators, and antenna. (b) PCB layouts and dimensions of the master and slave boards. (c) Assembled PCBs and 3D model illustrating integration within the capsule body. (d) Data flow and software architecture for sensor fusion and feedback control, showing IMU and camera data fused via an EKF and supplied to the MPC controller.
• Figure 4: Finite-element magnetic actuation characterization and corresponding free-body diagram for pitch dynamics modeling. (a) Example ANSYS Maxwell magnetostatic solution illustrating the coil–core assemblies, a single internal magnet, and the reported magnetic force components $(F_x,F_y,F_z)$ (newtons) and magnetic torque $T$ (newton-meters) for the vertical actuation mode at $1~\mathrm{A}$ and $\theta=30^\circ$. The near-zero $F_y$ component is consistent with the planar modeling assumption. (b) Free-body diagram of the capsule during pitch motion. Each internal magnet experiences a force $(F_{kx},F_{kz})$ and a direct magnetic torque $\tau_k$ due to the external electromagnetic field. The force and torque quantities obtained from the finite-element simulations in (a) are used to populate the magnetic actuation terms in the pitching dynamics, with the total magnetic moment about the rolling contact point given by the sum of direct torques and $r \times F$ contributions from both magnets.
• Figure 5: Sensing and real-time control architecture. PC 1 performs vision-based pitch estimation (and IMU acquisition/fusion when enabled) and sends the pitch estimate to PC 2 via TCP/IP. PC 2 runs LabVIEW, calls the MPC via a MATLAB Script Node, and drives each coil through a separate NI 9505 current-control module.