Robust Autonomous Control of a Magnetic Millirobot in In Vitro Cardiac Flow
Authors: Anuruddha Bhattacharjee, Xinhao Chen, Lamar O. Mair, Suraj Raval, Yancy Diaz-Mercado, Axel Krieger
Organizations: Laboratory for Computational Sensing and Robotics, Johns Hopkins University, Baltimore, MD 21218, USA. · Division of Magnetic Manipulation and Particle Research, Weinberg Medical Physics, Inc., Rockville, MD 20852, USA. · Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA.
Untethered magnetic millirobots offer significant potential for minimally invasive cardiac therapies; however, achieving reliable autonomous control in pulsatile cardiac flow remains challenging. This work presents a vision-guided control framework enabling precise autonomous navigation of a magnetic millirobot in an in vitro heart phantom under physiologically relevant flow conditions. The system integrates UNet-based localization, A* path planning, and a sliding mode controller with a disturbance observer (SMC-DOB) designed for multi-coil electromagnetic actuation. Although drag forces are estimated using steady-state CFD simulations, the controller compensates for transient pulsatile disturbances during closed-loop operation. In static fluid, the SMC-DOB achieved sub-millimeter accuracy (root-mean-square error, RMSE = 0.49 mm), outperforming PID and MPC baselines. Under moderate pulsatile flow (7 cm/s peak, 20 cP), it reduced RMSE by 37% and peak error by 2.4× compared to PID. It further maintained RMSE below 2 mm (0.27 body lengths) under elevated pulsatile flow (10 cm/s peak, 20 cP) and under low-viscosity conditions (4.3 cP, 7 cm/s peak), where baseline controllers exhibited unstable or failed tracking. These results demonstrate robust closed-loop magnetic control under time-varying cardiac flow disturbances and support the feasibility of autonomous millirobot navigation for targeted drug delivery.
Figures & tables
Fig. 1: Conceptual illustration of targeted cardiac drug delivery using magnetically actuated millirobot to treat infective endocarditis.
Fig. 2: (a) Experimental system: (i) Twelve-coil electromagnetic actuation setup surrounding the heart phantom, with a top-mounted camera for vision-based feedback control; (ii) Enlarged view of the heart phantom showing the internal flow circuit, where a peristaltic pump recreates right atrial and ventricular flow; (iii) Magnetic millirobot capsule containing an embedded permanent magnet, a drug chamber, and micro-holes for controlled drug release. (b) Finite element simulations of the electromagnetic system used to characterize magnetic flux density and field gradients under different coil activation patterns.
Fig. 3: (a) Computational mesh of the heart phantom model with two flow inlets and an outlet and (b) velocity magnitude contour plot for 4.3 cP fluid at the plane of robot control (i.e., z = 8 mm, where z = 0 mm is the plane passing through the centerline of the inlets and outlets) and 0.295 cm/s flow speed at each inlet.
Fig. 4: A* planned trajectory (yellow) within the user-defined canal mask with 5 mm wall clearance and 50% centerline bias. Start (blue star) and end (red star) points are connected through resampled waypoints (magenta), and the green spline indicates the user-selected canal boundary.
Controller
Viscosity
RMSE
P95
Max
(cP)
(mm)
(mm)
(mm)
PID
20
0.82±0.02
1.78±0.05
2.70±0.15
MPC
20
1.57±0.04
2.77±0.14
4.40±0.38
SMC-DOB
20
0.49±0.01
0.86±0.03
1.64±0.21
PID
4.3
— failed to complete trajectory
MPC
4.3
— failed to complete trajectory
TABLE I: Baseline trajectory tracking in static fluid. Values represent mean ± standard deviations across three trials per condition.
Fig. 5: Trajectory tracking under moderate flow conditions (20 cP; 7 cm/s peak speed). Representative video snapshots show the millirobot’s path, color gradient from start ( ti ) to end ( tf ), inside the heart phantom using (a) PID and (b) SMC–DOB controllers. (c) Tracking error over time. SMC–DOB maintained a tighter trajectory tracking and reduced error spikes compared to PID, demonstrating improved robustness to flow disturbances.
Fig. 6: Trajectory tracking under moderate flow (20 cP; 7 cm/s peak velocity) and elevated flow (20 cP; 10 cm/s peak velocity) using SMC-DOB controller. (a) Overlaid centroid positions of the millirobot for both conditions in comparison to the desired trajectory in the heart phantom. (b) Tracking error over time for both cases.
Fig. 7: Tracking performance of the SMC-DOB controller in 20 cP and 4.3 cP fluids under moderate pulsatile flow (7 cm/s peak speed). (a) Overlaid centroid trajectories showing increased oscillations in the low-viscosity case, particularly within the recirculation zone between inlet-1 and inlet-2. (b) Comparison of RMSE, P95, and maximum errors across three trials for both viscosities.
Fig. 8: Comparison of SMC-DOB and SMC (no DOB) in moderate flow (20 cP, 7 cm/s peak). Bars show RMSE, P95, and maximum tracking errors across three trials.
Department of Mechanical Engineering, University of Delaware, Newark 19716, USA. · Department of Animal and Food Sciences, University of Delaware, Newark 19716, USA. · School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA.