Model Predictive Control for Magnetically-Actuated Cellbots

Abstract

This paper presents a control framework for magnetically actuated cellbots, which combines Model Predictive Control (MPC) with Gaussian Processes (GPs) as a disturbance estimator for precise trajectory tracking. To address the challenges posed by unmodeled dynamics, we integrate data-driven modeling with model-based control to accurately track desired trajectories using relatively small data. To the best of our knowledge, this is the first work to integrate data-driven modeling with model-based control for the magnetic actuation of cellbots. The GP effectively learns and predicts unmodeled disturbances, providing uncertainty bounds as well. We validate our method through experiments with cellbots, demonstrating improved trajectory tracking accuracy.

Figures (6)

• Figure 1: Overview of the Control Framework: Initially, experimental data is collected offline to estimate $\hat{a}_0$ and train the GP for $\hat{\bm{D}}$. These are then used in an MPC framework to model the system dynamics.
• Figure 2: (a) Microscopy photo of a cellbot, showing the $\mu$bots (black disks) inside the cell; (b)The experimental setup used for cellbot control.
• Figure 3: Comparison of the learned model, actual data, and the linear model with GP disturbance. The top and bottom graphs correspond to the x and y directions, respectively. The inset plots zoom in on the time range between 40 and 45 seconds. The blue, red and green curves represent the learned model, linear model without GP and the actual velocity($\mu m/s$), respectively. The light and dark gray bands indicate two standard deviations (65%) of uncertainty and three standard deviations (95%).
• Figure 4: Model predictions after the circular (a) and iterative training (b), respectively. The top and bottom graphs correspond to the x and y directions, respectively. Iterative training noticeably enhances the model's accuracy. We used the same color coding as in Fig \ref{['fig:traindata']}.
• Figure 5: Trajectories after circular (a) and iterative (b) training. In (b), the inset zoom in on the lower left shows a closer look at the differences in the trajectories.