Model Predictive Control with Reference Learning for Soft Robotic Intracranial Pressure Waveform Modulation

Abstract

This paper introduces a learning-based control framework for a soft robotic actuator system designed to modulate intracranial pressure (ICP) waveforms, which is essential for studying cerebrospinal fluid dynamics and pathological processes underlying neurological disorders. A two-layer framework is proposed to safely achieve a desired ICP waveform modulation. First, a model predictive controller (MPC) with a disturbance observer is used for offset-free tracking of the system's motor position reference trajectory under safety constraints. Second, to address the unknown nonlinear dependence of ICP on the motor position, we employ a Bayesian optimization (BO) algorithm used for online learning of a motor position reference trajectory that yields the desired ICP modulation. The framework is experimentally validated using a test bench with a brain phantom that replicates realistic ICP dynamics in vitro. Compared to a previously employed proportional-integral-derivative controller, the MPC reduces mean and maximum motor position reference tracking errors by 83 % and 73 %, respectively. In less than 20 iterations, the BO algorithm learns a motor position reference trajectory that yields an ICP waveform with the desired mean and amplitude.

Figures (6)

• Figure 1: Schematic overview of the experimental hardware setup. The soft robotic actuator system has been developed in Fluerenbrock2024TBME and is used for intracranial pressure (ICP) modulation. The mechatronic test bench has been developed in Castelar2022 and is used for the physical replication of ICP waveforms. The balloon catheter of the soft robotic actuator system is inserted into the brain phantom of the test bench to enable ICP waveform modulation. The pressure measurements of the brain phantom and the electrocardiogram (ECG) of the cerebrospinal fluid (CSF) model used for simulating physiological ICP waveforms are fed back to the soft robotic actuator system.
• Figure 2: Visualization of the periodically triggered and pulse-shaped reference trajectory for the motor position of the soft robotic actuator system. The delay and magnitude (red arrows) are tunable parameters that are determined via Bayesian optimization. The next pulse can only be triggered by the detection of an QRS complex in the electrocardiogram after the previous pulse has been completed. In between pulses, the motor is regulated to its baseline position (gray line).
• Figure 3: Reference tracking experiment: Comparison of the baseline proportional-integral-derivative (PID) controller, the model predictive controller (MPC) without disturbance observer, and the MPC with disturbance observer (offset-free MPC). The upper panels show the motor position, whereas the lower panels show the motor current. Controllers were tested with the same 60 reference trajectory, similar to Figure \ref{['fig:reference']} but without negative magnitudes.
• Figure 4: Waveform modulation experiments at 90: Results of the Bayesian optimization (BO) algorithm used for tuning the delay and magnitude parameter of the controller's motor position reference trajectory. The top panels show the posterior mean of the Gaussian process (GP), the middle panels show the posterior variance of the GP, and the bottom panels show the acquisition function based on the upper confidence bound in \ref{['eq:bo_acq_fun']}. Red dots represent evaluated parameters, whereas orange crosses represent new parameter candidates computed by maximizing the acquisition function. The $n=5$ samples in the leftmost plots represent the randomly sampled parameters used for initialization of the BO algorithm.
• Figure 5: Waveform modulation experiment at 90: Results of the actuation-based intracranial pressure (ICP) waveform modulation during the first six iterations of the Bayesian optimization (BO) algorithm used for automated reference learning. The upper panel shows the ICP inside the brain phantom of the test bench, whereas the lower panel shows the motor position of the soft robotic actuator system. Changes in the parameterization $\theta$ of the reference trajectory, i.e., BO iterations, are highlighted by vertical dashed lines. A minimum of five cycles were performed per parameter setting.