Robust 3-D Path Following Control Framework for Magnetic Helical Millirobots Subject to Fluid Flow and Input Saturation.

Precise trajectory control is imperative to ensure the safety and efficacy of in vivo therapy employing the magnetic helical millirobots. However, achieving accurate 3-D path following of helical millirobots under fluid flow conditions remains challenging due to the presence of the lumped disturbances, encompassing complex fluid dynamics and input frequency saturation. This study proposes a robust 3-D path following control framework that combines a disturbance observer for perturbation estimation with an adaptive finite-time sliding mode controller for autonomous navigation along the reference trajectories. First, a magnetic helical millirobot's kinematic model based on the 3-D hand position approach is established. Subsequently, a robust smooth differentiator is implemented as an observer to estimate disturbances within a finite time. We then investigate an adaptive finite-time sliding mode controller incorporating an auxiliary system to mitigate the estimated disturbance and achieve precise 3-D path tracking while respecting the input constraints. The adaptive mechanism of this controller ensures fast convergence of the system while alleviating the chattering effects. Finally, we provide a rigorous theoretical analysis of the finite-time stability of the closed-loop system based on the Lyapunov functions. Utilizing a robotically-actuated magnetic manipulation system, experimental results demonstrate the efficacy of the proposed approach in terms of the control accuracy and convergence time.