Extended State Observer Based-Optimal Control of a Microrobot Navigation Along a Trajectory Generated by a Joystick Device

Trajectory tracking of microrobots presents a significant challenge in biomedical research applications such as drug delivery and artery unclogging. Microrobots are inherently subject to uncertainties and unmodeled dynamics, complicating their control. Additionally, the overheating of coils in the electromagnetic actuation system can limit controller performance. In this paper, we propose an observer-based optimal control strategy for microrobots, where the desired trajectory is generated online by means of a joystick. The control law addresses the problem of coils overheating by minimizing energy consumption while achieving trajectory tracking despite uncertainties and unmodeled dynamics. For practical implementation, we introduce a modified nonlinear extended state observer to estimate the entire state of the microrobot. Analytical tuning approaches for the control law and observer are developed using D-pole placement technique and Kharitonov’s theorem. This solution is an alternative to the use of cooling systems, which require more energy consummation and often reduce the performance of the controller. The tracking performance of the proposed control strategy is evaluated through simulation and experimental tests on a dedicated platform. Both simulation and practical results demonstrate the effectiveness of the developed control strategy. Note to Practitioners—This work is motivated by the fact that ensuring effective targeted drug delivery and safe navigation of magnetic microrobots in biomedical applications requires an electromagnetic actuation system (EMA) with minimal magnetic energy consumption and coil heating. This can be accomplished through the optimal design of the EMA and the incorporation of a cooling system. However, while this solution is interesting, it can make the EMA cumbersome and heavy, which reduces the performance of the controller in tracking the desired trajectory. Besides, the use of a cooling system implies increased energy consumption. Thus, in this work, we develop and implement a control strategy that combines optimal control with an observer to minimize magnetic energy and, consequently, coil heating. The performance of this control strategy in forcing the microrobot to track a reference trajectory, generated in real-time using a joystick, is demonstrated through experiments conducted in an endovascular environment at different scales. The results show that the proposed control strategy successfully achieves trajectory tracking despite uncertainties and environmental disturbances, with no coil heating.