Independent Control of Multiple Degrees of Freedom Local Magnetic Actuators With Magnetic Cross-Coupling Compensation

Abstract

This letter tackles the problem of independent control of multiple degrees of freedom (DoF) systems based on local magnetic actuation (LMA). This is achieved by means of a modular disturbance rejection scheme, with the aim of enhancing the range of use of multiple-DoF LMAs in dexterous surgical manipulators. An LMA actuation unit consists of a pair of permanent magnets, characterized by diametrical magnetization, acting as magnetic gears across the abdominal wall. In this study, the model of the LMA and the time-varying magnetic disturbances owing to the proximity of multiple units are discussed. Subsequently, the developed model is capitalized in order to establish a Kalman state observer for the purpose of developing a sensor-free endoscopic manipulator suited to infer the state of the internal side of the LMA. Afterwards, the same model is used to develop an adaptive feedforward compensator system, with the aim of balancing the magnetic torques acting on the LMAs from the neighboring units in the case of unknown and frequency-varying sinusoidal disturbances. The effect of a magnetic shield, realized by means of MuMetal is also analyzed. The overall control system is modular with respect to the number of units and requires no centralized intelligence. The proposed scheme is subsequently validated by means of experiments performed on a benchtop platform, showing the effectiveness of the proposed approach. In particular, the proposed state observer presents a root mean square error (RMSE) ranging from $\boldsymbol {\text{28}}$ to $\boldsymbol {\text{47}}$ $\boldsymbol {\text{rpm}}$ in the estimation of the rotational velocity of the internal magnet and an RMSE of $\boldsymbol {\text{1.18}}$ $\boldsymbol {}$ to $\boldsymbol {\text{1.41}}$ $\boldsymbol {\text{mNm}}$ in the estimation of a load torque. The disturbance compensation system provides a reduction of ${\text{40}}$ $\%$ to $\boldsymbol {\text{50}}$ $\%$ in the disturbance caused by interacting LMA units.