An Extended Generalized Prandtl-Ishlinskii Hysteresis Model for I2RIS Robot

Retinal surgery requires extreme precision due to constrained anatomical spaces in the human retina. To assist surgeons achieve this level of accuracy, the Improved Integrated Robotic Intraocular Snake (I2RIS) with dexterous capability has been developed. However, such flexible tendon-driven robots often suffer from hysteresis problems, which significantly challenges precise control and positioning. In particular, we observed multi-stage hysteresis phenomena in the small-scale I2RIS. In this paper, we propose an Extended Generalized Prandtl-Ishlinskii (EGPI) model to increase the fitting accuracy of the hysteresis. The model incorporates a novel switching mechanism that enables it to describe multi-stage hysteresis in the regions of monotonic input. Experimental validation on I2RIS data demonstrates that the EGPI model outperforms the conventional Generalized Prandtl-Ishlinskii (GPI) model in terms of RMSE, NRMSE, and MAE across multiple motor input directions. The EGPI model in our study highlights the potential in modeling multi-stage hysteresis in minimally invasive flexible robots.

💡 Research Summary

This paper addresses a critical challenge in the precise control of flexible tendon-driven robots for retinal microsurgery, specifically focusing on the Improved Integrated Robotic Intraocular Snake (I2RIS). The I2RIS robot offers enhanced dexterity for delicate procedures within the confined space of the eye. However, its tendon-driven design introduces significant hysteresis—a nonlinear phenomenon where the output (robot tip position) depends not only on the current input (motor command) but also on the history of previous inputs. This hysteresis, compounded by effects like tendon elongation and friction, severely complicates accurate positioning. The authors make a key observation: the hysteresis in the small-scale I2RIS exhibits “multi-stage” behavior, where multiple distinct dead zones or transition phases appear even within a monotonically increasing or decreasing input range. Conventional hysteresis models, including the widely used Generalized Prandtl-Ishlinskii (GPI) model, struggle to capture this complex multi-stage characteristic.

The core contribution of this work is the proposal of an Extended Generalized Prandtl-Ishlinskii (EGPI) model. The GPI model forms the foundation, using a weighted sum of generalized play operators with envelope functions to model asymmetric hysteresis loops. The EGPI model’s innovation lies in introducing a novel switching mechanism. Instead of a single, continuous GPI model, the EGPI framework employs multiple GPI sub-models, each with its own set of envelope functions. A switching rule, triggered when the input crosses predefined “flag points,” determines which sub-model is active. This allows the EGPI model to segment a monotonic input phase into several stages, each with potentially different hysteresis properties. For instance, the simulation demonstrates an EGPI model creating two distinct dead zones (S1, S2) during input increase and two more (S3, S4) during decrease, which a single GPI model cannot achieve.

For modeling the specific hysteresis of the I2RIS robot, the authors tailor the EGPI structure. Since experimental data shows two clear hysteresis stages during the decreasing input phase, they construct an EGPI model with two GPI components (Π1