Static Modeling of Miniaturized Pneumatic Artificial Muscles, Kinematic Analysis, and Experiments on an Endoscopic End-Effector

In this paper, we present the design, development, modeling, and experimental validation of an endoscopic attachment that can be used to independently position an endoscopic catheter tip at a desired location. Three miniaturized pneumatic artificial muscles (MPAMs) are used in a flexible endoscopic attachment, each MPAM is of 1.2 mm diameter and 45 mm in length and placed approximately 120 degrees apart within a pair of concentric springs. Pressurizing one or more MPAMs allows the tip to be positioned in a workspace, which is approximately a hemispherical section of radius 45 mm. We present a new and improved theoretical model for pressure-deformation relationship of a MPAM using static equations of a pressurized thick cylinder and constraints due to the braids. Comparison with existing models show that the proposed model performs better and the errors predicted by the model are less than 5% with experiments. A new forward kinematic model relating the position and orientation of the tip of the end-effector with changes in MPAM lengths is developed. Finally, we present experimental results conducted on a prototype endoscopic attachment and show that our model could predict the pose of the end-effector with a maximum error of 2
$\pm$
1 mm.