IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 24, NO. 4, AUGUST 2019 1429 Static Modeling of Miniaturized Pneumatic Artiﬁcial Muscles, Kinematic Analysis, and Experiments on an Endoscopic End-Effector Ashwin K. P. and Ashitava Ghosal Abstract—In this paper, we present the design, de- velopment, 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 approxi- mately 120 degrees apart within a pair of concentric springs. Pressurizing one or more MPAMs allows the tip to be posi- tioned in a workspace, which is approximately a hemispheri- cal 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 ± 1 mm. Index Terms—Actuated endoscopic end-effector, experi- mental validation, kinematics of end-effector, miniaturized McKibben actuator, pressure-deformation relationship. I. INTRODUCTION A n endoscope is a diagnostic instrument, which is inserted into a patient’s gastrointestinal (GI) tract from the mouth with the primary objective of real-time inspection. The device is a ﬂexible tube of approximately 1.5 m length and about 12 mm in diameter. It contains a camera and lighting system, as well as a nozzle for pumping air and water from its distal tip. Most of modern endoscopes are also equipped with one or two channels through which a medical instrument (catheter) can be pushed Manuscript received November 30, 2017; revised March 29, 2018, August 13, 2018, January 17, 2019, and March 21, 2019; accepted May 9, 2019. Date of publication May 14, 2019; date of current version August 14, 2019. Recommended by Technical Editor M. Tavakoli. This work was supported by a grant from the Robert Bosch Centre for Cyber Physical Systems, IISc Bangalore. (Corresponding author: Ashitava Ghosal.) The authors are with the Department of Mechanical Engineering, In- dian Institute of Science, Bengaluru 560012, India (e-mail:, ashwinkp@ iisc.ac.in; asitava@iisc.ac.in). This paper has supplementary downloadable material available at http://ieeexplore.ieee.org, provided by the authors. Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/TMECH.2019.2916783 from the holding end till its working end protrudes from the dis- tal tip of the endoscope. Though all endoscopes have a provision to actuate the distal tip of the endoscope in vertical and horizon- tal directions, endoscopes in general do not have a provision to actuate the catheter independent of the camera. A few automated endoscopic platforms have the ability to actuate gripping tools for performing surgery [1], [2]. In these platforms, positioning is achieved using an end-effector, which is essentially a cable driven continuum robot [3], [4]. While it is possible to achieve precise control using cable actuation [4]–[6], the device can be- come a stiff structure when deployed and can potentially restrict the endoscope to achieve a desired shape. However, for medi- cal applications, devices which are soft and ﬂexible have many advantages and there has been considerable focus in developing soft endoscopic devices [7]. McKibben actuators are more suitable in such applications since the actuators are compliant/ﬂexible even in its actuated state and are lighter in weight. A McKibben actuator consists of an inﬂatable bladder, which is braided on the lateral outer sur- face using a helical mesh of ﬂexible but inextensible ﬁbers [8]. Air is pumped into the bladder from one end while the other end is sealed, allowing the bladder to inﬂate. However, the inexten- sible braid restricts the deformation of the bladder in such a way that when the braiding angle is less than 54.7 ◦ , the bladder con- tracts along its length [9]. Miniaturized versions of pneumatic artiﬁcial muscle (PAM), i.e., MPAM, would be ideal for medical robotics due to the following characteristics: a) they have high load carrying capacity, b) their stiffness can be controlled by the internal pressure, c) they have low weight, d) they are less expensive to manufacture (see also [10]–[13]). Although in [14], it is shown that the compliance in the cable actuated robots can be monitored using load cells and, hence, controlled (they use it to measure hard tissue properties), we believe that the MPAMs are inherently more compliant and the compliance can be better controlled. The similarity of PAMs with biological muscles and an advancement in control strate- gies have made the actuators popular in bioinspired robotics and medical robotics (see [15]–[19]). It is also observed from the above-mentioned references that accurate model to depict the physics of pneumatic muscles is an essential requirement for improved performance of control system [20]. One of the earliest attempts in modeling McKibben actuators was made by Schulte [9]. Many researchers improved upon this basic model by considering other physical effects such as fric- 1083-4435 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.