# Open Loop Position Control of Soft Hydraulic Actuators for Minimally Invasive Surgery
## 1 Introduction  
Colorectal cancer is the fourth most common type of cancer in the UK with over 42,000 cases diagnosed in 2017 and was the second most lethal cancer in the UK in 2018 [1]. Globally, there were approximately 1.4 million cases of colorectal cancer and 700,000 deaths in 2021, and cases are predicted to increase 60% by 2030 to 2.2 million cases and 1.1 million deaths [2, 3]. In the field of minimally invasive surgery (MIS) of the gastrointestinal (GI) tract, the flexible endoscope is one of the most important tools. Colonoscopy with a flexible endoscope is the gold standard for colorectal cancer diagnosis; however, surgical procedures performed with a flexible endoscope remain technically challenging. To tackle increasing cases of gastric cancer more effectively, a technique known as endoscopic submucosal dissection (ESD) was developed. ESD provides improved outcomes for patients in comparison to piecemeal endoscopic mucosal resection (p-EMR), a commonly used technique. In particular, the recurrence rates for ESD are greatly reduced compared to EMR due to the ability to remove cancerous tissue _en bloc_ with ESD [4]. Size of the lesion is an important factor for the difference in recurrence rates, with EMR performing worse for lesions greater than 20 mm in diameter [5]. However, ESD is a very technically challenging procedure to perform with a flexible endoscope due to high risks of perforation and bleeding, as well as longer procedure times [6]. As such, the _Cyclops_ cable-driven parallel robot was developed to make ESD easier to perform [7; 8]. The robot consists of a support structure connected to the endoscope tip that can deploy (increase in volume) to provide space for two surgical instruments to manoeuvre. One disadvantage of this system is friction between the long force transmission cables that are used to actuate the surgical instruments and the Bowden tubes containing them. The cables measure around 2 m because they pass alongside the flexible endoscope. Loops form in the cables as they conform to the shape of the lower intestine, meaning that the Bowden tubes act as a series of capstans with unknown contact angles. The friction in the cables increases exponentially with contact angle, so the friction can become significant with many tight bends and will be different from patient to patient. Two effects of friction are that it causes slack in the cables, which negatively impacts controllability of the instruments, and it prevents accurate measurement of the tension, therefore preventing estimation of the forces exerted on the instruments. The _Cyclops_ robot is also made from materials more rigid than the soft tissues of the body. In [9], the metal support structure was replaced with an inflatable structure to improve integration with the endoscope and make the robot less invasive, using approaches from the field of soft robotics. Soft robots are constructed from soft materials, have compliant structures, and are often inspired by biology [10; 11]. The robot developed in [12] was inspired by nature and exhibits multiple modes of operation as a result of its soft construction. The capability to alter a robot's structure in real time, among other advantages over rigid robots, means that more effective interactions with dynamically changing environments are made possible by soft robots [13], which has benefits in the application of MIS. The biologically inspired STIFF-FLOP manipulator was designed for use in laparoscopic surgery [14] and brought attention to the application of soft robotics in MIS [15]. As noted in [16], though, theory developed for conventional robotics often cannot be applied to soft robotic devices, so controlling soft robotics devices can be difficult. Other disadvantages of soft robotic approaches reported in the literature are low force exertion [17] and the difficulty of integrating sensors [18].