# Kinematic Modelling and Experimental Validation of a Foldable Pneumatic Soft Manipulator
## 1 Introduction  
Soft manipulators are an important type of soft robot, which have become a research focus in recent years [1; 2]. In messy and crowded environments, such as a mine site, or scientific exploration, the collision between the traditional rigid manipulator and the environment may damage the scene, causing a secondary disaster [3]. Thus, the soft manipulator shows a good supplementary application. In space manipulation, the space manipulator was firstly installed on the space shuttle in 1980s. Traditional space manipulators have a large volume and weight, which results in a great challenge and a high cost to the rocket [4; 5]. If the space manipulator can be folded into a small volume with a light weight before launch, it will definitely have a much greater prospect in space missions. Moreover, this kind of foldable pneumatic manipulator will also have a wide application in future industrial fields, physical human-robot interactions, and many other fields. For example, the ultralight pneumatic arm with a long range can be used in disaster rescue and home or healthcare applications [6; 7; 8]. It can also work in underwater environments just like a soft electronic fish [9; 10]. In confined spaces, where traditional rigid equipment cannot work, the pneumatic soft manipulator shows competent performance [11; 12; 13; 14]. Currently, pneumatic soft manipulators have been developed rapidly. There are several kinds of typical prototypes presenting in the literature reports. [PERSON] et al. [15; 16; 17] designed and developed the octopus-inspired OctArm series of soft robot manipulators, each of which is constructed using air muscle extensors with three control channels per section that provide two axes bending and extension. [PERSON] et al. [18; 19] presented a soft manipulator for minimally invasive surgery (MIS) inspired by thebiological capabilities of the octopus arm, which was composed of three identical fluidic actuators allowing omnidirectional bending and elongation. [PERSON] et al. [PERSON] et al. (2018); [PERSON] et al. (2019); [PERSON] et al. (2020) presented a design of a soft manipulator, which used one whole bellows as the main structure and was driven by a series of cables. [PERSON] et al. [PERSON] et al. (2019) designed a pneumatic soft manipulator composed of an inflatable structure, which was entirely composed of plastic film. [PERSON] et al. [PERSON] et al. (2017, 2020) proposed a design scheme of an inflatable robotic arm that could generate a twisting motion. [PERSON] et al. [PERSON] et al. (2019); [PERSON] et al. (2019) proposed an inflatable soft manipulator controlled by cables. [PERSON] et al. [PERSON] et al. (2019) proposed a design scheme of a pneumatic arm that used pneumatic bellows as the driving actuator. [PERSON] et al. [PERSON] et al. (2019) presented a design of a continuum arm, which has the ability to extend and bend, based on McKibben pneumatic muscle actuators (PMA). [PERSON] et al. [PERSON] et al. (2019) presented fabric-based soft robotic modules composing of an inflatable beam and fabric-based rotary actuator, which was designed with origami-inspired V-shaped pleats. [PERSON] et al. [PERSON] et al. (2019) proposed a mechatronics-embedded soft module powered via a single air tube due to an air supply sharing design. In these above investigations, the pneumatic manipulators are driven by pressured air or cables. The focus is mainly on the design and fabrication of the pneumatic actuators without considering the foldability of the manipulator, which is an important factor to its application in confined storage environments, such as applications in space and underwater. In this paper, a pneumatic soft manipulator with the foldability to switch between a contraction state and an expanded state is designed and developed. In the second part, the design schematic of the soft manipulator is proposed, and the kinematic model of one foldable pneumatic module is developed.