Modelling and Simulation of Pneumatic Sources for Soft Robotic Applications Matheus S. Xavier, Andrew J. Fleming and Yuen K. Yong 1 Abstract— The mathematical models for two widely used pneumatic systems in the soft robotics community are pre- sented: syringe pumps and compressed air systems. These models enable prediction and optimisation of performance of soft actuators under pressurisation, allowing the user to select pneumatic components for a desired behaviour. Analytical models are confirmed with simulations devel- oped using SimScape Fluids and SimScape Electrical within Simulink/MATLAB. By using a polytropic law, the models show agreement with the simulations with less than 10% discrepancy for the typical pressures used with soft actuators. Syringe pumps are shown to be much slower compared to the compressed air systems. In the latter, the addition of an air receiver allows very short actuation time. I. I NTRODUCTION The rising interest in soft robots is outlined in recent papers reviewing fabrication procedures [1], biological in- spiration [2], actuation methods [3], sensing [4], control [5], stiffening techniques [6] and biomedical applications [7]. The building blocks of soft robots are the soft actuators. One important category of soft actuator is the fluidic elastomer actuator (elastic inflatable actuator), whereby actuation is performed using pneumatics or hydraulics [8]. While these actuators have been extensively used in the literature, the fluid power systems used within the soft robotics commu- nity have received less attention. In [9], the authors have compared pneumatic energy sources used in autonomous and wearable soft robots and provided a system-level framework to support the design of untethered pneumatic soft robots, nevertheless the dynamics of actuation is not discussed. The basic components of a compressed air pneumatic system are the air compressor, the receiver and the valves. Positive displacement compressors are the most widely used and deliver a fixed volume of fluid each cycle, regardless of the pressure at the outlet port [10]. Valves are used to control the direction, flow rate and pressure of the compressed air. The air receiver (storage reservoir or gas tank) is used to store a given volume of compressed air and offers larger system capacity and reduction of pressure changes during short-term demand [11]. The latter is particularly relevant for the intermittent demand commonly experienced in soft robotics. Pressure control in the air receiver is normally achieved using on/off controllers by starting the compressor when the receiver pressure falls below some minimum value and stopping it when pressure rises to a satisfactory level. The most popular pneumatic control architecture for soft robotics is the fluidic control board [12], an open source hardware platform available from the Soft Robotics Toolkit that was originally employed in the experimental 1 All authors are with the Precision Mechatronics Lab at the School of Electrical Engineering and Computer Science, The Univer- sity of Newcastle, Callaghan, NSW, Australia {matheus.xavier, andrew.fleming, yuenkuan.yong}@newcastle.edu.au platform of [13], [14]. The board consists mainly of a diaphragm pump and a set of solenoid valves. MOSFETs allow the use of Pulse-Width Modulation (PWM) to control the pressure of fluid passing through the valves. Pressure sensors provide feedback on the behaviour of the system. Basic control options are manually adjusting switches and knobs or automated simple codes running on the included Arduino microcontroller. Advanced control options can be implemented using LabVIEW or Simulink. Manual pressurisation of syringes, while monitoring the pressure, is the simplest method for evaluation of the behaviour of soft actuators. This method has been employed in characterisation studies to investigate the relation between the geometrical parameters or material characteristics and the bending and extension of soft actuators [15]. Some studies have also used this method to validate FEM results [16]. An automatic alternative is the use of syringe pumps [17]. In order to convert the rotational motion of the motors into linear motion of the syringe plunger, syringe pumps can rely on a rack and pinion [18], [19] or lead screw mechanisms [20]–[22]. In the latter, the motor rotates a threaded rod that drives a nut attached to a 3D printed syringe plunger adapter. The analytical modelling of syringe pumps has been essentially limited to hydraulic systems. In addition, most models only consider the flow rate being dispensed by the syringe, with no consideration given to pressure dynamics. In [23]–[25], the Poiseuille equation is used to establish the flow rate considering fully developed laminar flow. The flow rate can also be determined by relating the volume of fluid for a single pitch movement and the time required for the rotation [19], [26]. In [27], the authors have used the lumped parameter approach to develop a second-order relation between the output flow rate and velocity of the piston motion for hydraulic fluid (constant bulk modulus). A. Contributions of this work In soft robotics, many of the studies using pneumatic control systems are focused in characterisation, in which the speed of actuation is not a concern. However, this is relevant for practical applications of soft robots. While pneumatic energy sources are widely used in soft robotics [9], their modelling has not yet been adequately described. In particular, the modelling of syringe pumps has been limited to the output flow of hydraulic fluids with little attention to pressure dynamics. Therefore, in this work, the analytical modelling for the two most widely used pneumatic systems in soft robotics are presented: compressed air systems (similar to the fluidic control board) and syringe pumps. The models presented here allow the user to not only predict performance but also to derive component specifications for a given set of soft-robotic performance requirements. 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Boston, USA (Virtual Conference), July 6-9, 2020 978-1-7281-6794-7/20/$31.00 ©2020 IEEE 916 Authorized licensed use limited to: University of Newcastle. Downloaded on August 10,2020 at 23:59:02 UTC from IEEE Xplore. Restrictions apply.