Movie S8. Application on a quadruped robot

3.Discussion

We present the IEAR mechanism to achieve high-speed and low-energy actuation of m-SPAs in various pneumatic soft machines and robots. A dynamic model of m-SPAs is developed to guide the analysis of the actuation mechanism, which agrees well with the experiments on the exemplary m-SPAs, the Double Bellows and the Triple Bellows. These experiments also demonstrate the ability of IEAR to improve actuation speed and reduce energy consumption. Moreover, we observe an improvement in the supplied air pressure \(p_{tank}\)  and a decrease in the system power, which may result from the enhanced performance of the air supply and the reduction of required energy input to the IEAR-assisted system, respectively. Lastly, we demonstrate the practical feasibility and broad potential of IEAR with applications on a robotic fin, fabric-based finger, and quadruped robot.
As demonstrated in our experiments, the dynamic model of m-SPAs can give accurate pressure and actuation frequency. Although there are some errors, it is not easy for the dynamic pressure modeling of soft robots, especially for these m-SPAs with coupled interaction between chambers. These errors mainly come from the ignorance of actuator mass, the inaccuracy of actuator volume modeling and the inconsistency of commercial solenoid valves. Indeed, this model is generally applicable to both rigid and soft multi-chamber actuators, as long as the volume-pressure function Equation (3)  can be established. Based on our dynamic model of m-SPAs and some practical models for mass flow \cite{Joshi.2021b,Joshi.2021,Cheng.2018,Jungong.2008,Kawashima.2004,KUROSHITA_2002,Robinson.2015,Woods.2014}, a reverse design for air passage and actuation could be feasible and may lead to higher-performing soft machines and robots.
In this study, we present a group of comparative experiments with EEAR, where we find that IEAR performs better in improving actuation speed and energy efficiency, and the combination of IEAR and EEAR can greatly reinforce the performance of EEAR under high working pressure (Figure S9g-k and Supplementary Note 9). These experiments verify the ability of IEAR to achieve high-speed and low-energy actuation of m-SPAs. However, since the air in this study flows only between a pair of chambers at each step, further investigation is required to study simultaneous flow among a network of chambers. For a more lightweight system with IEAR, soft circuits supporting onboard control should also be investigated as a replacement for the rigid valve island by adopting soft pumps, microfluidic-activated valves, and smart fluids \cite{McDonald.2021}. Thus, a wider range of soft machines and robots, including fully untethered robotic systems \cite{Rich.2018}, might benefit from our IEAR mechanism.

4.Methods

4.1 Materials of the pneumatic control system

The components of the pneumatic system include a micro air pump (KZP-PE, Kamoer Fluid Tech Co., Ltd., China, Supplementary Note 10), a 3D-printed air tank and a valve island (DSM IMAGE8200 pro, WeNext Technology Co., Ltd., China), 12 solenoid valves (0520D, Foshan Weizi Electronic Technology Co., Ltd., China), two current sensors (Huaibei Vidias Electronic Technology Co., Ltd, China), a temperature sensor (Quanzhou Guanhangda Electronic Technology Co., Ltd, China), four pressure sensors (MPX4250DP, Freescale Semiconductor, USA), a relay (Risym, China) for the air pump, two solid-state relay panels (customized) for solenoid valves, two high-precision programmable linear power supplies (SS-L303SPV, Dong Guan Great Electronics Co., Ltd., China), and a controller (microLabBox 1202, dSPACE, Germany).
The electrical current data is used for power measurement, and the temperature sensor is inserted into the air tank to record the temperature of compressed air. In this study, the actual temperature of compressed air is generally 17-24 ℃, and we approximate the temperature as a constant 20℃ for simplification, which has little influence on the results under the thermodynamic scale of temperature. For the pressure sensors, one measures \(p_{tank}\) , and the other three are assigned to \(p_1\) ,\(p_2\) , and \(p_3\) . All the pneumatic components and actuators are connected by silicone tubes (Daoguan, China) with an inner diameter of 2 mm and an outer diameter of 4 mm. When the output pressure of the pump changes, the pump power varies following the experimentally obtained law (Figure S2c). Due to these inductive components, such as solenoid valves and pumps, the high precision programmable linear power supplies are used to avoid voltage fluctuation. In all the experiments, the sampling frequency of the system is set to 1 kHz.