•A simple, compact elastomeric valve is used to control soft-robotic actuators•Up to five actuators are activated in different patterns•The pattern can be changed on the fly by mechanical reprogramming•We demonstrate a four-legged robot that requires nothing but a pump to walk Soft robotics is an emerging research field fueled by a vision of adaptative behavior in unpredictable environments and safe cooperation with humans. Soft robots possess so-called embodied intelligence, for example, in soft grippers that conform to arbitrarily shaped objects. However, higher-level adaptivity remains elusive. To bring this goal a step closer to reality, we introduce a compact soft valve. Fluidic circuits with our valves transform a continuous flow of air into timed pulses that activate up to five actuators in different sequences. We can select which sequence is executed, and excitingly, the system can switch between sequences in response to a physical cue. We demonstrate real-life applicability by controlling a four-legged walker. As such, our work leads the way toward fully autonomous soft robots that interact with their environment, for example, triggering drug release inside our body or changing gait to move past obstacles, without any electronics. Despite exciting developments in soft robotics, fully autonomous systems remain elusive. Fluidic circuits could enable fully embedded control of soft robots without using electronics. In this work, we introduce a simple and compact soft valve with intentional hysteresis, analogous to an electronic relaxation oscillator. By integrating the valve with a soft actuator, we transform a continuous inflow to cyclic activation. Importantly, we show that our circuits can activate up to five actuators in various sequences and that we can physically reprogram the activation order by varying the (initial) conditions in the fluidic circuit. Moreover, we show the feasibility of our approach under more realistic conditions by building a four-legged robot. Our work paves the way toward fully autonomous soft robots that can interact with their environment to reprogram their behavior, e.g., to trigger targeted drug release inside our body or to change gait to move past obstacles. Despite exciting developments in soft robotics, fully autonomous systems remain elusive. Fluidic circuits could enable fully embedded control of soft robots without using electronics. In this work, we introduce a simple and compact soft valve with intentional hysteresis, analogous to an electronic relaxation oscillator. By integrating the valve with a soft actuator, we transform a continuous inflow to cyclic activation. Importantly, we show that our circuits can activate up to five actuators in various sequences and that we can physically reprogram the activation order by varying the (initial) conditions in the fluidic circuit. Moreover, we show the feasibility of our approach under more realistic conditions by building a four-legged robot. Our work paves the way toward fully autonomous soft robots that can interact with their environment to reprogram their behavior, e.g., to trigger targeted drug release inside our body or to change gait to move past obstacles. Soft robots are compliant enough to be deformed by interactions with their environment while being stiff enough to perform meaningful action. Prime examples of soft robots are starfish-like grippers that are soft enough to wrap around an object without knowing its shape yet strong enough to lift significant weight.1Bao G. Fang H. Chen L. Wan Y. Xu F. Yang Q. Zhang L. Soft robotics: academic insights and perspectives through bibliometric analysis.Soft Robot. 2018; 5: 229-241https://doi.org/10.1089/soro.2017.0135Crossref PubMed Scopus (96) Google Scholar Similar robotic systems can also achieve locomotion, enabling soft walking robots that require less control to navigate unknown terrain than traditional rigid robots.2Tolley M.T. Shepherd R.F. Mosadegh B. Galloway K.C. Wehner M. Karpelson M. Wood R.J. Whitesides G.M. A resilient, untethered soft robot.Soft Robot. 2014; 1: 213-223https://doi.org/10.1089/soro.2014.0008Crossref Scopus (698) Google Scholar While soft robots have found real-world adoption as end effectors on robotic arms for pick-and-place applications3Shintake J. Cacucciolo V. Floreano D. Shea H. Soft robotic grippers.Adv. Mater. 2018; 30: 1707035https://doi.org/10.1002/adma.201707035Crossref Scopus (666) Google Scholar and have, for example, been applied for medical rehabilitation4Polygerinos P. Wang Z. Galloway K.C. Wood R.J. Walsh C.J. Soft robotic glove for combined assistance and at-home rehabilitation.Robot. Auton. Syst. 2015; 73: 135-143https://doi.org/10.1016/j.robot.2014.08.014Crossref Scopus (934) Google Scholar and implants,5Payne C.J. Wamala I. Abah C. Thalhofer T. Saeed M. Bautista-Salinas D. Horvath M.A. Vasilyev N.V. Roche E.T. Pigula F.A. Walsh C.J. An implantable extracardiac soft robotic device for the failing heart: mechanical coupling and synchronization.Soft Robot. 2017; 4: 241-250https://doi.org/10.1089/soro.2016.0076Crossref PubMed Scopus (42) Google Scholar soft mobile robots remain elusive. This may be explained by the fact that locomotion requires the control of multiple actuators instead of a single stimulus to control the grasping motion of a soft gripper. In order to build fully soft-robotic systems that operate autonomously, we need to embody such robots with more intelligence by embedding computation.6Rus D. Tolley M.T. Design, fabrication and control of soft robots.Nature. 2015; 521: 467-475https://doi.org/10.1038/nature14543Crossref PubMed Scopus (2951) Google Scholar Typical fluidic actuators consist of a silicone matrix embedded with channels and chambers.7Suzumori K. Iikura S. Tanaka H. Applying a flexible microactuator to robotic mechanisms.IEEE Control Syst. 1992; 12: 21-27https://doi.org/10.1109/37.120448Crossref Scopus (219) Google Scholar, 8Shepherd R.F. Ilievski F. Choi W. Morin S.A. Stokes A.A. Mazzeo A.D. Chen X. Wang M. Whitesides G.M. Multigait soft robot.Proc. Natl. Acad. Sci. U S A. 2011; 108: 20400-20403https://doi.org/10.1073/pnas.1116564108Crossref PubMed Scopus (1433) Google Scholar, 9Marchese A.D. Katzschmann R.K. Rus D. A recipe for soft fluidic elastomer robots.Soft Robot. 2015; 2: 7-25https://doi.org/10.1089/soro.2014.0022Crossref PubMed Scopus (398) Google Scholar, 10Polygerinos P. Correll N. Morin S.A. Mosadegh B. Onal C.D. Petersen K. Cianchetti M. Tolley M.T. Shepherd R.F. Soft robotics: Review of fluid-driven intrinsically soft devices; manufacturing, sensing, control, and applications in human-robot interaction.Adv. Eng. Mater. 2017; 19: 1700016https://doi.org/10.1002/adem.201700016Crossref Scopus (497) Google Scholar, 11Gorissen B. Reynaerts D. Konishi S. Yoshida K. Kim J.W. De Volder M. Elastic inflatable Actuators for soft robotic applications.Adv. Mater. 2017; 29: 1604977https://doi.org/10.1002/adma.201604977Crossref Scopus (206) Google Scholar When subjected to a pressurized fluid, these actuators bend, extend, contract, or twist in order to make a robot walk,8Shepherd R.F. Ilievski F. Choi W. Morin S.A. Stokes A.A. Mazzeo A.D. Chen X. Wang M. Whitesides G.M. Multigait soft robot.Proc. Natl. Acad. Sci. U S A. 2011; 108: 20400-20403https://doi.org/10.1073/pnas.1116564108Crossref PubMed Scopus (1433) Google Scholar jump,12Bartlett N.W. Tolley M.T. Overvelde J.T.B. Weaver J.C. Mosadegh B. Bertoldi K. Whitesides G.M. Wood R.J. A 3D-printed, functionally graded soft robot powered by combustion.Science. 2015; 349: 161-165https://doi.org/10.1126/science.aab0129Crossref PubMed Scopus (650) Google Scholar or swim.13Katzschmann R.K. DelPreto J. MacCurdy R. Rus D. Exploration of underwater life with an acoustically controlled soft robotic fish.Sci. Robot. 2018; 3: eaar3449https://doi.org/10.1126/SCIROBOTICS.AAR3449Crossref PubMed Scopus (290) Google Scholar Importantly, for the robots to perform certain tasks, their individual limbs need to be activated in a specific sequence. The typical approach is to use one or more manually operated or motor-controlled syringes14Marchese A.D. Tedrake R. Rus D. Dynamics and trajectory optimization for a soft spatial fluidic elastomer manipulator.Int. J. Robot Res. 2016; 35: 1000-1019https://doi.org/10.1177/0278364915587926Crossref Scopus (131) Google Scholar or (electro-)mechanical valves.4Polygerinos P. Wang Z. Galloway K.C. Wood R.J. Walsh C.J. Soft robotic glove for combined assistance and at-home rehabilitation.Robot. Auton. Syst. 2015; 73: 135-143https://doi.org/10.1016/j.robot.2014.08.014Crossref Scopus (934) Google Scholar Due to the weight of these rigid components, they are typically not placed on the robot, such that fluidic tethers are needed. Similarly, the tethers provide the ability to externally reprogram the actuation sequence when needed. Recently, efforts have been made to replace the electronic control using only fluidic elements. Making use of interactions between the mechanical and fluidic properties of actuators, valves, and channels, these methods point the way to autonomous soft robots with all of their intelligence embedded in their elastomeric bodies.15Wehner M. Truby R.L. Fitzgerald D.J. Mosadegh B. Whitesides G.M. Lewis J.A. Wood R.J. An integrated design and fabrication strategy for entirely soft, autonomous robots.Nature. 2016; 536: 451-455https://doi.org/10.1038/nature19100Crossref PubMed Scopus (1210) Google Scholar,16Drotman D. Jadhav S. Sharp D. Chan C. Tolley M.T. Electronics-free pneumatic circuits for controlling soft-legged robots.Sci. Robot. 2021; 6: eaay2627https://doi.org/10.1126/SCIROBOTICS.AAY2627Crossref PubMed Scopus (52) Google Scholar Analogously to electronics, in soft fluidic control, we can identify innovations on the component level as well as the circuit level, and it is clear that advances on both levels are needed to improve the complexity of the behavior that can be embodied in the soft robots. So far, mostly low-level functions have been demonstrated, where sequences of actions can be triggered in the robot by externally supplied time-varying pressure inputs. For example, sequential activation of soft fluidic actuators has been achieved by connecting actuators in series with tubes of optimized diameter and length.17Vasios N. Gross A.J. Soifer S. Overvelde J.T. Bertoldi K. Harnessing viscous flow to simplify the actuation of fluidic soft robots.Soft Robot. 2020; 7: 1-9https://doi.org/10.1089/soro.2018.0149Crossref PubMed Scopus (44) Google Scholar Besides combining components with a linear response, a combination of actuators with a nonmonotonic pressure-volume relation can also be designed to actuate in a given sequence.18Overvelde J.T.B. Kloek T. D’haen J.J.A. Bertoldi K. Jonas J.A.D. Bertoldi K. Amplifying the response of soft actuators by harnessing snap-through instabilities.Proc. Natl. Acad. Sci. U.S.A. 2015; 112: 10863-10868https://doi.org/10.1073/pnas.1504947112Crossref PubMed Scopus (141) Google Scholar,19Gorissen B. Milana E. Baeyens A. Broeders E. Christiaens J. Collin K. Reynaerts D. De Volder M. Hardware sequencing of inflatable nonlinear actuators for autonomous soft robots.Adv. Mater. 2019; 31: 1804598https://doi.org/10.1002/adma.201804598Crossref Scopus (33) Google Scholar A combination of viscous friction and nonlinear actuators can be exploited for peristaltic motion20Glozman D. Hassidov N. Senesh M. Shoham M. A self-propelled inflatable earthworm-like endoscope actuated by single supply line.IEEE Trans. Biomed. Eng. 2010; 57: 1264-1272https://doi.org/10.1109/TBME.2010.2040617Crossref PubMed Scopus (52) Google Scholar or to expand the number of possible state transitions.21Ben-Haim E. Salem L. Or Y. Gat A.D. Single-input control of multiple fluid-driven elastic actuators via interaction between bistability and viscosity.Soft Robot. 2020; 7: 259-265https://doi.org/10.1089/soro.2019.0060Crossref PubMed Scopus (14) Google Scholar Another example is so-called band-pass valves that let low flows through but block high flows, which allows setting the pressure of multiple actuators individually using a single time-controlled pressure source.22Napp N. Araki B. Tolley M.T. Nagpal R. Wood R.J. Simple passive valves for addressable pneumatic actuation.in: Proc. - IEEE Int. Conf. Robot. Autom.2014: 1440-1445https://doi.org/10.1109/ICRA.2014.6907041Crossref Scopus (31) Google Scholar Finally, following design principles from digital electronics, fluidic transistors can be arranged to control grasping and locomotion states using three fluidic drive lines23Mahon S.T. Buchoux A. Sayed M.E. Teng L. Stokes A.A. Soft robots for extreme environments: removing electronic control.in: RobotSoft 2019 - 2019 IEEE Int. Conf. Soft Robot. 2019: 782-787https://doi.org/10.1109/ROBOSOFT.2019.8722755Crossref Scopus (24) Google Scholar or to control eight outputs from three inputs.24Bartlett N.W. Becker K.P. Wood R.J. A fluidic demultiplexer for controlling large arrays of soft actuators.Soft Matter. 2020; 16: 5871-5877https://doi.org/10.1039/c9sm02502bCrossref PubMed Scopus (21) Google Scholar The key limitation for all of the above-mentioned systems is that they rely on externally timed inputs and therefore require tethers to operate. To our knowledge, there are only two examples of untethered soft robots with fluidic embedded control, and both of these breakthrough results originate from their ability to generate timed signals on the robot itself. The first example is a three-dimensional (3D)-printed octopus-inspired robot that employs a micro-fluidic oscillator25Mosadegh B. Kuo C.H. Tung Y.C. Torisawa Y.S. Bersano-Begey T. Tavana H. Takayama S. Integrated elastomeric components for autonomous regulation of sequential and oscillatory flow switching in microfluidic devices.Nat. Phys. 2010; 6: 433-437https://doi.org/10.1038/nphys1637Crossref PubMed Scopus (216) Google Scholar to alternate between two groups of actuators.15Wehner M. Truby R.L. Fitzgerald D.J. Mosadegh B. Whitesides G.M. Lewis J.A. Wood R.J. An integrated design and fabrication strategy for entirely soft, autonomous robots.Nature. 2016; 536: 451-455https://doi.org/10.1038/nature19100Crossref PubMed Scopus (1210) Google Scholar The second untethered soft robot16Drotman D. Jadhav S. Sharp D. Chan C. Tolley M.T. Electronics-free pneumatic circuits for controlling soft-legged robots.Sci. Robot. 2021; 6: eaay2627https://doi.org/10.1126/SCIROBOTICS.AAY2627Crossref PubMed Scopus (52) Google Scholar uses soft ring oscillators26Preston D.J. Rothemund P. Jiang H.J. Nemitz M.P. Rawson J. Suo Z. Whitesides G.M. Digital logic for soft devices.Proc. Natl. Acad. Sci. U S A. 2019; 116: 7750-7759https://doi.org/10.1073/pnas.1820672116Crossref PubMed Scopus (94) Google Scholar that, when provided with a constant pressure, generate cyclical, timed pressure signals to three different groups of actuator chambers each.27Drotman D. Jadhav S. Karimi M. Dezonia P. Tolley M.T. 3D printed soft actuators for a legged robot capable of navigating unstructured terrain.in: Proc. - IEEE Int. Conf. Robot. Autom.2017: 5532-5538https://doi.org/10.1109/ICRA.2017.7989652Crossref Scopus (119) Google Scholar This control system implements a soft, bistable valve that can be used as a switch and for cyclic activation of a single actuator28Rothemund P. Ainla A. Belding L. Preston D.J. Kurihara S. Suo Z. Whitesides G.M. A soft, bistable valve for autonomous control of soft actuators.Sci. Robot. 2018; 3: eaar7986https://doi.org/10.1126/SCIROBOTICS.AAR7986Crossref PubMed Scopus (187) Google Scholar or that can be used in digital logic circuits.29Preston D.J. Jiang H.J. Sanchez V. Rothemund P. Rawson J. Nemitz M.P. Lee W.K. Suo Z. Walsh C.J. Whitesides G.M. A soft ring oscillator.Sci. Robot. 2019; 4: 1-10https://doi.org/10.1126/scirobotics.aaw5496Crossref Scopus (72) Google Scholar In all these applications, cyclic and programmable activation of multiple actuators is key in moving toward autonomous behavior in soft robots. In the previous two examples of untethered robots, the employed oscillators have only been demonstrated to activate up to a maximum of three degrees of freedom each. More importantly, they fundamentally only support a single sequence, such that reprogramming the actuators’ activation order requires “rewiring” of the system.16Drotman D. Jadhav S. Sharp D. Chan C. Tolley M.T. Electronics-free pneumatic circuits for controlling soft-legged robots.Sci. Robot. 2021; 6: eaay2627https://doi.org/10.1126/SCIROBOTICS.AAY2627Crossref PubMed Scopus (52) Google Scholar To overcome these limitations, in this work, we introduce an extremely simple design for a soft valve that can be directly integrated with soft actuators. In contrast to the straightforward design and fabrication, the behavior of the valve is highly nonlinear and shows mechanical and fluidic hysteresis, which we harness to activate and reprogram up to five actuators in sequences. We first introduce the design of the valve and show it in its most basic arrangement where it forms a single relaxation oscillator. The valve oscillates under continuous inflow of air, such that no external timing is required. We show that this oscillator can be used to cyclically activate a soft bending actuator placed behind the valve. We then connect two valves and actuators in parallel and analyze an instability that leads to alternating activation of the two actuators. Supported by a model that describes fluidic circuits including multiple valves in parallel, we experimentally demonstrate a novel way to control the sequence and timing of up to five actuators. This number is limited by imperfections due to production tolerances, and we show how the allowed imperfection level scales with the number of degrees of freedom. Moreover, we show that the fluidic circuit can repeatedly change its sequence of activation in response to an external stimulus. Finally, we show that we can directly integrate a fluidic control system into a soft robot and demonstrate our approach under more realistic conditions. As such, our proposed fluidic relaxation oscillator enables new kinds of medical and mobile robotics applications and brings the concept of fully autonomous soft robotics a step closer to realization. With the aim of building a soft fluidic control system for soft robots, we start by developing a fluidic relaxation oscillator that transforms a continuous flow into a pulsatile flow. We do so by fabricating an elastic valve (Figure 1A ), which is placed directly in a fluid flow. The valve consists of a curved membrane that contains three slits that meet at its apex. In this work, we use valves with thickness T = 0.75 mm, angle θ=75∘, radius a0 = 2.5 mm, and the slits have length L = 0.75 mm (Figure 1B). These values result in Δpopen≈60kPa, Δpclose≈5kPa, and Ropen≈2kPa/ standard liter per minute (SLPM). The valve is fabricated by casting a silicone elastomer (Dragon Skin 20, Smooth-On) in a 3D-printed mold, after which the slits are machined using a laser cutter. It is then placed in a 3D-printed holder to create a robust, self-contained unit (Figure 1B; experimental procedures). Importantly, the membrane exhibits a mechanical instability that translates into fluidic hysteresis (Figure 1C). Upon applying an increasing pressure to the curved membrane, it will undergo several stages, as shown in Figure 1D. (1) For very low pressures, the valve is not completely closed due to the finite width of the laser-cut slits, and some fluid can flow through the opening. (2) An increasing pressure closes the slits, such that no fluid can pass through the valve. (3) Upon reaching a critical pressure difference Δpopen, the curved membrane snaps to an inverted state, opening the slits and letting fluid through. In this open state, the valve acts as a flow restriction. (4) Importantly, when decreasing the pressure, the membrane does not snap back at the same point, and instead, (5) the valve closes at a lower pressure difference Δpclose. Next, we apply a continuous air inflow Q = 1 SLPM to the valve and measure pressure before, as well as flow rate through, the valve. Interestingly, we observe that a system containing only the valve transforms a continuous inflow into a pulsatile outflow (Figures 1E and 1G; Video S1). Note that the behavior of the valve is highly repeatable, as shown by the small deviation between 500 cycles overlaid in Figure 1H, even for the dynamics that occur during the unstable transitions. Moreover, we find that for this specific design of the valve, the cycle frequency can be tuned in a range between f≈ 0.3 and 5 Hz by varying the inflow rate from Qin = 0.2 to 4.5 SLPM (and up to f≈ 17 Hz by minimizing the capacitance C0 by removing the flow sensor), as shown in Figure S1. For higher values of inflow, the valve stops oscillating and remains open. Details on the durability of the valve obtained by performing an experiment lasting 10 h are shown in Figure S2. eyJraWQiOiI4ZjUxYWNhY2IzYjhiNjNlNzFlYmIzYWFmYTU5NmZmYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiJiYWM5NTQ2YjA4YmVkMTAwZmYxYWJmNTE2MDA5NDk4NSIsImtpZCI6IjhmNTFhY2FjYjNiOGI2M2U3MWViYjNhYWZhNTk2ZmZjIiwiZXhwIjoxNjcxMzE5Njc2fQ.etILQkZVHwSMCR8L2IOiB26xsk5RnlGqB_NVQ4GtLK45pA2_Cpcg3R91bN8r5WMkoG4ye6Sy_JHOp0SGo0fv4qa1NVw6O7bBtnD-ZqLUZ-oW7ONssUlJheR2yE-9dbA_G2sZ8qOqyH9aa3l_cX-OyUB-wl6X7ivmcq_TAiqUOXEiWHKz298Q7Rb6C4-a4Bv_3stGipxMRhf6HLt14kDdUkkqgobAMrxDN5TogpvPOlbuGB9og8XAh5q7XuxDq3TC0QQDuLa0hYghaRFfEsPoeP9x5WpXvcoBnsUBBN-gzAgGtugcTvrOyy21J2IBkmPfefV_fKJ0ZHByEeqZCPsDkQ Download .mp4 (3.34 MB) Help with .mp4 files Video S1. A hysteretic valve that transforms a continuous flow into a pulsatile flowA soft and compact hysteric valve transforms a continuous inflow into pulsatile outflow. The dome-shaped silicone membrane exhibits mechanical hysteresis that translates to hysteresis in the fluidic domain. A laser-cut slit opens when the membrane is in the buckled state. To explain the oscillating behavior, we make use of the analogy between fluidics and electronics, in which pressure can be described by a voltage and fluid flow by a current30Oh K.W. Lee K. Ahn B. Furlani E.P. Design of pressure-driven microfluidic networks using electric circuit analogy.Lab Chip. 2012; 12: 515-545https://doi.org/10.1039/c2lc20799kCrossref PubMed Scopus (449) Google Scholar (Figure 1F; experimental procedures). Using this analogy, we model the hysteretic valve as a voltage-controlled switch with a resistance Ropen and Rclosed≫Ropen in its open and closed states (note that our definition of open is opposite to electronics and indicates that air can flow through the valve), respectively. Moreover, we model the combined deformation of the valve and compressibility of the air contained in the tubes before the valve as a capacitor C0. This provides the energy storage that is required for the system to oscillate. To simulate constant inflow, we drive the system with a current source. This circuit then forms a fluidic relaxation oscillator, characterized by the periodic, relatively slow build up and fast release of pressure. Note that in electronics, the same effect can be witnessed in a Pearson-Anson oscillator,31Pearson S.O. Anson H.S.G. The neon tube as a means of producing intermittent currents.Proc. Phys. Soc. Lond. 1921; 34: 204-212https://doi.org/10.1088/1478-7814/34/1/341Crossref Scopus (17) Google Scholar where a neon tube provides the required hysteresis. This also explains why the valve stops oscillating at higher flow rates, as the pressure difference caused by the drag force of the constant flow prevents the valve from snapping back. These three components (current source, capacitor, and hysteretic switch) are enough to accurately capture the oscillating response of the system, as can be seen in Figure 1G from the comparison between our model and experiments. Note that, here, we always use air in our fluidic circuits, such that a fixed volume acts as a capacitance through the compressibility of the air. However, the same results could be obtained using, for example, water, although in that case an elastic chamber is required to achieve capacitance. Moreover, we should also note that in our simulations, we did not model the dynamic effects that are visible in Figures 1G and 1H during valve opening and closing. This does not affect the descriptive power of the model since the effective time scales are sufficiently separated. Next, we couple our fluidic relaxation oscillator to a soft bending actuator to achieve cyclic activation (Figure 2A ; Video S2). We fabricate a modified PneuNet actuator based on a design that was previously used in an untethered soft robot,2Tolley M.T. Shepherd R.F. Mosadegh B. Galloway K.C. Wehner M. Karpelson M. Wood R.J. Whitesides G.M. A resilient, untethered soft robot.Soft Robot. 2014; 1: 213-223https://doi.org/10.1089/soro.2014.0008Crossref Scopus (698) Google Scholar,32Ilievski F. Mazzeo A.D. Shepherd R.F. Chen X. Whitesides G.M. Soft robotics for chemists.Angew. Chem. Int. Ed. 2011; 50: 1890-1895https://doi.org/10.1002/anie.201006464Crossref PubMed Scopus (858) Google Scholar where we limit the required amount of air to inflate the actuator33Mosadegh B. Polygerinos P. Keplinger C. Wennstedt S. Shepherd R.F. Gupta U. Shim J. Bertoldi K. Walsh C.J. Whitesides G.M. Pneumatic networks for soft robotics that actuate rapidly.Adv. Funct. Mater. 2014; 24: 2163-2170https://doi.org/10.1002/adfm.201303288Crossref Scopus (938) Google Scholar (Figure S3). To integrate the actuator with the hysteretic valve, we use a 3D-printed clamp to hold the valve and actuator in place and to connect the valve to an inflow. The actuator has an outflow port to which we connect a silicone tube. We furthermore connect an air chamber in front of the valve to be able to vary the volume of air that will be compressed prior to each actuation (C0) and add one or more needles to act as a flow restriction (R) after the outflow tube to reduce the rate at which the air leaves the actuator while being vented to atmosphere (Figure 2A). eyJraWQiOiI4ZjUxYWNhY2IzYjhiNjNlNzFlYmIzYWFmYTU5NmZmYyIsImFsZyI6IlJTMjU2In0.eyJzdWIiOiIwZTkwMzg2NGVlODdhZjgzYzI1ZGQ3MmE4YjdiNDI4YSIsImtpZCI6IjhmNTFhY2FjYjNiOGI2M2U3MWViYjNhYWZhNTk2ZmZjIiwiZXhwIjoxNjcxMzE5Njc2fQ.NnYTM1NhmHqPu9_aBzgdXp7C_hmoS2v4kcWkxNPGWlnpk4zv2VAUYl8LmmPuOvIt8BXmf8eXl8TdoSSrq4AQXn-b5EMTeu3ORF8A3LOeL70J00jvz2YSGq-_OLNdMJKVLKwkXhN1Tqs_gd5XDP0qc7X6OmBzWcYkxxqybJ1plyJxfldJPhI5Kene_1CkQZ4mIsKoClF5E3dQLDCANTW_p3P7ABEz2DHKqJIpKmnxPVamBDKVscH5HkDyKcQGVzSZNNfkEFx4Nc----KzhO1JJmudHAv1SwINiOo8dg5dMTglfV1J5CVEiKm63FC4wcmZ_03HeLgqWNhjfV2c3HM1vA Download .mp4 (4.02 MB) Help with .mp4 files Video S2. Cyclic activation of a single actuatorDifferent combinations of fluidic component values C0/Cact and R/Ropen result in different actuator behavior, with the same maximum actuator pressure pact,max≈20kPa. To determine the circuit parameters that are needed to achieve a desired motion profile of the actuator (i.e., maximum and minimum pressure and cycle frequency), we first perform a numerical study by considering the equivalent electronic schematic as shown in Figure 2B (experimental procedures). Given a specific (nonlinear) pressure volume relation of the actuator (Figure S3) and the parameters of our hysteretic valve, we can still choose the flow rate (Qin), size of the air chamber (C0), and the outflow restriction (R). For example, Figure 2C shows the resulting activation frequency f of the actuator when varying C0 (normalized by the initial actuator capacitance Cact,0) and R (normalized by the hysteretic valve resistance Ropen) for a constant inflow of Qin = 1 SLPM. The same analysis is shown in Figure S4 for a range of flow rates. While these results show that we can tune the frequency of activation, different combinations of C0 and R lead to different actuator pressurization. To illustrate this, we consider all possible parameter combinations that lead to a maximum pressure in the actuator pact,max = 20 kPa, as indicated by the line in Figure 2C. We choose this value as it is high enough to achieve significant deformation of the actuators but does not cause excessive fatigue. Along this line, we can identify two regimes. At low outflow resistance R (i.e., higher C0), deflation of the actuator occurs more rapidly than inflation of the air chamber, such that the actuator empties completely before being activated again. Therefore, it is at zero pressure for part of the cycle (Figure 2D, case 3). In contrast, at high outflow resistance R (i.e., lower C0), the inflation of the air chamber is initially faster than the deflation of the actuator. Therefore, a new equilibrium is found where pact,min>0, such that the actuator no longer goes back to its undeformed shape (Figure 2D, case 1). At the boundary of these two regimes, we find the actuator to always be in motion while still fully deflating during each cycle. The dashed line in Figure 2C approximates this boundary for different values of pact,max, where we have set the minimum pressure in the actuator equal to pact,min = 1 kPa. We can now identify the unique combination of parameters {C0/Cact,0,R/Ropen} that leads to pact,max = 20 kPa and pact,min = 1 kPa for Qin = 1 SLPM (Figure 2D, case 2). A typical soft robot contains multiple actuators that need to be activated in a certain pattern to achieve a desired behavior, such as locomotion. In order to determine if we can use our hysteretic valve to control fluidic circuits that contain more than one actuator, we next focus on fluidic circuits that contain two actuators. While it is straightforward to achieve simultaneous activation of any number of actuators by connecting them all to a single val