Main

Animals are composed of multifunctional biological systems that allow them to grow, respond to sensory input, and extract and store energy from their environment. The human circulatory system is an excellent example of this multifunctionality. In addition to transporting oxygen and nutrients throughout the body, the circulatory system removes waste products, regulates internal temperature and cellular pH levels, and assists in fighting off disease and infection1. Furthermore, the network of blood vessels comprising the circulatory system is deeply intertwined with the muscular, skeletal and other organ systems. Robots, by contrast, are typically composed of isolated power, actuation, sensory and control systems, each of which are optimized for specific tasks. The clear gaps in mobility, adaptability and efficiency between robots and animals motivate tighter integration between these fundamental functional components via bioinspired design.

Energy storage is one of the major barriers to achieving long-duration autonomy in robots. Typically, a block of material serves a singular function as a robot’s storage battery, which results in sub-linear scaling of overall system energy density with total energy—added battery packs increase weight and necessitate additional modifications to maintain overall performance. Considering multifunctionality allows size, weight and power trade-offs to be re-evaluated. Some examples of batteries serving multiple functions are: (1) heavy lead–acid batteries that are used for weight balancing in forklifts2, (2) flexible batteries that function as flapping-wing surfaces3 and (3) structural batteries4,5 that simultaneously act as load-bearing members and energy-storage elements in satellites and unmanned aerial vehicles6,7. We now identify hydraulic fluids, used as force-transmission and actuating media in the machinery of robots, as another area of opportunity for multifunctional energy storage.

Redox flow batteries (RFBs) are a potential candidate for this application. RFBs utilize flowable liquid or semi-solid components and are known for their fast response times, safety and design flexibility8,9,10,11,12,13,14, but have lower energy and power densities relative to lithium ion batteries8,15. The use of RFBs has historically been limited to large-scale stationary applications9,16,17, where cost and scalability are more important than portability and form factor.

Here we present an RFB-inspired design that enables a new combination of functions in a mobile robot: hydraulic force transmission, actuation and energy storage for a geometric increase in system-wide energy density. This concept can be generalized to other machines and robots, but here we demonstrate its effectiveness through an untethered, lionfish-inspired aquatic soft robot. This robot contains an energy dense, synthetic vascular system comprised of interconnected zinc iodide flow-cell batteries that supply power to onboard pumps and electronics through electrochemical redox reactions (Fig. 1). Simultaneously, pumping the liquid half-cell transmits mechanical work to the fins, allowing the robot to swim. The complete robotic fish has a system energy density of 53 J g−1 and can swim for long durations (maximum theoretical operating time, 36.7 h; see Methods section ‘Power and energy calculations’) at 1.56 body lengths per minute, upstream. The robot can also fan its pectoral fins, a behaviour that lionfish use to communicate18.

Fig. 1: A lionfish-inspired robot powered by a multifunctional zinc iodide RFB.
figure 1

a, Renderings of the robot with the liquid catholyte in the tail fin (red) and the dorsal and pectoral fins (yellow) highlighted. b, Schematic of the zinc iodide RFB. c, The assembled robot swimming underwater via tail fin actuation. SHE, standard hydrogen electrode.

Our robot’s energy-storage mechanism is modelled after hybrid RFBs, in that the liquid catholyte—the electrolyte that surrounds the cathode—contains a solid species (zinc) that is deposited on an electrode (the anode) during charging. Our device shares many of the advantages of RFBs, including independent control over power density (via the electrode area) and energy density (via the catholyte and total electrolyte volume), design flexibility and low material cost8,9,19,20. Whereas conventional RFB designs are made from rigid materials, our synthetic vascular system contains flexible electrodes and a cation-exchange membrane encased in a soft silicone skin, allowing it to bend (bending stiffness, K = 7.17 N cm2) and dilate to accommodate fin movement. We chose a zinc iodide chemistry owing to its previously demonstrated high energy density (Γ > 200 W h l−1)10 relative to many other RFB chemistries8,21, near-neutral pH and low viscosity. We circumvented the traditional drawbacks of aqueous RFB designs (that is, the lower volumetric power density and operating voltage) by wiring our fin battery cells in series to increase the output voltage and by distributing the battery electrodes throughout the large fin areas (Atotal = 432 cm2) to maximize the overall power density.

Flow battery construction and electrochemistry

Figure 1b shows a schematic representation of our multifunctional battery. Energy is stored between a redox couple of solid zinc in the anode and highly soluble (theoretically up to 7.0 M)11 triiodide \(\left({{\rm{I}}}_{3}^{-}\right)\) in the aqueous catholyte. The zinc is oxidized during discharge, releasing electrons and soluble zinc ions. The electrons flow through the robot’s electronics to the catholyte, powering the microcontroller and pumps that circulate the catholyte solution. The zinc ions simultaneously flow through the electrolyte and cation-exchange membrane to the catholyte, where the triiodide is reduced to iodide, balancing the charge. The circulating catholyte replenishes the local concentration of \({{\rm{I}}}_{3}^{-}{{\rm{/I}}}^{-}\), which maintains a constant power density during cycling. The combination of a solid anode and highly soluble catholyte enables a high theoretical energy density11, Γ ≈ 322 W h l−1 (see Methods), about half that of a Tesla model S lithium ion battery (Γ = 676 W h l−1).

Figure 2 shows a cross-sectional diagram of the tail and pectoral fin actuator cells. We used replica moulding22,23 to create the silicone exterior of the robot, within which we patterned internal channels for fluidic actuation and larger cavities to hold the pumps and control hardware (Extended Data Fig. 1). We used 1-mm-thick pieces of carbon felt (G150, AvCarb) to create the flexible electrodes. We wove nickel wire (0.25 mm diameter) and three-ply stainless steel thread (Adafruit) into the anode and cathode felts, respectively, to improve the electrical conductivity. The resulting anode–felt composite was capable of mechanically supporting electroplated zinc as the active material, and the cathode–felt composite provided an oxidation-resistant high-surface-area electrode for the iodide reaction. We placed a Nafion 115 (Dupont) cation-exchange membrane between the felt composites and used a silicone epoxy sealant (Silpoxy, Smooth-On) to make it watertight.

Fig. 2: Assembly of the fin cell and actuation.
figure 2

a, b, Schematic representations (not to scale) of the tail fin (a) and a pectoral fin (b) with their components labelled. A diagram detailing the actuation mechanisms of each fin is also shown. c, Underwater tail fin actuation. d, Underwater fanning of the pectoral fins.

Fin actuation

Tail actuation (Fig. 2a, c, Supplementary Video 1) was initiated when catholyte was pumped from the left (sinistral) side of the tail to the right (dextral) side. Figure 2a shows how the pumped catholyte pressurizes and inflates the sinistral pleated segments and produces subatmospheric pressure to compress the dextral segments. The opposing pressures provide a torque around the stiffer components at the centre of the robot’s tail, which translates into a bending motion. Cycling the catholyte between the sides of the tail results in a swimming motion that is approximately carangiform in nature24,25.

A separate peristaltic pump controls the fanning of the pectoral fins. The catholyte is stored in the two sets of dorsal fins, which are each linked to either the left or right pectoral fin. As catholyte is pumped from the dorsal fins to the pectoral fins, the influx of liquid pushes the pectoral fins outward from the fish body (Fig. 2b, d, Supplementary Video 2). The movement of the catholyte from the dorsal fin to the pectoral fins reaches a constant flow velocity in under 5 s. The tail fin and pectoral fin RFB cells are separate in this design, and an embedded microcontroller selects the operational pump and also controls the direction of catholyte flow.

Battery cell characterization

We used soft materials in the construction of our battery cells to enable bending and flexing of the fins during actuation without sacrificing power or performance. We determined the bending stiffness of the cells to quantify battery compliance. Sometimes referred to as ‘flexural rigidity’ or ‘flexural stiffness’, bending stiffness, K = EI, is defined as the product of a material’s elastic modulus, E, and its area moment of inertia, I. The bending stiffness of fish bodies and tails has been studied at length to understand their swimming biomechanics26,27. We calculated the bending stiffness of the cells in a simplified geometry by performing buckling experiments on both the batteries and their individual component materials. By measuring the maximum force that initiates buckling, F, we could determine the bending stiffness using Euler’s equation for the buckling of columns,

$$F=\frac{{{\rm{\pi }}}^{2}EI}{{(\alpha L)}^{2}}$$

where α is the column effective length factor and L is the unsupported length of the column. We used the manufacturing techniques discussed previously to create a rectangular battery cell with the same cross-section of materials found within the body of the fish (Fig. 3a, b). Figure 3c shows the buckling data for this composite cell and its component materials. The results for each material are shown in Extended Data Table 1. The bending stiffness of the composite battery cell was K = 7.17 N cm2. Of the component materials, the silicone skin had the greatest bending stiffness, K = 1.13 N cm2.

Fig. 3: Testing the bending stiffness of the battery cells.
figure 3

a, The components of the composite cell testing blank. b, A cross-sectional diagram of the assembled testing blank. c, d, A graph of the measured force versus test grip displacement during buckling testing of the composite cell (n = 8; c) and the individual cell components (n = 8; d). Error bars show 1σ uncertainties.

We characterized the energy-storage performance of our RFB cells using the pelvic fin batteries (Fig. 4a). Figure 4b shows cyclic voltammetry measurements of the 0.1 M ZnI2 electrolyte with 10% ethanol scanned at 50 mV s−1. The −1.1 V and 0.5 V peaks correspond to Zn/Zn2+ and \({{\rm{I}}}_{3}^{-}{{\rm{/I}}}^{-}\) redox pairs. The sharp zinc reduction peak indicates that there is little water reduction, which is important for preventing hydrogen gas buildup. We measured the pelvic fin energy density and power density using galvanostatic discharge at different current densities. Figure 4c shows our measured energy density, Γ ≈ 124 W h l−1, with respect to the volume of the catholyte, at J ≈ 5 mA cm−2 discharge current density. The maximum and average discharge voltages were 1.06 V and 1.00 V, respectively.

Fig. 4: Characterization of the pelvic fin battery cells.
figure 4

a, The pelvic fin battery cell with labelled components. b, Cyclic voltammetry measurements on 0.1 M zinc iodide electrolyte. c, Galvanostatic discharge curve of the pelvic fin battery at 5 mA cm−2. d, Polarization plot. e, Electrochemical impedance spectroscopy, with subscripts Re and Im indicating the real and imaginary parts of Z. Rint, full-cell resistance. f, The fractional increase in the energy density of our system (red) as a function of the electrolytic hydraulic fluid energy density. The effect of different volume fractions of liquid and solid battery is also shown; black, 50:50 and blue, 75:25. The solid battery is represented by a high-energy density (400 W h l−1) lithium ion battery.

To meet the power requirements of the electric pump and onboard electronics (2.05 W; see Methods), we engineered the electrode materials and component spacing to reduce the internal ohmic voltage losses. Figure 4d shows a polarization curve for the pelvic fin cell, which achieved a peak power density of Z ≈ 13.4 mW cm−2. The voltage loss when 0 < J < 15 mA cm−2 is primarily ohmic and is low owing to a full-cell resistance of 0.86 Ω, measured using electrochemical impedance spectroscopy (Fig. 4e). The maximum power density of the robot, normalized by the total fluid volume in the vascular system, was determined to be 19.2 mW cm−3 (see Methods). Figure 4f shows how the inclusion of electrolytic fluid (Γ ≈ 124 W h l−1; volume of the catholyte, Vcatholyte = 0.216 l and density ρ ≈ 1.64 g ml−1) increases the energy density of hydraulically actuated systems; for our system, this increase is more than 325%. The y axis indicates the fractional increase in the total volumetric energy density of our robot relative to an identical hypothetical design that uses a non-energized liquid, for example, water, as its hydraulic fluid (see Methods). This simple model can be modified and applied to other systems infused with electrolytic fluids to evaluate how different design considerations, such as the volume fraction of fluidic and solid energy sources (Fig. 4f), the energy content of those sources and the concentration of electrolyte (Extended Data Fig. 2), may contribute to increases in the system-wide energy density.

We measured the catholyte capacity and coulombic efficiency of our pelvic fin battery after more than 100 h of continuous charge and discharge cycles at J ≈ 4 mA cm−2 (Extended Data Fig. 3). The capacity starts to fade after approximately ten cycles owing to dehydration and catholyte absorption into the silicone. Better encapsulation techniques can solve this issue, as demonstrated by optimized ZnI2 RFBs capable of operating for more than 1,000 cycles28. Using the data collected from the pelvic fin cells, we calculated the maximum operating time of the robot to be 36.7 h during tail fin actuation (see Methods). We expect the swimming performance of the robot to remain consistent during operation because the discharge voltage remains constant for most of the battery’s discharge (Fig. 4c).

Electronics and control systems

Figure 5a, b displays the robot actuation-control components. Power from the battery cells was delivered to either the tail fin pump (MGD1000S-PK-V, TCS Micropumps) or the pectoral fin pump (Yosoo16325, Yosoo) by way of transistor switches connected to the microcontroller (Arduino Uno), which we remotely toggled via a wireless Bluetooth adaptor (HC-05, DSD Tech). During tail actuation, a pump controller (EQi-MG1, TCS Micropumps) that was modulated by the microcontroller alternated the catholyte flow direction. To control the catholyte flow direction in the pectoral fins, we used a double-pole, double-throw (DPDT) relay (RY5W-K, Fujitsu) to alternate the pectoral fin pump polarity. We configured the tubing and the pelvic fin pump to resemble a heart pumping blood through the fish’s body (Fig. 5c).

Fig. 5: Synthetic vascular system schematic and swimming demonstration.
figure 5

a, Block diagram showing the configuration of the pumping, control and electronics components of the robot’s synthetic vascular system. b, One-half of the disassembled robot, showing how the pumps and control hardware are housed internally. c, A peristaltic pump, configured to resemble a heart, transporting catholyte from the dorsal fins to the pectoral fins. d, Untethered swimming demonstration in a salt-water tank.

To power the microcontroller for each of the pumps, we stepped up the combined output voltage of the batteries to 12 V using a boost converter (DD2412SA_12V, Canton Electronics). During testing, we used a 3-V lithium ion battery (a CRV3) in series with the RFB cells to maintain the minimum voltage requirement for the boost converter and to ensure a high power-conversion efficiency. The additional battery allowed more than 5 V to be delivered to the input terminal of the boost converter. However, the battery was not essential to our electronics configuration, and could be replaced by a second, low-input voltage boost converter.

We performed underwater actuation tests with the fully assembled robot in a 200-gallon (about 909 l) salt-water tank. The robot achieved a forward swimming speed of 1.56 body lengths per minute, against a small current from the tank’s water-circulation pump, when the tail fin was actuated (Fig. 5d, Supplementary Video 3). We attached a weight to the underside of the robot to ensure that it was fully submerged in the tank; we believe that the swimming performance of the robot was partly limited by its buoyancy, which was not optimized in this first demonstration study. Future iterations of this design could circumvent this problem with fewer air pockets embedded in the fish body or by filling those pockets with an appropriate ballast material.

Discussion

Our work shows that energy-dense hydraulic liquids can be embedded and circulated within robots to both mechanically actuate and electrically power them, with large increases in the overall system energy density. We implemented this multifunctional, synthetic vascular system into the body of an untethered aquatic robot and demonstrated appreciable swimming speeds against a current via tail fin actuation, as well as the ability to fan the pectoral fins. We used a safe and established zinc iodide RFB chemistry, and measured the maximum energy density with respect to the volume of the catholyte Γ = 124 W h l−1 at J = 5 mA cm−2, the power density Z = 13.4 mW cm−2 at J = 20 mA cm−2, the full-cell resistance (0.86 Ω) and the cycling characteristics of the pelvic fin cells. We also created a compliant (K = 7.17 N cm2) half-flow-cell battery with biologically inspired form factors that comprise the structural elements of the robot, analogous to muscle and cartilage in fish.

We used soft robots to demonstrate this vascularized ‘robot blood’, because they are a versatile platform for illustrating new methods of energy storage and converting energy into motion29,30. Several fish-inspired robots, both fully and partially soft-bodied, have been exhibited previously31,32,33,34,35,36,37,38,39,40; the Massachusetts Institute of Technology’s SoFi31 is notable for its exploration and remote control capabilities and its three-dimensional manoeuvrability. Our work differs from these other robots in that it combines structure, actuation, force transmission and electrochemical energy storage within its synthetic vascular system to create a fully integrated multifunctional design. However, further optimization of the battery chemistry, electronics configuration, hydraulic systems and structural design of the robot will be needed to match the performance of robots like SoFi.

In our design, the actuation force and frequency of the tail fin are limited owing to the pumping configuration, which switches the direction of the pump-shaft rotation to reverse flow. Electronics or different catholyte compositions8,41 that would boost the battery voltage to deliver maximum power to the pumps would increase swimming performance, as would a continuously circulating pump with a flow-reversing manifold that causes a single outlet to flow through many flow channels back into the input of the pump. Additionally, optimized actuator designs and a more hydrodynamic form factor would decrease drag and increase swimming efficiency.

Power density is another area where future design improvements can be made. RFBs with power densities in excess of 1,300 mW cm−2 have been achieved previously through careful optimization of the spacing, thickness, design and configuration of battery components42. Compressing the felt electrodes43, employing smaller actuators with reduced spacing between the electrodes or using optimized current collectors (for example, stacked carbon paper44,45) are additional methods of increasing power density that would maintain the flexibility of our flow cells. Synthetic vascular systems that increase system energy density favour implementation in centimetre-scale actuators or larger, owing to the increases in both the total energy and the actuation amplitude associated with larger electrolyte volumes. Synthetic vascular systems implemented into smaller robots would benefit from higher power density, but would probably require increases in fluidic energy density and improvements in microscale pumps.

Methods

RFB components

The anode and cathode electrodes in the RFB cells were composed of a soft graphite felt (G150, AvCarb) that was cut to the desired form factor and reduced to approximately 1 mm in thickness (25% of the original thickness). For the anode, we wove strands of nickel wire (0.01 gauge Monel, Malin) through the felt to increase electrical conductivity. For the cathode, we similarly wove into the felt three-ply, 316L stainless steel conductive thread (number 641, Adafruit), which was resistant to oxidation from the triiodide in the catholyte. The cation-exchange membrane was composed of Nafion 115 (DuPont) cut to the desired shape. A layer of Sulky Soft ’n’ Sheer fabric (Sulky) was embossed around the perimeter of the membrane using an impulse heat sealer to reinforce the Nafion. Excess fabric was trimmed away before final assembly. Silicone parts were fabricated by mould casting. The moulds were designed in SolidWorks (Dassault Systèmes) and 3D-printed on a polyjet printer (Objet30 Scholar Stratasys) using Veroblue material. After printing, we heated the moulds at 70 °C for 3 h to prevent cure inhibition. Silicone prepolymer (Dragonskin 20 or EcoFlex 30, Smooth-On) was mixed, de-gassed, poured into the moulds, and levelled before curing overnight. To improve the locomotion efficiency of the tail fins, a polyethylene mesh was inserted into the moulds before the silicone was cast to prevent unnecessary stretching (which naturally directs energy away from the desired tail bending). Only areas of the tail fin that, during actuation, remain flexible but do not stretch were reinforced with the mesh.

Catholyte

The catholyte was made with 0.1–3 M zinc iodide in distilled water. 10% ethanol was added to reduce zinc dendrite formation and increase triiodide stability.

Battery assembly

The flexible battery cells were fabricated by assembling an anode, a cation-exchange membrane and a cathode in series. These components were placed into the recessed cavity between two moulded silicone layers that formed the exterior skin of the battery (Figs. 2, 3). The anode and cathode electrodes were free-standing and not attached to the silicone skins, except where the steel thread and nickel wire were threaded through the silicone. The silicone layers with direct contact with the catholyte and that were not stretched during the robot’s actuation were laminated with a polypropylene film. The silicone skins, along with the cation-exchange membrane between them, were compression-sealed together using a silicone epoxy (Silpoxy, Smooth-On). Finally, the catholyte was injected into the cathode compartment of the battery, and the injection holes were sealed with the silicone epoxy.

Mechanical testing

We performed buckling tests using a Zwick Roell z010 instrument to determine the bending stiffness of the battery cell and its component materials. We used the battery assembly procedure detailed previously to create a 10 cm × 5 cm rectangular battery cell with the same cross-section of materials found within the robot. The catholyte was omitted from the battery cell for convenience (see Extended Data Fig. 4 and Methods section ‘Testing the bending stiffness of liquid-infused battery cells’). All tests on the battery and its component materials were conducted at room temperature using a strain rate of 25 mm min−1, a grip-to-grip distance of 50 mm and a preload force of 0.05 N. The composite cell was tested using a 10-kN load cell, and the individual component materials of the composite were tested with a 20-N load cell. The data was averaged across the common strain range and plotted (n = 8) in Origin (Fig. 3c). The peak force (critical load) recorded during buckling was used to calculate the bending stiffness of the materials.

Electronics and robot control

A 6 W, 2–24 V to 12 V d.c. (direct current) step-up/step-down voltage regulator module (DD2412SA_12V, Canton Electronics) was used to increase the output voltage of the battery cells. A standard 3-V CRV3 battery was put in series with the battery cells during actuation tests to ensure that the total voltage of the cells continuously exceeded the 2 V minimum of the voltage regulator module. An Arduino Uno was fitted with a wireless Bluetooth module (HC-05, DSD Tech) and embedded in the body of the robot to allow for wireless control. A 6-V d.c. peristaltic dosing pump (Yosoo16325, Yosoo) was used to transfer the catholyte between the dorsal fins and the pectoral fins. We chose this pump because it does not directly interface with the fluid and can be reversed by changing the motor polarization. A 5-V d.c. DPDT Signal Relay Module (RY5W-K, Fujitsu) was used with the dorsal fins to switch between forward and reverse fanning. A lightweight, self-priming pump (MGD1000S-PK-V, TCS Micropumps) was used for tail actuation. This pump’s high flow rate (500 ml min−1) for its small size (61 mm × 32 mm × 30 mm) made it ideal for our design. We controlled the direction and power of this pump using the EQi-MG1 brushless pump controller (TCS Micropumps). Simple transistors were used as low-power switches for turning each pump on and off.

Charge and discharge methods

We used a Neware CT-3008 as our battery testing system. The battery cells were galvanostatically charged and discharged.

Cyclic voltammetry

Cyclic voltammetry measurements were conducted on a CHI600 workstation (Model 600E, CH Instruments). The voltage was scanned from −1.6 V to 1.0 V versus a Ag/AgCl reference electrode at 50 mV s−1 in 0.1 M ZnI with 10% ethanol. Graphite was used for the working and counter electrodes.

Electrochemical impedance spectroscopy

We conducted electrochemical impedance spectroscopy measurements on a charged pelvic fin battery cell using a 1260A Solartron Impedance Analyzer from 0.1 kHz to 50 kHz.

Catholyte and cation-exchange membrane design specifications

The total area of the battery cell membranes (Nafion 115) in the tail fin system was 216 cm2. The left and right sides of the tail fin cell had membrane areas of 70 cm2 each, and the left and right pelvic fin cells, which are electrically connected to the tail, had membrane areas of 38 cm2 each. The total area of the battery cell membranes in the dorsal–pectoral fin system was, as for the tail fin system, also 216 cm2. The left and right pectoral fin cells had membrane areas of 54 cm2 each, as did the left and right dorsal fin cells. The total area of the battery cell membranes in the robot was 432 cm2. The total area of the anode and cathode electrodes was thus 864 cm2.

The total catholyte volume in the robot (Vcatholyte) was 0.216 l. This volume was divided evenly between the tail fin system and the dorsal–pectoral fin system (0.108 l each). The total anolyte volume in the tail fin system was 0.043 l. (Here, anolyte refers to the non-flowable electrolyte housed in the anode half-cell to facilitate ion and electron transfer.) Similarly, the total anolyte volume in the dorsal–pectoral fin system was 0.043 l. The total volume of ZnI2 electrolyte in the robot was thus 0.302 l.

Power and energy calculations

The maximum power density of the pelvic fin battery cell, serving as a surrogate for the entire robot, was determined to be 13.4 mW cm−2 (Fig. 4d). When normalized for the total electrolyte volume within the battery cells, the power density was calculated to be (13.4 mW cm−2 × 432 cm2)/302 cm3 = 19.2 mW cm−3. The total energy content of the catholyte was calculated to be 124 W h l−1 × 0.216 l = 26.784 W h. Using reported specifications, the total energy content of the CRV3 battery was calculated to be 2,700 mA h × 3 V = 8.1 W h. The total energy content of the robot was consequently 34.884 W h, or approximately 126 kJ. The total dry mass (excluding any onboard batteries or energized fluid) of the robot was measured at 1.844 kg. Including the CRV3 battery and the ZnI2 electrolyte, the mass of the robot was estimated to be 2.38 kg. The energy density of the entire robot was therefore (126 kJ/2.38 kg) ≈ 53 J g−1.

The maximum theoretical energy density of a ZnI2 solution is 332 W h l−1 at the solubility limit of ZnI2 in water. This is approximately half the 676 W h l−1 maximum energy density of a Tesla Model S lithium ion battery (see https://www.batteryspace.com/prod-specs/NCR18650B.pdf).

During tail fin actuation, the power consumption of the tail fin pump was calculated to be 5 V × Itailpump = 1.25 W, where Itailpump = 0.25 A is the current in the tail fin pump. The power through the electronics is [5 V × (2Itransistor + 2Ipins + IArduino)]/0.8 = 0.58 W, where Itransistor = 0.0036 A is the current in each of the transistors, Ipins = 0.02 A is the current in each of the two Arduino pins, IArduino = 0.045 A is the current in the Arduino and 0.8 is a factor resulting from the 12-V boost efficiency. The total power required for tail fin actuation was therefore 1.25 W + 0.58 W = 1.83 W. The current through each tail fin cell was calculated to be 1.83 W/5 V = 0.365 A. This gives a current density in the tail fin battery of 0.365 A/216 cm2 = 1.7 mA cm−2 (compared to approximately 20 mA cm−2 at peak power, see Fig. 4d). With an average battery discharge of about 1 V and a peak catholyte energy density of about 124 W h l−1 (Fig. 4c), the total operating time of the robot during tail fin actuation, with respect to the volume of catholyte, is therefore (124 W h l−1 × 0.108 l)/(0.365 A × 1 V) = 36.7 h.

During pectoral fin actuation, the power through the pectoral fin pump was calculated to be 5 V × Ipectoralpump = 0.5 W, where Ipectoralpump = 0.1 A is the current in the pectoral fin pump. In a similar fashion to above, the power through the electronics was calculated to be [5 V × (Itransistor + IDPDT +2Ipins + IArduino)]/0.8 = 1.55 W, where values are as described above, IDPDT = 0.16 A is the current in the DPDT and 0.8 is again a factor resulting from the 12-V boost efficiency. Therefore, the total power required for pectoral fin actuation was 1.55 W + 0.5 W = 2.05 W. The current through each cell of the dorsal–pectoral fin system was 2.05 W/5 V = 0.41 A. This gives a current density throughout the dorsal–pectoral fin battery of 0.41 A/216 cm2 = 1.9 mA cm−2 (compared to about 20 mA cm−2 at peak power). With an average battery discharge of about 1 V and a peak catholyte energy density of about 124 W h l−1 (Fig. 4c), the total operating time of the robot during pectoral fin actuation, with respect to the volume of the catholyte, was calculated to be (124 W h l−1 × 0.108 l)/(0.41 A × 1 V) = 32.7 h.

Fractional increase in energy density from electrolytic hydraulic fluid

The equation used to calculate the increase in energy density associated with the inclusion of an electrolytic hydraulic fluid is as follows:

$${\rm{F}}{\rm{r}}{\rm{a}}{\rm{c}}{\rm{t}}{\rm{i}}{\rm{o}}{\rm{n}}{\rm{a}}{\rm{l}}\,{\rm{i}}{\rm{n}}{\rm{c}}{\rm{r}}{\rm{e}}{\rm{a}}{\rm{s}}{\rm{e}}=\frac{{\Gamma }_{+{\rm{e}}{\rm{n}}{\rm{e}}{\rm{r}}{\rm{g}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{f}}{\rm{l}}{\rm{u}}{\rm{i}}{\rm{d}}}^{{\rm{s}}{\rm{y}}{\rm{s}}{\rm{t}}{\rm{e}}{\rm{m}}}}{{\Gamma }_{-{\rm{e}}{\rm{n}}{\rm{e}}{\rm{r}}{\rm{g}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{f}}{\rm{l}}{\rm{u}}{\rm{i}}{\rm{d}}}^{{\rm{s}}{\rm{y}}{\rm{s}}{\rm{t}}{\rm{e}}{\rm{m}}}}=\frac{({\Gamma }_{{\rm{f}}}{V}_{{\rm{f}}}+{\Gamma }_{{\rm{s}}}{V}_{{\rm{s}}})/{V}_{{\rm{t}}{\rm{o}}{\rm{t}}}}{({\Gamma }_{{\rm{s}}}{V}_{{\rm{s}}})/{V}_{{\rm{t}}{\rm{o}}{\rm{t}}}}-1$$

This quantity represents the ratio of energy densities between our proposed robot design, and an equivalent, identical design that uses a non-energized hydraulic fluid. This relationship isolates the energy density increase attributed to just the electrolytic hydraulic fluid. Here \({\Gamma }_{+{\rm{e}}{\rm{n}}{\rm{e}}{\rm{r}}{\rm{g}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{f}}{\rm{l}}{\rm{u}}{\rm{i}}{\rm{d}}}^{{\rm{s}}{\rm{y}}{\rm{s}}{\rm{t}}{\rm{e}}{\rm{m}}}\) is the energy density of a system with electrolytic hydraulic fluid; \({\Gamma }_{-{\rm{e}}{\rm{n}}{\rm{e}}{\rm{r}}{\rm{g}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{f}}{\rm{l}}{\rm{u}}{\rm{i}}{\rm{d}}}^{{\rm{s}}{\rm{y}}{\rm{s}}{\rm{t}}{\rm{e}}{\rm{m}}}\) is the energy density of a system without electrolytic hydraulic fluid, where a non-energized fluid (for example, water) is used for hydraulic actuation; Γf is the energy density of the electrolytic hydraulic fluid (124 W h l−1 in this work); Γs is the energy density of the solid battery components (400 W h l−1 is used for each calculation in Fig. 4f); Vf is the electrolytic fluid volume or volume fraction when normalized (91% in our system); Vs is the solid battery volume, or volume fraction when normalized (9% in our system); and Vtot is the total volume of the actuation and energy storage components of the robot or system of interest.

The value 1, or 100%, is subtracted from this term so that it represents a fractional increase relative to \({\Gamma }_{-{\rm{e}}{\rm{n}}{\rm{e}}{\rm{r}}{\rm{g}}{\rm{i}}{\rm{z}}{\rm{e}}{\rm{d}}\,{\rm{f}}{\rm{l}}{\rm{u}}{\rm{i}}{\rm{d}}}^{{\rm{s}}{\rm{y}}{\rm{s}}{\rm{t}}{\rm{e}}{\rm{m}}}\) (for example, a result of 1 when evaluating the above equation indicates a 100% increase—a doubling—of the energy density of the system). This equation can be adapted to calculate the fractional increase in energy density for other electrolytic hydraulic systems with, for example, different electrolyte and solid battery volumes (as shown in Fig. 4f), different solid battery energy densities (by varying Γs), different electrolyte energy densities (by varying Γf) and concentrations (as shown in Extended Data Fig. 2).This equation also gives insight into the design considerations and trade-offs associated with different hydraulic system configurations. As an example, the addition of solid batteries to our hydraulically powered device would increase the total energy content of the device (while decreasing the fractional increase in energy from the electrolytic hydraulic fluid), but this would also greatly diminish the dexterity of our robot. A larger volume fraction devoted to solid battery structure would increase weight and decrease actuator amplitude (owing to a reduction in hydraulic fluid). At a certain point, we would need to add additional structures to the robot to support the added weight of the solid batteries, which would further result in sub-linear scaling of energy density. Using a larger volume fraction of electrolytic fluid, as we show, allows for larger actuation amplitudes and more complicated locomotion manoeuvres, without large increases to the weight of the device. However, the lower energy density of the electrolytic fluid, relative to solid lithium ion batteries, also results in a reduced total energy content. Future applications of our synthetic vascular system should be informed by these design trade-offs.

Testing the bending stiffness of liquid-infused battery cells

Figure 3 shows the bending stiffness data for a composite battery cell and its component materials. During these tests, we omitted the catholyte from the battery cell owing to the risk of damaging the electronics of the compression testing device in the event of a leak. We acknowledge, however, that the addition of an incompressible fluid to our test cells would probably increase the stiffness of those cells.

We conducted an additional buckling experiment; the results of which are displayed in Extended Data Fig. 4. In this experiment we carefully injected an appropriate volume of water into the battery test cells to simulate the presence of the ZnI2 catholyte solution. When the cell was filled with water, a number of imperceptibly small leaks became visible at the edges of the composite cell, where the two silicone layers and the Nafion 115 membrane were previously attached with silicone epoxy. We sealed these leaks with a minimal amount of silicone epoxy which, upon drying, is stiffer than any individual element of the battery cell. This step was necessary to ensure that no liquid escaped during the buckling tests (n = 8), because this would have affected our data and potentially damaged our testing device.

The average force F in buckling was determined to be 12.54 N, which gives a calculated bending stiffness value of 7.94 N cm2. This presents a roughly 10% increase on the calculated value of 7.17 N cm2 for the composite cell without the added liquid. We observed that the flexible silicone (Dragonskin 20, Smooth-On) comprising the outer layer of the cells is capable of expanding to accommodate displaced fluid while maintaining the same internal volume during buckling. As a result, the encapsulated liquid does not dramatically increase the stiffness of the cells. We also believe that the added silicone epoxy contributed at least in part to the observed increase in the stiffness of the cells. Considering these associated measurement errors, we are unable to precisely quantify the increase in stiffness owing to the presence of liquid in the battery cells, although we are confident that the stiffness probably increases with the addition of the liquid.

Statistical information

Sample size, mean and standard deviation are reported for all datasets where applicable. No statistical methods were used to predetermine the sample sizes for stiffness testing or battery performance characterization. All statistical analyses were performed in Microsoft Excel (Excel for Mac, version 15.25, 2016) and Origin (Academic Version, 2016).