Solar‐Driven Soft Robots

Abstract Stimuli‐responsive materials have been lately employed in soft robotics enabling new classes of robots that can emulate biological systems. The untethered operation of soft materials with high power light, magnetic field, and electric field has been previously demonstrated. While electric and magnetic fields can be stimulants for untethered actuation, their rapid decay as a function of distance limits their efficacy for long‐range operations. In contrast, light—in the form of sunlight or collimated from an artificial source (e.g., laser, Xenon lamps)—does not decay rapidly, making it suitable for long‐range excitation of untethered soft robots. In this work, an approach to harnessing sunlight for the untethered operation of soft robots is presented. By employing a selective solar absorber film and a low‐boiling point (34 °C) fluid, light‐operated soft robotic grippers are demonstrated, grasping and lifting objects almost 25 times the mass of the fluid in a controllable fashion. The method addresses one of the salient challenges in the field of untethered soft robotics. It precludes the use of bulky peripheral components (e.g., compressors, valves, or pressurized gas tank) and enables the untethered long‐range operation of soft robots.


Additional Experimental Information
The spectral power density of thermal electromagnetic radiation from a hot object, such as the sun, is governed by Planck's law of black-body radiation. To estimate the total power per area that a hot object radiates, we can integrate the spectral irradiance profile with respect to the wavelength. Similarly, by multiplying the spectral irradiance by the spectral absorption of the solar absorber film (equation 1), we can estimate the absorbed power per area of the film from the following: where λ is the wavelength, I(λ) is the spectral irradiance with a unit of W/m 2 /nm, and α f (λ) is the spectral absorption profile of the solar absorber film. From the solar spectral irradiance (direct+circumsolar AM 1.5) (1), we estimated the solar power density to be 1 kW/m 2 . This power density diminishes by a large factor in shadow or indoor environments. To simulate the solar spectrum for indoor experiments, we used Xenon (Xe) lamps. As shown in Figure S1, the irradiance spectrum of a Xe lamp is similar to the solar spectrum. Mercury-Xenon (HgXe) lamps offer a wider bandwidth but are more expensive than Xenon lamps. From the spectral irradiance profile of a 35 W, 75 W, and 150 W Xe lamp ( Figure   S1), we estimated the output power (at 50 cm) for each to be 3.53 W/m 2 , 10.45 W/m 2 , and 24.55 W/m 2 , respectively. By curve fitting the irradiance vs. input power data, we found the irradiance (at 50 cm) for a 55W Xe lamp to be 6.85 W/m 2 . This irradiance is almost 140 times smaller than that of the sun.
To enhance the intensity, we used a high beam headlight reflector with a diameter of 80 mm. Assuming the spectral irradiance is measured at r o (50 cm in our case) and the radius of the reflector is r r , we can find the amplification gain (G) of the reflector to be: (2) Evaluating equation 2 at the edge of the reflector gives us a gain of about 625, which yields an irradiance of about 4281 W/m 2 , more than four times than that of the sun. Radiation from the Xe lamp is in the form of a sphere. When placed in the axis of the reflector (parabolic in this work), the reflector reflects only a portion of the radiation. Therefore, the light is not a perfect collimated beam. Our measurements show that the light disperses as a function of distance from the reflector, as illustrated in Figure S1C. To better estimate the illumination intensity of the Xe lamp as a function of the distance from the device, we used the data in Figure S1C for the r r in equation 2. The experiment setup consisted of the device (with the soft robots) held by a clamp and a Xe lamp at a certain distance from the device. As shown in Figure S1D, the vapor pressure increases and pushes the liquid to the soft robots upon excitation. continuous-mode lamps (courtesy of Hamamatsu Photonics K.K.). (B) Irradiance vs. input power for a 35W, 75W, and 150W Xenon lamp measured at 50 cm without a reflector. The irradiance for a 55W Xe lamp (red square dot) is estimated from the curve fit to be around 6.85 W/m 2 . (C) Illumination radius of a Xe lamp as a function of distance from the reflector. Inset: thermal power measurement with a thermal power meter (Thorlabs S322C). At a short distance, there is about 10% difference between thermal power of the brightest spots (solid points) and darkest spots (hollow points) from the average coming from the beam. At a far distance, the difference from the average decreases to almost 3%. (D) The setup for actuation of the soft robotic prototypes. For the purpose of imaging the setup in one frame, the Xe lamp was placed very close to the device. We implemented a low-level control scheme in the actuation space to control the pressure of soft robot prototypes. Figure S2 shows the state machine and software flow of the device. Once the sensor and motor are initialized, the device enters the main loop where the pressure is continuously read. Based on the two upper and lower threshold pressure values, the microcontroller decides whether to rotate the motor to a 90 • position or a 0 • position. For the controller to be activated, the pressure must surpass the upper threshold limit once.    We can greatly simplify our solar-driven pressure chamber by assuming all its components (e.g., fluid, syringe, sensors, solar absorber, condenser) are at a same temperature T . By assuming an isothermal system, we reduce the complexity of the 3-D system to a simpler 1-D lumped capacitance system, which can more readily be solved for analytically. We first present our general modeling framework for the pressure chamber connected to a soft robotic gripper and then simplify it for the closed the closed pressure chamber. We start by setting a control volume around the pressure chamber (see Fig.S3). This control volume cuts through the connection with the soft robotic grippers, allowing to account for fluid outflow/inflow to/from a soft robotic gripper. Next, we apply the time-dependent first law for an open system to the whole pressure chamber, the ideal gas law to the gas layer and conservation of volume to the fluid and vapor system. The equations are presented below: First law for an open system: Where E syst is the control volume's internal energy, t is time,Q is the total thermal energy supplied to the system,Ẇ is the total work done by the system,ṁ in, out is the mass flow rate in and out of the system respectively and u, V and gz are the internal, kinetic and potential energies respectively. In the absence of a flow input, we have neglected the mass input to the systemṁ in . The individual terms in Eq. 3 can be further expanded into: where m i and c p,i are the mass and heat capacity of each components i of the system, h fg is the fluid's latent heat of vaporization, q sun is the solar or light flux, A is the surface area, τ syr is the transmittance of the syringe, α abs is the absorber absorbance, h conv is the convection coefficient with the ambient air (natural convection), is the surface emissivity,Ẇ s is the shaft work done by the system, P is the chamber's pressure, ρ is the density. The subscripts f and g refer to the fluid's liquid and gaseous phases respectively, abs refers to the absorber, syr refers to the syringe, cond refers to the condenser and amb refers to the ambient. Kinetic and potential energy are neglected due to the relatively slow velocity of the fluid at the output of the chamber and the small system dimensions.
Ideal gas law (for gas layer only): where V g is the gaseous phase volume on top of the fluid, R is the gas constant and M is the fluid's molar mass.
Volume Conservation: To account for the thermophysical properties of the fluid as well as the properties of the soft robotic grippers, the following equations were also used: Equation 11  We may combine the three main equations (Eqs. 3, 9 and 10) along with the set of other thermophysical properties equations to obtain a set of three differential equations with three unknowns T , m f and m g . We can numerically solve for this set of differential equations in MATLAB to obtain the time dependent temperature T and the fluid (m f ) and gas (m g ) masses. A similar approach is used in the case of the closed pressure chamber (no soft robotic gripper attached), although several equations must be changed to account for the change of an open system to a closed system.
Similarly to the open system case, the system of equations can be solved for numerically in MATLAB.
A summary of the assumptions made in the developing the model are listed below: • Isothermal system: All components (fluid, gas, glass syringe, sensors and condenser) are at the same temperature T .
• The system's masses and dimensions are taken from the experimental setup.
• The convective heat transfer coefficient (h conv ) is estimated from a lumped capacitance model during the cooling of the system from an initial above ambient temperature .
• Kinetic and potential energy are neglected.
• All thermophysical properties of the fluid are taken at 25 • C, except for the fluid vapor pressure.
• The fluid vapor pressure is fitted with a quadratic equation in the temperature range 16 • C to 40 • C for simplicity.
• The robotic gripper volume vs pressure relation is approximated as a Gaussian relation from experimental characterization.
• Diffusion kinetics of the fluid vapor in the gas volume are assumed to be much faster than the evaporation rate (i.e., uniform fluid vapor concentration in the whole gas volume). A 3-D numerical model was also built in COMSOL to validate our simpler analytical model and its assumptions, as well as give additional insights into the performance of the real device. Figure S4 shows the simulation domain corresponding to the pressure chamber in COMSOL. Using symmetry in the device (YZ and XZ planes), only a quarter of it was modeled to save computational time. The model couples heat transfer and laminar fluid flow to account for the effects of natural convection within the fluids (liquid and gas domains).

3D numerical model
The input solar flux was modeled as a boundary heat flux at the solar absorber.
Heat losses from the syringe and the condenser to the ambient were modeled using natural convection and radiative heat transfer. The heat transfer coefficients, the surface emissivity, the ambient temperature and the system's initial temperature (assumed isothermal) were set equal to that of the experiments. The volume of the liquid and gas phases are fixed, assuming negligible fluid evaporation. As such, evaporative heat flux at the liquid/vapor interface was also neglected. The model was solved using a time-dependent solver to capture the transient response of the system. The model's output are the time-dependent temperature profile and the fluid and gas velocity profiles. For comparison with the experiments, the fluid temperature was probed at the center of the syringe as well as 2.15 cm below and above.