A Non-Newtonian Fluid Robot

Recent developments in robotics and associated fields such as materials sciences and engineering have led to a paradigm shift towards unconventional robots inspired by living organisms and their properties and capabilities [2,,–5, 7, 8]. Such robots are highly adaptable for tasks in challenging environments. For example, soft, solid-state robots fabricated from elastic polymers and devoid of hard parts or joints could potentially withstand high mechanical loads and survive crushing and bending forces lethal to conventional machines.

However, the living organisms that inspire these robots are still largely constrained by structural and functional biological barriers. For example, skins and exoskeletons, which protect the integrity and chemical composition of organisms, substantially limit their morphological flexibility. Moreover, even organisms devoid of skeleton (Mollusca) tend to adhere to well-defined outlines and shapes, and while resilient to bending and crushing, they are highly vulnerable to cutting and shearing forces. These faults could impair the survivability of robots designed to operate in highly dynamic or hostile environments in which the conditions cannot be predicted a priori. But they could be addressed by shifting to nonliving matter as the source of inspiration for robots with a radical, distinctly non-biological set of behaviors and capabilities. In this work we have focused on fluid dynamics as a paradigm for this challenge.

Some properties required of a robot, such as motion and the ability to perform mechanical work, are natural to fluids; others, such as automatic actuation in response to cues, are less trivial. Most importantly, reliable and reproducible control of unbound fluids at high Reynolds numbers is extremely challenging. The mechanical properties and behavior of Newtonian (or approximately Newtonian) fluids, such as water under standard conditions, are largely invariant under applied forces and most other environmental cues. However, in contrast, non-Newtonian fluids exhibit diverse, peculiar behaviors deriving from the nonlinear relation between fluid deformation rate and shear stress, which is particular to each system [9]. The physics underlying properties of non-Newtonian fluids, such as shear thinning or thickening, is still only partly understood [1]. Despite that, as in other fields, incompleteness of theoretic understanding does not prevent successful implementation; hence, it is possible to assemble specific components to yield a non-Newtonian fluid with the desired properties in a manner analogous to programming a robot for a specific purpose. In the present study we designed a non-Newtonian fluid robot and studied its responses in various programming contexts.

To prove the feasibility of a non-Newtonian fluid robot that can be reliably and reproducibly fabricated and controlled, we examined various fluids with diverse compositions. For our prototype we chose a colloidal dispersion of starch microparticles in an aqueous fructose solution (concentration 58% w/v; mean particle diameter 6.41 μm; see  Appendix 1), to which shear strains were anisotropically applied through the surface by a 4 × 4 array of individually controlled audio transducers (Figure 1). To construct the control apparatus, the following parts were used: speakers (10-cm diameter, 40 W, 8 Ω), a Hewlett-Packard 33120A signal generator, 90-W AST 4x25 amplifiers, mini DVR cameras (25 fps), a digital video recording system, an oscilloscope (Agilent Technologies DSO1052B, 50 MHz, two-channel), and a Sensemode™ voltage sensor and data transceiver. The surface was made from standard artist canvas sheets (50 cm × 50 cm with wooden frame).

In order to reliably and reproducibly control the fluid robot, we preferred an empirical approach over simulations, and iteratively sought transducer usage sequences that manipulated the fluid as desired. We quickly observed that audio waves at specific outputs and frequencies created clearly visible viscosity gradients within the fluid, which drove the robot in the downhill direction between arbitrary points on the surface (Figure 2a,  Appendix 2, and Videos S1–S3, which can be found at www.mitpressjournals.org/doi/suppl/10.1162/ARTL_a_00194). At higher velocities produced by higher strains, the robot was significantly more condensed and rigid (Figure 2b–d; images were computationally analyzed as described in  Appendix 3). Repetitive experiments demonstrated that although the fluid could not be controlled to the extent of identical replication of previous shapes and trajectories, its statistical behavior was highly reproducible.

The described layout divides a 0.36-m² area into 16 auxels (audio pixels) of 225 cm² each. Even at this low spatial resolution, the fluid robot could be accurately controlled with minimal transducer utilization. For example, we found that the minimal number of transducers required for driving the robot along a straight path is two, and that this pair of transducers was sufficient to drive the robot across the entire surface length ( Appendix 5). Smaller auxels and alternative layouts (e.g., honeycomb arrayed auxels) could likely allow finer tuning of robot behavior.

Most robots are designed with the ability to do some form of mechanical work. We therefore investigated the ability of the fluid robot to carry loads that are significantly heavier than itself—in this case, metal weights. Our initial studies showed clear reduction in the velocity of the robot upon contact with the target weight (e.g., from 1 cm/s to 0.32 cm/s), indicating that a viscous drag force is created between the robot and the weight. Our calculations yielded a drag force of 0.07 N, which (assuming an object-to-surface kinetic friction of ≈0.4, and for a robot of the size used here and of the same colloidal dispersion) is sufficient to carry objects of ≈176 g—almost 6-fold heavier than the robot itself. This was confirmed by our measurements, in which the reduction in velocity of the loaded robot is visible (Figure 2e, Video S4 in the Online Supplement). Although the drag coefficient is not constant, our measurements were in good agreement with an approximation of the drag equation based on constant C_D (Table 2 in  Appendix 2). Analysis of robot locomotion using side-mounted cameras revealed a distinct behavior observed in all experiments, involving the robot's leading end (head) assuming a hump shape, sometimes up to 10-fold higher than the robot's tail (Figure 3a). Our video analysis showed that the tail (the rear part relative to the motion vector) remains consistently fluid throughout the experiment and continuously moves towards the head, which compresses and thickens as a result. This enables the tail fluid to physically climb on top of the head, creating the hump, which was consequently prominent when acceleration was high ( Appendix 2).

A fluid can change shape in ways that are impossible for living organisms, but may be highly desired in various settings. The morphological diversity of the fluid robot is limited mainly by surface tension, which depends on volume and composition and could be readily programmed by proper fluid assembly. The surface tension and thus the volume must be kept within a limited range, robots beneath it being too rigid and brittle to control, and ones above it too large to maintain integrity; but within this range the fluid exhibited remarkable shape flexibility, including changing aspect ratios and expanding its surface area by a factor of approximately 36 (Figure 3b, Video S5 in the Online Supplement). In addition, the robot can be split by vibration directed perpendicularly at the center of mass into two or more separate smaller robots, so long as none of them falls beneath the lower volume threshold. The parts can be controlled individually and be driven to merge to form a single robot again (Figure 3c, Video S6 in the Online Supplement). Similarly, the robot can percolate through porous barriers and gratings (Figure 3d, Videos S7, S8 in the Online Supplement).

We were interested in the possibility of programming the robot to exhibit the equivalents of computational and logic primitives. One straightforward example is to set the robot to function as a finite counter, halting or changing behavior when the defined sum has been reached. In this example the input can be matter directly absorbed by the robot, changing its chemical composition and subsequently its fluid behavior. To demonstrate this, we used aluminum oxide dough packets as input bits, and programmed the robot to halt upon absorbing three discrete packets out of four. This was done by assembling a robot that would become too rigid following the assimilation of exactly three packets (Figure 4a, Video S9 in the Online Supplement). Similar behaviors could be achieved with robot–robot collisions rather than robot–bit collisions.

This possibility leads to an attractive feature of fluid robotics: the integration of logic and chemistry, a concept raised previously in microfluidic systems with bubbles functioning as bits that carry chemical payloads [6]. As a proof-of-concept experiment we chose the carbodiimide-mediated cross-linking of amine-modified DNA with a protein. In this reaction, the carbodiimide reacts with carboxylic acid groups in the protein (mainly on the acidic amino acids aspartic acid [Asp/D] and glutamic acid [Glu/E]), forming an active O-acylisourea intermediate that is then displaced by nucleophilic attack from the primary amines on the modified DNA strands. The primary amine forms an amide bond with the original carboxyl group, and a carbodiimide by-product is released as a soluble urea derivative. Three discrete robots (volume of 10 mL each) carrying the reaction components—protein, amine-modified DNA, and the crosslinker (1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC), at a 1 : 10 : 5000 molar ratio, respectively—were driven to collide in a stepwise manner, with robot movement providing constant mixing. The entire experiment was performed at room temperature. Successful synthesis of the product was confirmed by solid-phase flow cytometry and spectrophotometry (Figure 4b).

Contemporary works in the field of unconventional robotics draw from a wide range of biological shapes and mechanisms of actuation. While all these robots exhibit peculiar capabilities, more diverse than those of conventional ones, they still adhere to the basic physics and architecture of living bodies, which constrains their behavior. For example, all living systems, from the single cell to complex organisms, have barriers protecting their internal environment from the outer one, such as membranes and skins, which crucially limit the shape diversity that a living organism can assume. Moreover, any organism has to maintain its structural integrity to prevent injury or death. Interestingly, bio-inspired robots inherit these constraints through their design, and they too must remain intact in order to remain functional and usually do not change their shape profoundly. This raises the question whether radically different designs of robots exist that are free of these limits, and could accordingly carry out tasks that are challenging for more conventional robots.

In this work we report a proof of concept for a reliably and reproducibly controlled robot based on the properties and behaviors of non-Newtonian fluids. Using non-Newtonian fluids as the basis of this design was crucial to enable arbitrary control over shape and motion, which was easily obtained by using audio waves created by the user. We describe here a “program” as a graphic representation of a temporal sequence of transducer outputs leading to a specific behavior ( Appendices 4– 5).

Although the physics of non-Newtonian fluids is still not well understood, it is possible to utilize the known observed behaviors and responses of these fluids in the design of robotic devices. We used an empirical approach to assemble a non-Newtonian fluid with the desired set of properties as well as to define control profiles for various tasks. No simulations were used in this process, but rather iterative trial and error, in which fluid composition was measured by observed performance in a process of directed evolution. Similarly, the control profiles were written after systematic evaluation of how the fluid responds to different spatiotemporal audio patterns. We believe that improved understanding of non-Newtonian fluids in the near future will simplify this process and enable reliable prediction of the behavior of specific compositions and their responses to specific audio wave patterns, and bring this process closer to conventional programming.

Fluid robots could have many interesting applications, and our study raises some interesting directions. For example, it highlights the fascinating possibility of utilizing fluid robots as components in a large, complex chemical assembly line. In this regard, further work could produce robots with specialized functions such as waste removal, affinity chromatography, dialysis from robot to robot, and more. The surface itself could include regions with heating or cooling, fluid guides and splitters, and similar topography-based rather than strain-based controls. Fluid robots could find applications in search and rescue tasks. For example, fluid robots could percolate and drip into areas where access is highly limited, such as the debris of collapsed buildings or mines, merging again below to form a robot that could carry weights and perform work.

Using audio waves to guide the robot on a surface might seem an essential flaw of the system, limiting its potential use to surfaces through which audio waves can be transmitted. However, further studies could likely extend the current design in many ways. Fluid robots can be controlled by unidirectional audio beams transmitted from commercially available devices. They can be driven to crawl upwards on inclined surfaces and climb to higher areas onboard continuous surfaces. The current proof-of-concept study did not attempt to assemble fluids with additional properties, such as magnetic or charged fluids which could be controlled by magnetic and electric fields orthogonal to mechanical shear forces. Overlaying similar modes of control would likely lead to very elaborate and capable designs.

Finally, further studies into mechanical devices made of non-Newtonian fluids could elucidate much of the physics underlying non-Newtonian fluid dynamics, and lead to improved designs with higher capabilities than the prototype presented here. It would be interesting to design fluid robots coated with a cell-inspired lipid bilayer, which could provide desired properties such as reducing water loss by evaporation, hydrophobic or electrostatic repulsion between robots, or even primitive mechanisms for self–nonself recognition, when two or more populations of robots navigate and operate in parallel within the same system, avoiding incidental mixing. In this regard, fluid robots could show unexpected similarities to primitive life forms.

The authors wish to thank Larisa Zlatin, Sivan Friedman, and all members of the Bachelet lab for valuable discussions and technical assistance.

The final assembly protocol for robots was as follows: 58% w/v starch microparticles (Figures 5–6), 7.15% v/v fructose-glucose solution (40% w/v fructose, 27% w/v glucose in DW), 7.15% v/v color solution (as described below). Color was introduced to enhance robot contrast for video analysis. See Table 1 and Figure 7.

See Table 2 and Figures 8 and 9.

Video footage was analyzed by a custom-made MATLAB (Mathworks, R2013a) code, which uses the image-processing toolbox for extracting velocity, area, and path.

Recorded information was integrated graphically into the videos by our code. Each speaker is represented by a circle in proximity to its original location as it appears in the video. An active speaker appears in a red color in a shade related to the speaker intensity. The red shades are divided into 10 levels. Assumed maximal speaker intensity of 900 V; thus every red level represents 90 V. The higher the intensity, the stronger the red color.

We used the following algorithm to calculate the aspect ratio of the spot.

As a preprocessing step before analysis, we converted each frame to a binary image to distinguish between the spot and the background. After detecting the spot, we were able to use MATLAB image-processing toolbox built-in functions to find its center and its area in each frame. Those functions get a binary image of an object and return the object's center in a 2D coordinate, and the area in pixels.

For calculating velocity we sampled two centers from two consecutive seconds and calculated the Euclidean distance between them. For calculating area per second and center per second we averaged the areas and the centers, respectively, obtained for an entire second. This appears in the following pseudocode:

See Figures 10,¹¹–12.

Scheme 1: A→B movement experiments: See Figure 13. A robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface at point A, yielding a robot ≈10 cm in diameter. Transducers 2 and 3 were activated in pulses for 30 s on average (time changes slightly between experiments) until the robot reached the third speaker lane. Transducers 10 and 11 were then activated in pulses for a time length of 10 s on average up until the robot reached point B. Transducers 2 and 3 were to remain active all the time.

Scheme 2: A→B→A experiments: See Figure 14. As in the A→B experiments, a robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface at point A, yielding a robot ≈10 cm in diameter. Transducers 2 and 3 were activated in pulses for 30 s on average (time changes slightly between experiments) until the robot reached the third speaker lane. Transducers 10 and 11 were then activated in pulses for a time length of 10 s on average up until the robot reached point B. At this point, all transducers were shut off, and transducers 14 and 15 became active for ≈30 s on average. After the robot reached speaker lane 2, transducers 6 and 7 were activated in the same manner as before for ≈10 s on average, pushing the robot back to point A.

Scheme 3: A→B→C experiments: See Figure 15. A robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface at point A, yielding a robot ≈10 cm in diameter. Transducers 2 and 3 were activated in pulses for 30 s on average (time changes slightly between experiments) until the robot reached the third speaker lane. Transducers 10 and 11 were then activated in pulses for a time length of 10 s on average up until the robot reached point B. At this point, all transducers were shut off, and transducers 11 and 15 became active for ≈20 s on average up until the robot reached point C.

Scheme 4: Load-carrying experiments: See Figure 16. A robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface at point A, yielding a robot ≈10 cm in diameter. A 100-g weight was placed upon the surface 10 cm in front of the robot. Transducers 2 and 3 were activated in pulses for ≈20 s on average (time changes slightly between experiments) until the robot reached and engulfed the weight. The transducers were kept on for ≈20 s more on average, until reaching line 3. Transducers 10 and 11 were then activated in pulses for a time length of 10 s on average up until the robot reached point B.

Scheme 5: Splitting and re-merging experiments: See Figure 17. A robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface between transducers 1, 2, and 5, yielding a robot ≈10 cm in diameter. Transducers 1, 2, and 5 were activated all at once for 10 s until the robot split into two parts. Transducer 5 was activated in pulses for a time length of 20 s, pushing the closer piece of the robot into the piece farther away. The two pieces merged back into a single robot.

Scheme 6: Shapeshifting experiments: See Figure 18. A robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface between transducers 2 and 7, yielding a robot ≈10 cm in diameter. Transducers 7 and 2 were activated in pulses for 20 s until the robot changed its shape into an elongated form. The transducers were then shut down, allowing the robot to return to a round shape.

Scheme 7: Counting experiment: See Figure 19. As in the A→B experiments, a robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface at point A, yielding a robot ≈10 cm in diameter. Four alumina bits (10 g of alumina nanoparticles in 10 mL of distilled water each) were placed along the path from point A to point B. Transducers 2 and 3 were activated in pulses for 100–110 s, pushing the robot towards point B while collecting the alumina bits on its way. At the third bit, the robot could not continue its movement.

Scheme 8: Percolation (movement through grating) experiment: See Figure 20. A robot (30 mL of 58% w/v starch microparticles, 7.15% v/v E-124 / E-143 coloring, 7.15% v/v fructose–glucose mixture) was applied onto the speaker surface at point A, yielding a robot of ≈10 cm in diameter. Gratings (five bolts 2 cm apart, connected by a wooden board) were placed upon the surface, about 10 cm away from the robot. Transducers 2 and 3 were activated in pulses for ≈60 s until the robot passed through the gratings.

Scheme 9: Chemical synthesis (biosynthesis): See Figure 21. As this experiment involved DNA and proteins, the robot composition was altered slightly. Three robots were made, each mixed with substances as shown in Table 3. 15 mL of R1 and 15 mL of R2 were applied onto the speaker surface 15 cm away from each other. Transducers 2 and 3 were activated in pulses for 20 s, followed by transducer 6. R1 and R2 were then merged into R1+2. Transducers 6 and 7 were activated, thus making R1+2 mix itself. At this point, 15 mL of R3 was applied onto the surface between transducers 6 and 10. Transducers 8 and 12 were then activated in pulses for about 15 s, pushing R1+2 onto R3, making the two robots merge. Transducers 7 and 11 were activated, allowing the robot to mix for 20 s. A sample of 20 mL was taken from the mixture and run in a centrifuge at 17,000g for 5 min. The supernatant was collected and mixed with streptavidin beads for 15 min. This final mixture was then tested with an Accuri BD6 FACS. BupH buffer and EDC were purchased from Pierce.