Session V40: Robophysics: Physics Meets Robotics I

Geometric mechanics for modelling bioinspired robots locomotion: from rigid to continuous (soft) systems

This talk presents recent geometric tools developed to model the locomotion dynamics of bio-inspired robots. Starting from the model of discrete rigid multibody systems we will rapidly shift to the case of continuous systems inspired from snakes and fish. To that end, we will build on the model of Cosserat media. This extended picture of geometric locomotion dynamics (inspired from fields' theory) will allow us to introduce models of swimming recently used in biorobotics. We will show how modeling a fish as a one-dimensional Cosserat medium allows to recover and extend the Large Amplitude Elongated Body theory of J. Lighthill and to apply it to an eel-like robot. In the same vein, modeling the mantle of cephalopods as a two dimensional Cosserat medium will build a basis for studying the jet propelling of a soft octopus like robot.   

Geometric Mechanics Reveals Optimal Complex Terrestrial Undulation Patterns

Geometric mechanics offers useful tools for intuitively analyzing biological and robotic locomotion. However, utility of these tools were previously restricted to systems that have only two internal degrees of freedom and in uniform media. We show kinematics of complex locomotors that make intermittent contacts with substrates can be approximated as a linear combination of two shape bases, and can be represented using two variables. Therefore, the tools of geometric mechanics can be used to analyze motions of locomotors with many degrees of freedom. To demonstrate the proposed technique, we present studies on two different types of snake gaits which utilize combinations of waves in the horizontal and vertical planes: sidewinding (in the sidewinder rattlesnake \textit{C. cerastes)} and lateral undulation (in the desert specialist snake \textit{C. occipitalis)}. \textit{C. cerastes} moves by generating posteriorly traveling body waves in the horizontal and vertical directions, with a relative phase offset equal to $\pm \frac{\pi }{2}$ while \textit{C. occipitalis }maintains a $\frac{\pi }{2}$ offset of a frequency doubled vertical wave. Geometric analysis reveals these coordination patterns enable optimal movement in the two different styles of undulatory terrestrial locomotion. More broadly, these examples demonstrate the utility of geometric mechanics in analyzing realistic biological and robotic locomotion.   

Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming

In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.   

Geometric Mechanics for Continuous Swimmers on Granular Material

Animal experiments have shown that \textit{Chionactis occipitalis }(N$=$10) effectively undulating on granular substrates exhibits a particular set of waveforms which can be approximated by a sinusoidal variation in curvature, i.e., a serpenoid wave. Furthermore, all snakes tested used a narrow subset of all available waveform parameters, measured as the relative curvature equal to 5.0\textpm 0.3, and number of waves on the body equal to1.8\textpm 0.1. We hypothesize that the serpenoid wave of a particular choice of parameters offers distinct benefit for locomotion on granular material. To test this hypothesis, we used a physical model (snake robot) to empirically explore the space of serpenoid motions, which is linearly spanned with two independent continuous serpenoid basis functions. The empirically derived height function map, which is a geometric mechanics tool for analyzing movements of cyclic gaits, showed that displacement per gait cycle increases with amplitude at small amplitudes, but reaches a peak value of 0.55 body-lengths at relative curvature equal to 6.0. This work signifies that with shape basis functions, geometric mechanics tools can be extended for continuous swimmers.   

A Cosserat-based formulation for elastic, axisymmetric shells with implications to the pulsed-jetting propulsion of soft-bodied aquatic vehicles

We take the cue from recent development in geometric-based modelling in order to describe the dynamics of a novel soft-structured aquatic vehicle. The Cosserat-like formulation for an axisymmetric, elastic shell subject to concentrated dynamic loadings lends itself to the case of this new vehicle, recently designed by the authors, which consists of a shell of rubber-like materials undergoing sequential stages of inflation and deflation in order to propel itself in water via pulsed-jetting. The experiments performed on the existing robotic prototypes are used for the validation of the geometric model. This is eventually employed for deriving an accurate measure of the efficiency of propulsion which explicitly accounts for the elastic energy involved during the propulsion routine. The model yields a-priori estimations of swimming efficiency based on vehicle specifications and mode of actuation. These provide invaluable information for both design optimization and control, as well as a means to study the biomechanics of soft-bodied aquatic organisms.   

Reverse engineering the euglenoid movement: from unicellular swimmers to bio-inspired robots.

Euglenids are unicelluar organisms living in freshwater, which are capable of moving either by beating a flagellum, or by executing dramatic shape changes. These are accomplished thanks to a complex structure made of interlocking pellicle strips, microtubules, and motor proteins. Relative sliding of the pellicle strips, suitably orchestrated, can cause the propagation of a bulge along the body, hence generating a propulsive force. We study the mechanisms by which the sliding of pellicle strips leads to shape control and locomotion, by means of both theory (through the mechanics of active surfaces and its coupling to computational fluid dynamics for the surrounding fluid) and experimental observations. Moreover, we implement them into a new concept of a surface with programmable shape, obtained by asssembling 3d-printed strips in a construct mimicking the biological template. We explore the range of possible geometries achievable by actuating these surfaces, to assess their potential in soft robotics applications. The subtle balance between constraints and flexibility leads to a wide variety of shapes that can be obtained with relatively simple controls, similar to the notion of morphological computation in biological systems.   

Robotics and Biology: Lets get Physical

Our research group investigates the core fundamentals of locomotion as it exists in biology and as it applies to locomoting robotic systems. Initially, our work advanced techniques found in geometric mechanics to design cyclic controllers, often called gaits, for snake robots, highly articulated mechanisms that can thread through tightly packed spaces to access locations people cannot. We had considerable success in designing snake robot gaits, but found our systems stymied in terrains characterized by sandy substrates. Sandy terrains and other granular media pose a challenge to snake robots because it is unclear how the mechanism interacts with environment: we cannot simply assume the robot is on hard-ground nor in a fluid. Simulating granular interactions can prove to be computationally intractable for real-time use on the robots. Therefore, we developed experimental tools that allowed us to sieve out models of the locomoting systems operating on granular media. We were then able to bring these models into harmony with the elegant formulation of our geometric mechanics approach. This allowed us to derive adaptive controllers for our snake robots in sandy terrains, and enabled us to gain deeper insight into of how biological systems move over similar terrains as well.   

Bio-inspired robot design for viscous fluids

Many modern micro-robots are designed for biomedical applications to transport drugs to targets or to operate tests in the body for diagnosis. However, most micro-robots simply mimic the morphology and the propulsive mechanism of micro-organisms without understanding the underlying physics of low-Re swimming. Two types of swimming motions have been observed in micro-organisms; stresslet and source-dipole swimming. The stresslet swimmer (e.g. E. coli) uses a rotating helical appendage, whereas the source-dipole swimmer (e.g. Paramecium) creates surface velocity for propulsion. Using this principle, we designed a robot to swim in very viscous fluids either by rotating a helix or creating surface velocity, simply by changing the orientation of the appendage. Further, we will discuss the performance of this robot (swimming speed and rotation speed) with respect to the number, winding angle, and radius of helices in a very viscous fluid.   

A microfluidic two-pump system inspired by liquid feeding in mosquitoes

Mosquitoes feed on nectar and blood using a two-pump system in the head-a smaller cibarial pump in line with a larger a pharyngeal pump, with a valve in between. To suck, mosquitoes transport the liquid (which may be a multi-component viscous fluid, blood) through a long micro-channel, the proboscis. In the engineering realm, microfluidic devices in biomedical applications, such as lab-on-a-chip technology, necessitate implementing a robust pump design to handle clogging and increase flow control compared to a single-pump system. In this talk, we introduce a microfluidic pump design inspired by the mosquito's two-pump system. The pumping performance (flow rate) in presence of impurities (air bubbles, soft clogs) is quantified as a function of phase difference and volume expansion of the pumps, and the elasticity of the valve.   

Propulsion of a two-sphere swimmer

We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant macroscopic swimming robot that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.   

Microstructural view of burrowing with a bioinspired digging robot

RoboClam is a burrowing technology inspired by Ensis directus, the Atlantic razor clam. Atlantic razor clams should only be strong enough to dig a few centimeters into the soil, yet they burrow to over 70 cm. The animal uses a clever trick to achieve this: by contracting its body, it agitates and locally fluidizes the soil, reducing the drag and energetic cost of burrowing. RoboClam technology, which is based on the digging mechanics of razor clams, may be valuable for subsea applications that could benefit from efficient burrowing, such as anchoring, mine detonation, and cable laying. We directly visualize the movement of soil grains during the contraction of RoboClam, using a novel index-matching technique along with particle tracking. We show that the size of the failure zone around contracting RoboClam can be theoretically predicted from the substrate and pore fluid properties, provided that the timescale of contraction is sufficiently large. We also show that the nonaffine motions of the grains are a small fraction of the motion within the fluidized zone, affirming the relevance of a continuum model for this system, even though the grain size is comparable to the size of RoboClam.   

Bipedal locomotion in granular media

Bipedal walking, locomotion characterized by alternating swing and double support phase, is well studied on ground where feet do not penetrate the substrate. On granular media like sand however, intrusion and extrusion phases also occur. In these phases, relative motion of the two feet requires that one or both feet slip through the material, degrading performance. To study walking in these phases, we designed and studied a planarized bipedal robot (1.6 kg, 42 cm) that walked in a fluidized bed of poppy seeds. We also simulated the robot in a multibody software environment (Chrono) using granular resistive force theory (RFT) to calculate foot forces. In experiment and simulation, the robot experienced slip during the intrusion phase, with the experiment presenting additional slip due to motor control error during the double support phase. This exaggerated slip gave insight (through analysis of ground reaction forces in simulation) into how slip occurs when relative motion exists between the two feet in the granular media, where the foot with higher relative drag forces (from its instantaneous orientation, rotation, relative direction of motion, and depth) remains stationary. With this relationship, we generated walking gaits for the robot to walk with minimal slip.   

Obstacle traversal and self-righting of bio-inspired robots reveal the physics of multi-modal locomotion

Most animals move in nature in a variety of locomotor modes. For example, to traverse obstacles like dense vegetation, cockroaches can climb over, push across, reorient their bodies to maneuver through slits, or even transition among these modes forming diverse locomotor pathways; if flipped over, they can also self-right using wings or legs to generate body pitch or roll. By contrast, most locomotion studies have focused on a single mode such as running, walking, or jumping, and robots are still far from capable of life-like, robust, multi-modal locomotion in the real world. Here, we present two recent studies using bio-inspired robots, together with new locomotion energy landscapes derived from locomotor-environment interaction physics, to begin to understand the physics of multi-modal locomotion. (1) Our experiment of a cockroach-inspired legged robot traversing grass-like beam obstacles reveals that, with a terradynamically ``streamlined'' rounded body like that of the insect, robot traversal becomes more probable by accessing locomotor pathways that overcome lower potential energy barriers. (2) Our experiment of a cockroach-inspired self-righting robot further suggests that body vibrations are crucial for exploring locomotion energy landscapes and reaching lower barrier pathways. Finally, we posit that our new framework of locomotion energy landscapes holds promise to better understand and predict multi-modal biological and robotic movement.   

Swarming Bristle-Bots: Exploring Properties of Active Matter

Active Matter describes an ubiquitous class of non-equilibrium systems that encompasses a diverse range of phenomena in the living and non-living realm. Examples are microscopic bio-filaments and their associated motor proteins, flocks of birds and fish, vibrated rods and disks, or nanoscale colloids actuated by catalytic activity on their surface. What unifies these systems is that they are all composed of self-driven units. In consequence, these systems are not driven into non-equilibrium by energy input at their boundary, but by local energy injection. As fascinating as these systems are, there are currently barely any laboratory systems that allow for controlled experiments in dry active matter. That is, systems not immersed in a fluid that can be observed without specialized equipment. Here we present a two-dimensional `active matter' system consisting of hundreds of macroscopic (\textasciitilde 0.05 m long), modified, commercially available bristle-bots. We show that this swarm of toys classifies as active matter as it exhibits properties such as dynamic phase separation. Because of their straight forward implementation, their size and controllability, such swarms can not only answer scientific questions, but they have great potential as educational tools in teaching labs and classrooms.