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Daniel I. Goldman

Publications and source records attributed to Daniel I. Goldman.

At least 55 records · Page 3Linked to original sources
arXiv2023

Geometry of contact: contact planning for multi-legged robots via spin models duality

Contact planning is crucial in locomoting systems.Specifically, appropriate contact planning can enable versatile behaviors (e.g., sidewinding in limbless locomotors) and facilitate speed-dependent gait transitions (e.g., walk-trot-gallop in quadrupedal locomotors). The challenges of contact planning include determining not only the sequence by which contact is made and broken between the locomotor and the environments, but also the sequence of internal shape changes (e.g., body bending and limb shoulder joint oscillation). Most state-of-art contact planning algorithms focused on conventional robots (e.g.biped and quadruped) and conventional tasks (e.g. forward locomotion), and there is a lack of study on general contact planning in multi-legged robots. In this paper, we show that using geometric mechanics framework, we can obtain the global optimal contact sequence given the internal shape changes sequence. Therefore, we simplify the contact planning problem to a graph optimization problem to identify the internal shape changes. Taking advantages of the spatio-temporal symmetry in locomotion, we map the graph optimization problem to special cases of spin models, which allows us to obtain the global optima in polynomial time. We apply our approach to develop new forward and sidewinding behaviors in a hexapod and a 12-legged centipede. We verify our predictions using numerical and robophysical models, and obtain novel and effective locomotion behaviors.

cs.RO↗
arXiv2022

Self-propulsion via slipping: frictional swimming in multi-legged locomotors

Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium, or on solid substrates dominated by friction. In the former, centralized coordination is believed to facilitate appropriate slipping through the medium for propulsion. In the latter, slip is often assumed minimal and thus avoided via decentralized controls. We discover in laboratory experiments that terrestrial locomotion of a meter scale multi-segmented/legged robophysical model resembles undulatory fluid swimming. Experiments varying waves of limb stepping and body bending reveal how these parameters result in effective terrestrial locomotion despite seemingly ineffective isotropic frictional contacts. Dissipation dominates over inertial effects in this macroscopic-scaled regime, resulting in essentially geometric locomotion akin to microscopic-scale swimming. Theoretical analysis demonstrates that the high-dimensional multi-segmented/legged dynamics can be simplified to a centralized low-dimensional model, which reveals an effective Resistive Force Theory with an acquired viscous drag anisotropy. We extend our low-dimensional, geometric analysis to illustrate how body undulation can aid performance in non-flat obstacle-rich terrains and also use the scheme to quantitatively model how body undulation affects performance of biological centipede locomotion (the desert centipede S. polymorpha) moving at relatively high speeds (~0.5 body lengths/sec). Our results could facilitate control of multilegged robots in complex terradynamic scenarios.

physics.bio-ph↗
arXiv2022

Amorphous Entangled Active Matter

The design of amorphous entangled systems, specifically from soft and active materials, has the potential to open exciting new classes of active, shape-shifting, and task-capable 'smart' materials. However, the global emergent mechanics that arises from the local interactions of individual particles are not well understood. In this study, we examine the emergent properties of amorphous entangled systems in three different examples: an in-silico "smarticle" collection, its robophysical chain, and living entangled aggregate of worm blobs (L. variegatus). In simulations, we examine how material properties change for a collective composed of dynamic three-link robots. We compare three methods of controlling entanglement in a collective: externally oscillations, shape-changes, and internal oscillations. We find that large-amplitude changes of the particle's shape using the shape-change procedure produced the highest average number of entanglements, with respect to the aspect ratio (l/w), improving the tensile strength of the collective. We demonstrate application of these simulations in two experimental systems: robotic chains and entangled worm blobs. In the robophysical models, we find emergent auxeticity behavior upon straining the confined collective. And finally, we show how the individual worm activity in a blob can be controlled through the ambient dissolved oxygen in water, leading to complex emergent properties of the living entangled collective, such as solid-like entanglement and tumbling. Taken together, our work reveals principles by which future shape-modulating, potentially soft robotic systems may dynamically alter their material properties, advancing our understanding of living entangled materials, while inspiring new classes of synthetic emergent super-materials.

cond-mat.soft↗
arXiv2022

Gliders in shape-changing active matter

We report in experiment and simulation the spontaneous formation of dynamically bound pairs of shape changing smarticle robots undergoing locally repulsive collisions. Borrowing terminology from Conway's simulated Game of Life, these physical `gliders' robustly emerge from an ensemble of individually undulating three-link two-motor smarticles and can remain bound for hundreds of undulations and travel for multiple robot dimensions. Gliders occur in two distinct binding symmetries and form over a wide range of angular flapping extent. This parameter sets the maximal concavity which influences formation probability and translation characteristics. Analysis of dynamics in simulation reveals the mechanism of effective dynamical attraction -- a result of the emergent interplay of appropriately oriented and timed repulsive interactions.

cond-mat.soft↗
arXiv2022

Oxygenation-Controlled Collective Dynamics in Aquatic Worm Blobs

Many types of organisms utilize group aggregation as a method for survival. The freshwater oligochaete, California blackworms Lumbriculus variegatus form tightly entangled structures, or worm "blobs", that have adapted to survive in extremely low levels of dissolved oxygen (DO). Individual blackworms adapt to hypoxic environments through respiration via their mucous body wall and posterior ciliated hindgut, which they wave above them. However, the change in collective behavior at different levels of DO is not known. Using a closed-loop respirometer with flow, we discover that the relative tail reaching activity flux in low DO is $\sim$75x higher than in the high DO condition. Additionally, when flow rate is increased to suspend the worm blobs upward, we find that the average exposed surface area of a blob in low DO is $\sim$1.4x higher than in high DO. Furthermore, we observe emergent properties that arise when a worm blob is exposed to extreme DO levels. Here we show that internal stress is generated when worm blobs are exposed to high DO levels, allowing them to be physically lifted off from the bottom of a conical container using a serrated endpiece. Our results demonstrate how both collective behavior and the emergent generation of internal stress in worm blobs change to accommodate differing levels of oxygen, which could be used to model and simulate swarm robots, self-assembly structures, or soft material entanglements.

cond-mat.soft↗
arXiv2022

Generalized Omega Turn Gait Enables Agile Limbless Robot Turning in Complex Environments

Reorientation (turning in plane) plays a critical role for all robots in any field application, especially those that in confined spaces. While important, reorientation remains a relatively unstudied problem for robots, including limbless mechanisms, often called snake robots. Instead of looking at snakes, we take inspiration from observations of the turning behavior of tiny nematode worms C. elegans. Our previous work presented an in-place and in-plane turning gait for limbless robots, called an omega turn, and prescribed it using a novel two-wave template. In this work, we advance omega turn-inspired controllers in three aspects: 1) we use geometric methods to vary joint angle amplitudes and forward wave spatial frequency in our turning equation to establish a wide and precise amplitude modulation and frequency modulation on omega turn; 2) we use this new relationship to enable robots with fewer internal degrees of freedom (i.e., fewer joints in the body) to achieve desirable performance, and 3) we apply compliant control methods to this relationship to handle unmodelled effects in the environment. We experimentally validate our approach on a limbless robot that the omega turn can produce effective and robust turning motion in various types of environments, such as granular media and rock pile.

cs.RO↗
arXiv2022

A general locomotion control framework for multi-legged locomotors

Serially connected robots are promising candidates for performing tasks in confined spaces such as search-and-rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve mobility. However, a challenge in designing and controlling such devices lies in the coordination of high-dimensional redundant modules in a way that improves mobility. Here we develop a general framework to control serially connected multi-legged robots. Specifically, we combine two approaches to build a general shape control scheme which can provide baseline patterns of self-deformation ("gaits") for effective locomotion in diverse robot morphologies. First, we take inspiration from a dimensionality reduction and a biological gait classification scheme to generate cyclic patterns of body deformation and foot lifting/lowering, which facilitate generation of arbitrary substrate contact patterns. Second, we use geometric mechanics methods to facilitates identification of optimal phasing of these undulations to maximize speed and/or stability. Our scheme allows the development of effective gaits in multi-legged robots locomoting on flat frictional terrain with diverse number of limbs (4, 6, 16, and even 0 limbs) and body actuation capabilities (including sidewinding gaits on limbless devices). By properly coordinating the body undulation and the leg placement, our framework combines the advantages of both limbless robots (modularity) and legged robots (mobility). We expect that our framework can provide general control schemes for the rapid deployment of general multi-legged robots, paving the ways toward machines that can traverse complex environments under real-life conditions.

cs.RO↗
arXiv2022

Coordinating tiny limbs and long bodies: geometric mechanics of diverse undulatory lizard locomotion

Although typically possessing four limbs and short bodies, lizards have evolved a diversity of body plans, from short-bodied and fully-limbed to elongate and nearly limbless. Such diversity in body morphology is hypothesized as adaptations to locomotion cluttered terrestrial environments, but the mode of propulsion -- e.g., the use of body and/or limbs to interact with the substrate -- and potential body/limb coordination remain unstudied. Here, we use biological experiments, a geometric theory of locomotion, and robophysical experiments to comparatively and systematically investigate such dynamics in a diverse sample of lizard morphologies. Locomotor field studies in short-limb, elongated lizards (Brachymeles) and laboratory studies of full-limbed lizards (Uma scoparia and Sceloporus olivaceus) and a limbless laterally undulating organism (Chionactis occipitalis) reveal that the body wave dynamics can be described by a combination of traveling and standing waves; the ratio of the amplitudes of these components is inversely related to limb length. We use geometric theory to analyze and explain the wave dynamics and body-leg coordination observations; the theory predicts that leg thrust modulates the body weight distribution and self-propulsion generation mechanism, which in turn facilitates the choice of body waves. We test our hypothesis in biological experiments by inducing the use of traveling wave in stereotyped lizards by modulating the ground penetration resistance, as well as in controlled non-biological experiments involving an undulating limbed robophysical model. Our models could be valuable in understanding functional constraints on the evolutionary process of elongation and limb reduction in lizards, as well as advancing robot designs.

physics.bio-ph↗
arXiv2022

Locomotion without force, and impulse via dissipation: Robotic swimming in curved space via geometric phase

Locomotion by shape changes (spermatozoon swimming, snake slithering, bird flapping) or gas expulsion (rocket firing) is assumed to require environmental interaction, due to conservation of momentum. As first noted in (Wisdom, 2003) and later in (Guéron, 2009) and (Avron et al, 2006), in curved space or spacetime the non-commutativity of translations permits translation without momentum exchange, just as falling cats and lizards can self-deform to reorient in flat space without environmental interaction. Translation in curved space can occur not only in gravitationally induced curved spacetime (where translation is predicted to be on the order of $10^{-23}$ m per gait cycle) but also in the curved surfaces encountered by locomotors in real-world environments. Here we show that a precision robophysical apparatus consisting of motors driven on curved tracks (and thereby confined to a spherical surface without a solid substrate) can self-propel without environmental momentum exchange (impulse) via shape changes that can generate gauge potentials that manifest as translations. Our system produces shape changes comparable to the environment's inverse curvatures and generates from zero momentum forward movement of $10^{-1}$ cm per gait cycle even while resisted by weak gravitational and frictional forces. Dissipation via friction eventually arrests the robot but also imbues it with momentum which can be released upon a cessation of shape changes. This work demonstrates how the interaction between environmental curvature, active driving and geometric phases yields rich, exotic phenomena.

cond-mat.soft↗
arXiv2021

Field-mediated locomotor dynamics on highly deformable surfaces

In many systems motion occurs on deformed and deformable surfaces, setting up the possibility for dynamical interactions solely mediated by the coupling of the entities with their environment. Here we study the "two-body" dynamics of robot locomotion on a highly deformable spandex membrane in two scenarios: one in which a robot orbits a large central depression and the other where the two robots affect each other's motion solely through mutual environmental deformations. Inspired by the resemblance of the orbits of the single robot with those of general relativistic orbits around black holes, we recast the vehicle plus membrane dynamics in physical space into the geodesic motion of a "test particle" in a fiducial curved space-time and demonstrate how this framework facilitates understanding the observed dynamics. The two-robot problem also exhibits a resemblance with Einstein's general relativistic view of gravity, which in the words of Wheeler: "spacetime tells matter how to move; matter tells spacetime how to curve." We generalize this case the mapping to include a reciprocal coupling that translates into robotic curvature-based control schemes which modify interaction (promoting avoidance or aggregation) without long-range sensing. Our work provides a starting point for developing a mechanical analog gravity system as well as develops a framework that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

cs.RO↗
arXiv2021

Reconstruction of Backbone Curves for Snake Robots

Snake robots composed of alternating single-axis pitch and yaw joints have many internal degrees of freedom, which make them capable of versatile three-dimensional locomotion. In motion planning process, snake robot motions are often designed kinematically by a chronological sequence of continuous backbone curves that capture desired macroscopic shapes of the robot. However, as the geometric arrangement of single-axis rotary joints creates constraints on the rotations in the robot, it is challenging for the robot to reconstruct an arbitrary 3D curve. When the robot configuration does not accurately achieve the desired shapes defined by these backbone curves, the robot can have unexpected contacts with the environment, such that the robot does not achieve the desired motion. In this work, we propose a method for snake robots to reconstruct desired backbone curves by posing an optimization problem that exploits the robot's geometric structure. We verified that our method enables fast and accurate curve-configuration conversions through its applications to commonly used 3D gaits. We also demonstrated via robot experiments that 1) our method results in smooth locomotion on the robot; 2) our method allows the robot to approach the numerically predicted locomotive performance of a sequence of continuous backbone curve.

cs.RO↗
arXiv2021

Programming Active Cohesive Granular Matter with Mechanically Induced Phase Changes

Active matter physics and swarm robotics have provided powerful tools for the study and control of ensembles driven by internal sources. At the macroscale, controlling swarms typically utilizes significant memory, processing power, and coordination unavailable at the microscale, e.g., for colloidal robots, which could be useful for fighting disease, fabricating intelligent textiles, and designing nanocomputers. To develop principles that that can leverage physics of interactions and thus can be utilized across scales, we take a two-pronged approach: a theoretical abstraction of self-organizing particle systems and an experimental robot system of active cohesive granular matter that intentionally lacks digital electronic computation and communication, using minimal (or no) sensing and control, to test theoretical predictions. We consider the problems of aggregation, dispersion, and collective transport. As predicted by the theory, as a parameter representing interparticle attraction increases, the robots transition from a dispersed phase to an aggregated one, forming a dense, compact collective. When aggregated, the collective can transport non-robot "impurities" in their environment, thus performing an emergent task driven by the physics underlying the transition. These results point to a fruitful interplay between algorithm design and active matter robophysics that can result in new nonequilibrium physics and principles for programming collectives without the need for complex algorithms or capabilities.

cond-mat.soft↗
arXiv2021

Low rattling: A predictive principle for self-organization in active collectives

Self-organization is frequently observed in active collectives, from ant rafts to molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random, while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally in shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing towards future approaches for design and control of active particle mixtures and metamaterials.

cond-mat.stat-mech↗
arXiv2020

Effect of two parallel intruders on net work during granular penetrations

The impact of single passive intruders into granular particles has been studied in detail. However, the impact force produced by multiple intruders separated at a distance from one another, and hence the effect of their presence in close proximity to one another, is largely unexplored. Here, we use numerical simulations and laboratory experiments to study the force response of two parallel rods intruding vertically into granular media while varying the gap spacing between them. We also explored the effect of variations in friction, intruder size, and particle size on the force response. The net work ($W$) of the two rods over the depth of intrusion was measured, and the instantaneous velocities of particles over the duration of intrusion were calculated by simulations. We found that the work done by the intruders changes with distance between them. We observed a peak in $W$ at a gap spacing of $\sim$3 particle diameters, which was up to 25% greater than $W$ at large separation (\textgreater 11 particle diameters), beyond which the net work plateaued. This peak was likely due to less particle flow between intruders as we found a larger number of strong forces---identified as force chains---in the particle domain at gaps surrounding the peak force. Although higher friction caused greater force generation during intrusion, the gap spacing between the intruders at which the peak work was generated remained unchanged. Larger intruder sizes resulted in greater net work with the peak in $W$ occurring at slightly larger intruder separations. Taken together, our results show that peak work done by two parallel intruders remained within a narrow range, remaining robust to most other tested parameters.

cond-mat.soft↗
arXiv2019

Towards a terramechanics for bio-inspired locomotion in granular environments

Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM.

physics.bio-ph↗
arXiv2019

A resistive force model of legged locomotion on granular media

Compared to agile legged animals, wheeled and tracked vehicles often suffer large performance loss on granular surfaces like sand and gravel. Understanding the mechanics of legged locomotion on granular media can aid the development of legged robots with improved mobility on granular surfaces; however, no general force model yet exists for granular media to predict ground reaction forces during complex limb intrusions. Inspired by a recent study of sand-swimming, we develop a resistive force model in the vertical plane for legged locomotion on granular media. We divide an intruder of complex morphology and kinematics, e.g., a bio-inspired robot L-leg rotated through uniform granular media (loosely packed ~ 1 mm diameter poppy seeds), into small segments, and measure stresses as a function of depth, orientation, and direction of motion using a model leg segment. Summation of segmental forces over the intruder predicts the net forces on both an L-leg and a reversed L-leg rotated through granular media with better accuracy than using simple one-dimensional penetration and drag force models. A multi-body dynamic simulation using the resistive force model predicts the speeds of a small legged robot (15 cm, 150 g) moving on granular media using both L-legs and reversed L-legs.

physics.bio-ph↗
arXiv2019

Modeling of the interaction of rigid wheels with dry granular media

We analyze the capabilities of various recently developed techniques, namely Resistive Force Theory (RFT) and continuum plasticity implemented with the Material Point Method (MPM), in capturing dynamics of wheel--dry granular media interactions. We compare results to more conventionally accepted methods of modeling wheel locomotion. While RFT is an empirical force model for arbitrarily-shaped bodies moving through granular media, MPM-based continuum modeling allows the simulation of full granular flow and stress fields. RFT allows for rapid evaluation of interaction forces on arbitrary shaped intruders based on a local surface stress formulation depending on depth, orientation, and movement of surface elements. We perform forced-slip experiments for three different wheel types and three different granular materials, and results are compared with RFT, continuum modeling, and a traditional terramechanics semi-empirical method. Results show that for the range of inputs considered, RFT can be reliably used to predict rigid wheel granular media interactions with accuracy exceeding that of traditional terramechanics methodology in several circumstances. Results also indicate that plasticity-based continuum modeling provides an accurate tool for wheel-soil interaction while providing more information to study the physical processes giving rise to resistive stresses in granular media.

cond-mat.soft↗