arXiv subjects

Mattia Gazzola

Publications and source records attributed to Mattia Gazzola.

At least 37 records · Page 2Linked to original sources

arXiv2022

A Sensory Feedback Control Law for Octopus Arm Movements

The main contribution of this paper is a novel sensory feedback control law for an octopus arm. The control law is inspired by, and helps integrate, several observations made by biologists. The proposed control law is distinct from prior work which has mainly focused on open-loop control strategies. Several analytical results are described including characterization of the equilibrium and its stability analysis. Numerical simulations demonstrate life-like motion of the soft octopus arm, qualitatively matching behavioral experiments. Quantitative comparison with bend propagation experiments helps provide the first explanation of such canonical motion using a sensory feedback control law. Several remarks are included that help draw parallels with natural pursuit strategies such as motion camouflage or classical pursuit.

eess.SY↗

arXiv2022

Soft streaming -- flow rectification via elastic boundaries

Viscous streaming is an efficient mechanism to exploit inertia at the microscale for flow control. While streaming from rigid features has been thoroughly investigated, when body compliance is involved, as in biological settings, little is known. Here, we investigate body elasticity effects on streaming in the minimal case of an immersed soft cylinder. Our study reveals an additional streaming process, available even in Stokes flows. Paving the way for advanced forms of flow manipulation, we illustrate how gained insights may translate to complex geometries beyond circular cylinders.

physics.flu-dyn↗

arXiv2021

A hyperelastic oscillatory Couette system

We report (semi-)analytical solutions of a problem involving a visco-hyperelastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls that undergo oscillatory motion. The resulting system dynamics are rationalized, based on fluid viscosity and solid elasticity, via wave and boundary-layer theory. This allows for physical interpretation of elasto-hydrodynamic coupling, potentially connecting to a broad set of biophysical phenomena and applications, from synovial joint mechanics to elastometry. Further, obtained solutions are demonstrated to be rigorous benchmarks for testing coupled incompressible fluid--hyperelastic solid and multiphase numerical solvers, towards which we highlight challenging parameter sets. Finally, we provide an interactive, online sandbox to build physical intuition, and open-source our code-base.

physics.flu-dyn↗

arXiv2021

Micromechanical origin of plasticity and hysteresis in nest-like packings

Disordered packings of unbonded, semiflexible fibers represent a class of materials spanning contexts and scales. From twig-based bird nests to unwoven textiles, bulk mechanics of disparate systems emerge from the bending of constituent slender elements about impermanent contacts. In experimental and computational packings of wooden sticks, we identify prominent features of their response to cyclic oedometric compression: non-linear stiffness, transient plasticity, and eventually repeatable velocity-independent hysteresis. We trace these features to their micromechanic origins, identified in characteristic appearance, disappearance, and displacement of internal contacts.

cond-mat.soft↗

arXiv2021

Multi-curvature viscous streaming: flow topology and particle manipulation

Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong inertial effects to which both fluid and immersed particles respond within short length (O(100) microns) and time (milliseconds) scales, rendering viscous streaming arguably the most efficient mechanism to exploit inertia at the microscale. Despite this potential, viscous streaming has been investigated in rather narrow conditions, mostly making use of bodies of uniform curvature (cylinders, spheres) for which induced flow topologies are constrained to only two regimes, classically referred to as single and double layer regimes. This severely limits the scope of potential applications, and sits in stark contrast to inertial focusing (the approach that perhaps has most defined the field of inertial microfluidics), where instead boundaries with multiple curvatures have long been utilised to magnify inertial effects, expand design space, and enable novel applications. Here, we demonstrate that a multi-curvature approach in viscous streaming dramatically extends the range of accessible flow topologies. We show that numerically predicted, but never experimentally observed, streaming flows can be physically reproduced, computationally engineered, and in turn used to enhance particle manipulation, filtering and separation in compact, robust, tunable and inexpensive devices. Overall, this study provides an avenue to unlock the utility of viscous streaming with potential applications in manufacturing, environment, health and medicine, from particle self-assembly to microplastics removal.

physics.flu-dyn↗

arXiv2021

Control-oriented Modeling of Bend Propagation in an Octopus Arm

Bend propagation in an octopus arm refers to a stereotypical maneuver whereby an octopus pushes a bend (localized region of large curvature) from the base to the tip of the arm. Bend propagation arises from the complex interplay between mechanics of the flexible arm, forces generated by internal muscles, and environmental effects (buoyancy and drag) from of the surrounding fluid. In part due to this complexity, much of prior modeling and analysis work has relied on the use of high dimensional computational models. The contribution of this paper is to present a control-oriented reduced order model based upon a novel parametrization of the curvature of the octopus arm. The parametrization is motivated by the experimental results. The reduced order model is related to and derived from a computational model which is also presented. The results from the two sets of models are compared using numerical simulations which is shown to lead to useful qualitative insights into bend propagation. A comparison between the reduced order model and experimental data is also reported.

physics.bio-ph↗

arXiv2021

A physics-informed, vision-based method to reconstruct all deformation modes in slender bodies

This paper is concerned with the problem of estimating (interpolating and smoothing) the shape (pose and the six modes of deformation) of a slender flexible body from multiple camera measurements. This problem is important in both biology, where slender, soft, and elastic structures are ubiquitously encountered across species, and in engineering, particularly in the area of soft robotics. The proposed mathematical formulation for shape estimation is physics-informed, based on the use of the special Cosserat rod theory whose equations encode slender body mechanics in the presence of bending, shearing, twisting and stretching. The approach is used to derive numerical algorithms which are experimentally demonstrated for fiber reinforced and cable-driven soft robot arms. These experimental demonstrations show that the methodology is accurate (<5 mm error, three times less than the arm diameter) and robust to noise and uncertainties.

cs.RO↗

arXiv2021

Three-dimensional geometry and topology effects in viscous streaming

Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations on resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization of streaming flows as function of changes in body geometry and topology, starting from the well-known case of a sphere to progressively arrive at toroidal shapes. We leverage direct numerical simulations and dynamical systems theory to systematically analyze the reorganization of streaming flows into a dynamically rich set of regimes, the origins of which are explained using bifurcation theory.

physics.flu-dyn↗

arXiv2021

Friction modulation in limbless, three-dimensional gaits and heterogeneous terrains

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood through the lens of local friction modulation. Via an `everything-is-friction' modeling approach, compounded by 3D simulations, the emergence and disappearance of a range of locomotory behaviors observed in nature is systematically explained in relation to inhabited environments. Our approach also simplifies the treatment of terrain heterogeneity, whereby even solid obstacles may be seen as high friction regions, which we confirm against experiments of snakes `diffracting' while traversing rows of posts [1], similar to optical waves. We further this optic analogy by illustrating snake refraction, reflection and lens focusing. We use these insights to engineer surface friction patterns and demonstrate passive snake navigation in complex topographies. Overall, our study outlines a unified view that connects active and passive 3D mechanics with heterogeneous interfacial effects to explain a broad set of biological observations, and potentially inspire engineering design.

physics.bio-ph↗

arXiv2021

Controlling a CyberOctopus Soft Arm with Muscle-like Actuation

This paper presents an application of the energy shaping methodology to control a flexible, elastic Cosserat rod model of a single octopus arm. The novel contributions of this work are two-fold: (i) a control-oriented modeling of the anatomically realistic internal muscular architecture of an octopus arm; and (ii) the integration of these muscle models into the energy shaping control methodology. The control-oriented modeling takes inspiration in equal parts from theories of nonlinear elasticity and energy shaping control. By introducing a stored energy function for muscles, the difficulties associated with explicitly solving the matching conditions of the energy shaping methodology are avoided. The overall control design problem is posed as a bilevel optimization problem. Its solution is obtained through iterative algorithms. The methodology is numerically implemented and demonstrated in a full-scale dynamic simulation environment Elastica. Two bio-inspired numerical experiments involving the control of octopus arms are reported.

cs.RO↗

arXiv2021

Optimal Control of a Soft CyberOctopus Arm

In this paper, we use the optimal control methodology to control a flexible, elastic Cosserat rod. An inspiration comes from stereotypical movement patterns in octopus arms, which are observed in a variety of manipulation tasks, such as reaching or fetching. To help uncover the mechanisms underlying these observed morphologies, we outline an optimal control-based framework. A single octopus arm is modeled as a Hamiltonian control system, where the continuum mechanics of the arm is modeled after the Cosserat rod theory, and internal, distributed muscle forces and couples are considered as controls. First order necessary optimality conditions are derived for an optimal control problem formulated for this infinite dimensional system. Solutions to this problem are obtained numerically by an iterative forward-backward algorithm. The state and adjoint equations are solved in a dynamic simulation environment, setting the stage for studying a broader class of optimal control problems. Trajectories that minimize control effort are demonstrated and qualitatively compared with observed behaviors.

math.OC↗

arXiv2021

An unrecognized force in inertial microfluidics

Describing effects of small but finite inertia on suspended particles is a fundamental fluid dynamical problem that has never been solved in full generality. Modern microfluidics has turned this academic problem into a practical challenge through the use of high-frequency oscillatory flows, perhaps the most efficient way to take advantage of inertial effects at low Reynolds numbers, to precisely manipulate particles, cells and vesicles without the need for charges or chemistry. The theoretical understanding of flow forces on particles has so far hinged on the pioneering work of Maxey and Riley (MR in the following), almost 40 years ago. We demonstrate here theoretically and computationally that oscillatory flows exert previously unexplained, significant and persistent forces, that these emerge from a combination of particle inertia and spatial flow variation, and that they can be quantitatively predicted through a generalization of MR.

physics.flu-dyn↗

arXiv2020

A remeshed vortex method for mixed rigid/soft body fluid--structure interaction

We outline a 2D algorithm for solving incompressible flow--structure interaction problems for mixed rigid/soft body representations, within a consistent framework based on the remeshed vortex method. We adopt the one--continuum formulation to represent both solid and fluid phases on an Eulerian grid, separated by a diffuse interface. Rigid solids are treated using Brinkman penalization while an inverse map technique is used to obtain elastic stresses in the hyper-elastic solid phase. We test our solver against a number of benchmark problems, which demonstrate physical accuracy and first to second order convergence in space and time. Benchmarks are complemented by additional investigations that illustrate the ability of our numerical scheme to capture essential fluid--structure interaction phenomena across a variety of scenarios involving internal muscular actuation, self propulsion, multi-body contact, heat transfer and rectified viscous streaming effects. Through these illustrations, we showcase the ability of our solver to robustly deal with different constitutive models and boundary conditions, solve disparate multi-physics problems and achieve faster time-to-solutions by sidestepping CFL time step restrictions.

physics.comp-ph↗

arXiv2020

Energy Shaping Control of a CyberOctopus Soft Arm

This paper entails application of the energy shaping methodology to control a flexible, elastic Cosserat rod model. Recent interest in such continuum models stems from applications in soft robotics, and from the growing recognition of the role of mechanics and embodiment in biological control strategies: octopuses are often regarded as iconic examples of this interplay. Here, the dynamics of the Cosserat rod, modeling a single octopus arm, are treated as a Hamiltonian system and the internal muscle actuators are modeled as distributed forces and couples. The proposed energy shaping control design procedure involves two steps: (1) a potential energy is designed such that its minimizer is the desired equilibrium configuration; (2) an energy shaping control law is implemented to reach the desired equilibrium. By interpreting the controlled Hamiltonian as a Lyapunov function, asymptotic stability of the equilibrium configuration is deduced. The energy shaping control law is shown to require only the deformations of the equilibrium configuration. A forward-backward algorithm is proposed to compute these deformations in an online iterative manner. The overall control design methodology is implemented and demonstrated in a dynamic simulation environment. Results of several bio-inspired numerical experiments involving the control of octopus arms are reported.

eess.SY↗

arXiv2020

Elastica: A compliant mechanics environment for soft robotic control

Soft robots are notoriously hard to control. This is partly due to the scarcity of models able to capture their complex continuum mechanics, resulting in a lack of control methodologies that take full advantage of body compliance. Currently available simulation methods are either too computational demanding or overly simplistic in their physical assumptions, leading to a paucity of available simulation resources for developing such control schemes. To address this, we introduce Elastica, a free, open-source simulation environment for soft, slender rods that can bend, twist, shear and stretch. We demonstrate how Elastica can be coupled with five state-of-the-art reinforcement learning algorithms to successfully control a soft, compliant robotic arm and complete increasingly challenging tasks.

cs.RO↗

arXiv2020

Centralized model predictive control with distributed adaptation

A centralized model predictive controller (MPC), which is unaware of local uncertainties, for an affine discrete time nonlinear system is presented. The local uncertainties are assumed to be matched, bounded and structured. In order to encounter disturbances and to improve performance, an adaptive control mechanism is employed locally. The proposed approach ensures input-to-state stability of closed-loop states and convergence to the equilibrium point. Moreover, uncertainties are learnt in terms of the given feature basis by using adaptive control mechanism. In addition, hard constraints on state and control are satisfied.

math.OC↗

arXiv2019

Shape curvature effects in viscous streaming

Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length-scales are involved has not been looked into, in rigorous detail. We propose a simplified setting to understand and explore the effect of multiple body curvatures on streaming flows, analyzing the system through the lens of bifurcation theory. Our setup consists of periodic, regular lattices of cylinders characterized by two distinct radii, so as to inject discrete curvatures into the system, which in turn affect the streaming field generated due to an oscillatory background flow. We demonstrate that our understanding based on this system can be then generalized to a variety of individual convex shapes presenting a spectrum of curvatures, explaining prior experimental and computational observations. Thus, this study illustrates a route towards the rational manipulation of viscous streaming flow topology, through regulated variation of object geometry.

physics.flu-dyn↗

arXiv2019

Perspective: Mechanics of randomly packed filaments -- the `bird nest' as meta-material

Systems of randomly packed, macroscopic elements, from jammed spherical grains to tangled long filaments, represent a broad class of disordered meta-materials with a wide range of applications and manifestations in nature. A `bird nest' presents itself at an interface between hard round grains described by granular physics to long soft filaments, the center of textile material science. All of these randomly packed systems exhibit forms of self assembly, evident through their robust packing statistics, and a common, unusual elastoplastic response to oedometric compression. In reviewing packing statistics, mechanical response characterization and consideration of boundary effects, we present a perspective that attempts to establish a link between the bulk and local behaviour of a pile of sand and a wad of cotton, demonstrating the nest's relationship with each. Finally, potential directions for impactful applications are outlined.

cond-mat.soft↗