Nick Gravish’s research while affiliated with University of California, San Diego and other places


Ad

What is this page?


This page lists works of an author who doesn't have a ResearchGate profile or hasn't added the works to their profile yet. It is automatically generated from public (personal) data to further our legitimate goal of comprehensive and accurate scientific recordkeeping. If you are this author and want this page removed, please let us know.

Publications (109)


FIG. 5. Experiment to measure the time to reach steady-state (τ ) with differing approximately linear forcespeed curves with effective viscosity of ∆F ∆V (See Fig. 4b). Plot shows the inverse of the startup time versus the effective viscosity parameter for an active contact system.
Active contacts create controllable friction
  • Preprint
  • File available

January 2025

·

12 Reads

Rohan Shah

·

Nick Gravish

Sliding friction between two dry surfaces is reasonably described by the speed-independent Amonton-Coulomb friction force law. However, there are many situations where the frictional contact points between two surfaces are "active" and may not all be moving at the same relative speed. In this work we study the sliding friction properties of a system with multiple active contacts each with independent and controllable speed. We demonstrate that multiple active contacts can produce controllable speed-dependent sliding friction forces, despite each individual contact exhibiting a speed-independent friction. We study in experiment a rotating carousel with ten speed-controlled wheels in frictional contact with the ground. We first vary the contact speeds and demonstrate that the equilibrium system speed is the median of the active contact speeds. Next we directly measure the ground reaction forces and observe how the contact speeds can control the force-speed curve of the system. In the final experiments we demonstrate how control of the force-speed curve can create sliding friction with a controllable effective viscosity and controllable sliding friction coefficient. Surprisingly, we are able to demonstrate that frictional contacts can create near frictionless sliding with appropriate force-speed control. By revealing how active contacts can shape the force-speed behavior of dry sliding friction systems we can better understand animal and robot locomotion, and furthermore open up opportunities for new engineered surfaces to control sliding friction.

Download

Stability and agility trade-offs in spring-wing systems

December 2024

·

12 Reads

Bioinspiration & Biomimetics

·

Ethan S Wold

·

Jeff Gau

·

[...]

·

Nick Gravish

Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases with N) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1<N<10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability.


Moth resonant mechanics are tuned to wingbeat frequency and energetic demands

June 2024

·

54 Reads

An insect’s wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect’s flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies.


The Weis-Fogh Number Describes Resonant Performance Tradeoffs in Flapping Insects

May 2024

·

30 Reads

·

1 Citation

Integrative and Comparative Biology

Synopsis Dimensionless numbers have long been used in comparative biomechanics to quantify competing scaling relationships and connect morphology to animal performance. While common in aerodynamics, few relate the biomechanics of the organism to the forces produced on the environment during flight. We discuss the Weis-Fogh number, N, as a dimensionless number specific to flapping flight, which describes the resonant properties of an insect and resulting tradeoffs between energetics and control. Originally defined by Torkel Weis-Fogh in his seminal 1973 paper, N measures the ratio of peak inertial to aerodynamic torque generated by an insect over a wingbeat. In this perspectives piece, we define N for comparative biologists and describe its interpretations as a ratio of torques and as the width of an insect’s resonance curve. We then discuss the range of N realized by insects and explain the fundamental tradeoffs between an insect’s aerodynamic efficiency, stability, and responsiveness that arise as a consequence of variation in N, both across and within species. N is therefore an especially useful quantity for comparative approaches to the role of mechanics and aerodynamics in insect flight.





Moth resonant mechanics are tuned to wingbeat frequency and energetic demands

February 2024

·

25 Reads

·

2 Citations

An insect’s wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic and kine-matic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off of their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favorable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography, and a “spring-wing” model of resonant aerodynamics to determine how components of an insect’s flight apparatus (thoracic properties, wing inertia, muscle strain, and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies.


Phylogenetic comparative analysis of insect wingbeat actuation reveals a probable single origin of asynchronous flight muscle
a, Synchronous muscle has a 1:1 relationship between neural activation (blue dots) and muscle contraction. Asynchronous muscle contraction is independent of the precise timing of neural activation (red dots), arising from delayed stretch activation². b, The physiological signature of an asynchronous muscle is that when impulsively stretched it produces a delayed force of magnitude Fa that peaks after a characteristic time t0, determined by the rising and falling rate constants r3 and r4 (Methods). c, Ancestral state reconstruction¹⁴ based on muscle ultrastructure (not physiology) reveals that a single evolutionary origin of asynchronous fibre types is more probable using an insect-wide phylogeny resolved to the ordinal level¹⁵. Tip states were identified from the literature (Methods). Pie charts represent the posterior probabilities of the ancestral state reconstruction at these particular nodes given an equal rates model of evolution (full posterior probabilities in Extended Data Fig. 3 and Supplementary Table 5). d, By iteratively constraining ancestral nodes (Methods), we find an 87% posterior probability that some node ancestral to Lepidoptera and Trichoptera (including M. sexta) was asynchronous (making this clade secondarily synchronous) as opposed to all nodes ancestral to Lepidoptera being synchronous (ancestral synchronous). Myr, million years.
Secondarily synchronous hawkmoth flight muscle exhibits delayed stretch activation, a hallmark of asynchronous flight
a, Intact, downstroke flight muscle (DLMs) from M. sexta (n = 9 independent moths from the same source colonies, each sampled a single time) was mounted on an ergometer and electrically stimulated at 150 Hz to establish tetanus. Muscle viability was maintained with a saline drip at a constant 35 °C. b, We applied stretch–hold–release–hold strains, matching in vivo strain amplitudes⁵⁵ of 4.5% while measuring stress normalized to tetanus. Positive strain (ε) and force are defined in the shortening direction (opposite stretch). The black line denotes mean muscle stress normalized to tetanic stress, grey lines show individual trials. c, Magnification of the region outlined in b shows the delayed stretch activation response, characteristic of asynchronous muscle physiology. A sum-of-exponentials mathematical formulation of delayed stretch activation (equation (5); red line) accurately fits the mean normalized stress (black line; shaded region is ±s.d.). The initial transient is the viscoelastic response of the muscle and the subsequent rise and fall is the stretch activation. d, Despite being synchronous, the delayed stretch activation rising rate constant (r3) of M. sexta lies near the prior empirical finding of a linear relationship between r3 and wingbeat frequency¹⁸ (123.4 ± 52.6 s⁻¹ at 25 Hz; the black star shows the mean, error bars (obscured) show s.d.). Non-lepidopteran data and the black regression line are replotted from Molloy et al.¹⁸, with error bars representing the full range of data. We scaled r3 values to ambient temperature using published relationships (equations (2) and (3) from Molloy et al.¹⁸). e, Peak stress for M. sexta delayed stretch activation (Fa), tetanic force (Tet) and twitch. Delayed stretch activation (dSA) stress is shown with (IIR) and without (Emp) infinite impulse response correction (Methods). Box plots denote mean and quartiles, and whiskers are 1.5 × the interquartile range.
Transitions between synchronous and asynchronous modes in simulation and robotics
a, A unified biophysical model combines hawkmoth body mechanics (equation (3)) with time-periodic, neurogenic (synchronous) and delayed stretch activation (asynchronous) forcing. Stretch activation is implemented as a feedback filter (or convolution) of wing angle (ϕ) converted to muscle strain rate (ε̇\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\varepsilon }$$\end{document}) and scaled to wingstroke conditions (µFa) (equations (10) and (11)). The parameterKr interpolates between the two sources of muscle force (equation (1)). b, Kr and stretch activation time-to-peak normalized to the mechanical natural frequency (t0/Tn) define a parameter space. High-power flapping occurs at both extremes, but intermediate modes only generate appreciable power along a bridge where the rate of stretch activation approximately matches the synchronous drive (25 Hz). M. sexta is plotted on the basis of estimates of t0/Tn and K̃r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widetilde{K}}_{r}$$\end{document} from quasi-static data. c, Emergent wingbeat frequencies (f) normalized by the synchronous drive frequency (fs). Dark blue indicates regions where the emergent wingbeat frequency is entrained to the synchronous driving frequency (f = fs). The red regions indicate where the asynchronous dynamics dominate (f ≠ fs). The grey line indicates the boundary between synchronous- and asynchronous-dominant dynamics. d, A robophysical system (roboflapper) implementing both types of actuation, plus real-world fluid physics and friction. e,f, Results from the setup in d are qualitatively similar to the simulations in b,c, but with a region of no wingstrokes due to system friction with low Kr and high t0/Tn. g, A centimetre-scale robotic wing modelled after the Harvard robobee¹², consisting of (1) a wing; (2) a transmission; (3) a carbon fibre frame; (4) a piezoelectric bending actuator; and (5) a wing displacement sensor. h, A single hybrid robobee transitioning from synchronous (Kr = 1, blue) to asynchronous (Kr = 0, red) in real time. Transitions are smooth when synchronous and asynchronous frequencies are approximately equal (blue and red markers, respectively). i, When the frequencies differ, interference causes frequency and amplitude fluctuations in the transition regime.
Bridging two insect flight modes in evolution, physiology and robophysics

October 2023

·

283 Reads

·

12 Citations

Nature

Since taking flight, insects have undergone repeated evolutionary transitions between two seemingly distinct flight modes1–3. Some insects neurally activate their muscles synchronously with each wingstroke. However, many insects have achieved wingbeat frequencies beyond the speed limit of typical neuromuscular systems by evolving flight muscles that are asynchronous with neural activation and activate in response to mechanical stretch2–8. These modes reflect the two fundamental ways of generating rhythmic movement: time-periodic forcing versus emergent oscillations from self-excitation8–10. How repeated evolutionary transitions have occurred and what governs the switching between these distinct modes remain unknown. Here we find that, despite widespread asynchronous actuation in insects across the phylogeny3,6, asynchrony probably evolved only once at the order level, with many reversions to the ancestral, synchronous mode. A synchronous moth species, evolved from an asynchronous ancestor, still preserves the stretch-activated muscle physiology. Numerical and robophysical analyses of a unified biophysical framework reveal that rather than a dichotomy, these two modes are two regimes of the same dynamics. Insects can transition between flight modes across a bridge in physiological parameter space. Finally, we integrate these two actuation modes into an insect-scale robot11–13 that enables transitions between modes and unlocks a new self-excited wingstroke strategy for engineered flight. Together, this framework accounts for repeated transitions in insect flight evolution and shows how flight modes can flip with changes in physiological parameters.


Multimodal Locomotion in a Soft Robot Through Hierarchical Actuation

July 2023

·

65 Reads

·

7 Citations

Soft Robotics

Soft and continuum robots present the opportunity for extremely large ranges of motion, which can enable dexterous, adaptive, and multimodal locomotion behaviors. However, as the number of degrees of freedom (DOF) of a robot increases, the number of actuators should also increase to achieve the full actuation potential. This presents a dilemma in mobile soft robot design: physical space and power requirements restrict the number and type of actuators available and may ultimately limit the movement capabilities of soft robots with high-DOF appendages. Restrictions on actuation of continuum appendages ultimately may limit the various movement capabilities of soft robots. In this work, we demonstrate multimodal behaviors in an underwater robot called "Hexapus." A hierarchical actuation design for multiappendage soft robots is presented in which a single high-power motor actuates all appendages for locomotion, while smaller low-power motors augment the shape of each appendage. The flexible appendages are designed to be capable of hyperextension for thrust, and flexion for grasping with a peak pullout force of 32 N. For propulsion, we incorporate an elastic membrane connected across the base of each tentacle, which is stretched slowly by the high-power motor and released rapidly through a slip-gear mechanism. Through this actuation arrangement, Hexapus is capable of underwater locomotion with low cost of transport (COT = 1.44 at 16.5 mm/s) while swimming and a variety of multimodal locomotion behaviors, including swimming, turning, grasping, and crawling, which we demonstrate in experiment.


Ad

Citations (63)


... We call this combination of elastic, inertial, and aerodynamic mechanisms a 'spring-wing' system [5]. While significant research focus has been devoted to the aerodynamic force generation of flapping wings (see review in [6]), relatively fewer studies have focused on understanding the implications of elastic energy storage and return for flight dynamics and control [3,4,[7][8][9][10]. ...

Reference:

Stability and agility trade-offs in spring-wing systems
The Weis-Fogh Number Describes Resonant Performance Tradeoffs in Flapping Insects
  • Citing Article
  • May 2024

Integrative and Comparative Biology

... Compliance within the wing hinge can be modeled as a multi-axis torsional spring [40]. Modeling efforts have been used to elucidate the effect of wing flexibility on thorax deformation [41], to explore resonance phenomena [42], the implications of resonance on flight energetics [43], and to explore the interactions of flight muscle with system properties [44,45]. ...

Bridging two insect flight modes in evolution, physiology and robophysics

Nature

... They developed a control loop structure based on singular value decomposition that can drive the 2 √ N rows and columns of a hydraulic cylinder robotic array to any shape [24,25,26,27,28,17,29,30]. In this method, a 'control coupler' valve is also needed for each cylinder to integrate the row and column control messages, which are fluid pressures [31]. More recently, Jadhav et al. designed a compact fluidic logic module to regulate the input row and column pressures for a pneumatic soft linear actuator array [32]. Besides fluidic actuators, a robotic surface made of ionic polymer stripes are controlled using peripheral voltages based on pre-trained neural networks [33]. ...

Scalable Fluidic Matrix Circuits for Controlling Large Arrays of Individually Addressable Actuators

... In granular matter, propulsion can be achieved through non-reciprocal and complicated mechanisms [1], such as undulation for slender swimmers [34][35][36][37], fluidization [38,39], and adding compliance to flapping swimmers [40,41]. Here, we ask whether simple and reciprocal motion, considered by the scallop theorem, can cause locomotion in granular matter. ...

Toward Robotic Sensing and Swimming in Granular Environments using Underactuated Appendages

... But damping is also at work: exoskeletal structures also dissipate energy via viscoelastic effects within the partiallysclerotised chitin-protein matrix of which they are composed (Aberle et al., 2017). Empirical evidence from dynamic mechanical analysis (DMA) across a range of species and locomotor systems-including hawkmoth flight motors (Gau et al., 2019;Wold et al., 2023); beetle elytra (Lomakin et al., 2010); and cockroach legs (Dudek and Full, 2006;Dudek and Full, 2007)indicates that this damping is often largely frequency-or rate-independent: a property consistent with the characteristics of chitin and other cuticle polymers (Aberle et al., 2017;Martin and T., 1962;Sun et al., 2016), and which can lead to favourable control properties (Dudek and Full, 2007;Wold et al., 2023). ...

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations

... Bumblebees travel large distances from their nest during foraging bouts [27][28][29], presumably searching for resources if they are not navigating directly to a previously learned patch. Recent work showed that bumblebees prefer to fly upwind [41], which primes them to utilize olfactory navigation if they encounter an 'acceptable' odor-plume [42,43]. If, as our opaque-panel tests indicate, experienced foraging bees are less flexible in terms of accepting disrupted color+odor combinations they are more likely to pass over discovered patches whose odors have been modulated by human activity. ...

Going against the flow: bumblebees prefer to fly upwind and display more variable kinematics when flying downwind

Journal of Experimental Biology

... One approach is to design Synthetic Nervous Systems (SNS), networks of conductance-based neurons and synapses which can be used to model animal nervous systems [4,5] and control robots [6][7][8]. Some strengths of SNS networks include that they can be tuned using analytic design rules [9,10] and that results obtained controlling robotic hardware can propose neurobiological hypotheses [11,12]. ...

A virtuous cycle between invertebrate and robotics research: perspective on a decade of Living Machines research

... A sprawl-tuned autonomous robot (STAR) uses variable leg sprawl angle to adapt its stiffness and height 50 . Passively telescoping legs on another robot can compress in a programmed direction and allow it to passively traverse narrow channels 51 . Other examples of folding robots include a compliant legged articulated robotic insect (CLARI) 18 , a cockroach-inspired soft legged robot 52 , a hybrid mobile robot with controllable stiffness 53 , and a foldable drone 54 . ...

Directionally Compliant Legs Enabling Crevasse Traversal in Small Ground‐Based Robots