arXiv subjects

Yizhar Or

Publications and source records attributed to Yizhar Or.

30 records · Page 2Linked to original sources

arXiv2021

Experimental Verification of Stability Theory for a Planar Rigid Body with Two Unilateral Frictional Contacts

Stability of equilibrium states in mechanical systems with multiple unilateral frictional contacts is an important practical requirement, with high relevance for robotic applications. In our previous work, we theoretically analyzed finite-time Lyapunov stability for a minimal model of planar rigid body with two frictional point contacts. Assuming inelastic impacts and Coulomb friction, conditions for stability and instability of an equilibrium configuration have been derived. In this work, we present for the first time an experimental demonstration of this stability theory, using a variable-structure rigid ''biped'' with frictional footpads on an inclined plane. By changing the biped's center-of-mass location, we attain different equilibrium states, which respond to small perturbations by divergence or convergence, showing remarkable agreement with the predictions of the stability theory. Using high-speed recording of video movies, good quantitative agreement between experiments and numerical simulations is obtained, and limitations of the rigid-body model and inelastic impact assumptions are also studied. The results prove the utility and practical value of our stability theory.

cs.RO↗

arXiv2020

Dynamic Inchworm Crawling: Performance Analysis and Optimization of a Three-link Robot

Inchworm crawling allows for both quasistatic and dynamic gaits at a wide range of actuation frequencies. This locomotion mechanism is common in nonskeletal animals and exploited extensively in the bio-inspired field of soft robotics. In this work we develop and simulate the hybrid dynamic crawling of a three-link robot, with passive frictional contacts. We fabricate and experimentally test such robot under periodic inputs of joints' angles, with good agreement to the theoretical predictions. This allows to comprehend and exploit the effects of inertia in order to find optimal performance in inputs' parameters. A simple criterion of robustness to uncertainties in friction is proposed. Tuning the inputs according to this criterion improves the robustness of low-frequency actuation, while increasing the frequency allows for gaits with both high advancement velocity and robustness. Finally, the advantages of uneven mass distribution are studied. Time-scaling technique is introduced to shape inputs that achieve similar effect without reassembling the robot. A machine-learning based optimization is applied to these inputs to further improve the robot's performance in traveling distance.

cs.RO↗

arXiv2019

Understanding Legged Crawling for Soft-Robotics

Crawling is a common locomotion mechanism in soft robots and nonskeletal animals. In this work we propose modeling soft-robotic legged locomotion by approximating it with an equivalent articulated robot with elastic joints. For concreteness we study our soft robot with two bending actuators via an articulated three-link model. The solution of statically indeterminate systems with stick-slip contact transitions requires for a novel hybrid-quasitatic analysis. Then, we utilize our analysis to investigate the influence of phase-shifted harmonic inputs on performance of crawling gaits, including sensitivity analysis to friction uncertainties and energetic cost of transport. We achieve optimal values of gait parameters. Finally, we fabricate and test a fluid-driven soft robot. The experiments display remarkable agreement with the theoretical analysis, proving that our simple model correctly captures and explains the fundamental principles of inchworm crawling and can be applied to other soft-robotic legged robots.

cond-mat.soft↗

arXiv2019

Leveraging viscous peeling in soft actuators and reconfigurable microchannel networks

The research fields of microfluidics and soft robotics both involve complex small-scale internal channel networks, embedded within a solid structure. This work examines leveraging viscous peeling as a mechanism to create and activate soft actuators and microchannel networks, including complex elements such as valves, without the need for fabrication of structures with micron-scale internal cavities. We consider configurations composed of an internal slender structure embedded within another elastic solid. Pressurized viscous fluid is introduced into the interface between the two solids, thus peeling the two elastic structures and creating internal cavities. Since the gap between the solids is determined by the externally applied pressure, the characteristic size of the fluidic network may vary in time and be much smaller than the resolution of the fabrication method. This work presents a model for the highly nonlinear elastic-viscous dynamics governing the flow and deformation of such configurations. Fabrication and experimental demonstrations of micron-scale valves and channel-networks created from millimeter scale structures are presented, as well as the transient dynamics of viscous peeling based soft actuators. The experimental data is compared with the suggested model, showing very good agreement.

physics.flu-dyn↗

arXiv2019

Single-Input Control of Multiple Fluid-Driven Elastic Actuators Via Interaction Between Bi-Stability and Viscosity

A leading concept in soft robotics actuation, as well as in microfluidics applications such as valves in lab-on-a-chip devices, is applying pressurized flow in cavities embedded within elastic bodies. Generating complex deformation patterns typically requires control of several inputs, which greatly complicates the system's operation. In this work, we present a novel method for single-input control of a serial chain of bi-stable elastic chambers connected by thin tubes. Controlling a single flow rate at the chain's inlet, we induce an irreversible sequence of transitions that can reach any desired state combination of all bi-stable elements. Mathematical formulation and analysis of the system's dynamics reveal that these transitions are enabled thanks to bi-stability combined with pressure lag induced by viscous resistance. The results are demonstrated via numerical simulations combined with experiments for chains of up to 5 chambers, using water-diluted glycerol as the injected fluid. The proposed technique has a promising potential for development of sophisticated soft actuators with minimalistic control.

cond-mat.soft↗

arXiv2019

Inertial self-propulsion of spherical microswimmers by rotation-translation coupling

We study swimming of small spherical particles who regulate fluid flow on their surface by applying tangential squirming strokes. We derive translational and rotational velocities for any given stroke which is not restricted by axial symmetry as assumed usually. The formulation includes inertia of both the fluid and the swimmer, motivated by inertia's relevance for large Volvox colonies. We show that inertial contribution to mean speed comes from dynamic coupling between translation and rotation, which occurs only for strokes that break axial symmetry. Remarkably, this effect enables overcoming the scallop theorem on impossibility of propulsion by time-reversible stroke. We study examples of tangential strokes of axisymmetric travelling wave, and of asymmetric time-reversible flapping. In the latter case, we find that inertia-driven mean speed is optimized for flapping frequency and swimmer's size which fall well within the range of realistic physical values for Volvox colonies. We conjecture that similarly to Paramecium, large Volvox could use time-reversible strokes for inertia-driven swimming coupled with their rotations.

physics.flu-dyn↗

arXiv2019

Energy-optimal strokes for multi-link microswimmers: Purcell's loops and Taylor's waves reconciled

Micron-scale swimmers move in the realm of negligible inertia, dominated by viscous drag forces. In this paper, we formulate the leading-order dynamics of a slender multi-link (N-link) microswimmer assuming small-amplitude undulations about its straight configuration. The energy-optimal stroke to achieve a given prescribed displacement in a given time period is obtained as the largest eigenvalue solution of a constrained optimal control problem. Remarkably, the optimal stroke is an ellipse lying within a two-dimensional plane in the (N-1)-dimensional space of joint angles, where N can be arbitrarily large. For large N, the optimal stroke is a traveling wave of bending, modulo edge effects. If the number of shape variables is small, we can consider the same problem when the prescribed displacement in one time period is large, and not attainable with small variations of the joint angles. The fully nonlinear optimal control problem is solved numerically for the cases N=3 (Purcell's three-link swimmer) and N=5 showing that, as the prescribed displacement becomes small, the optimal solutions obtained using the small-amplitude assumption are recovered. We also show that, when the prescribed displacements become large, the picture is different. For N=3 we recover the non-convex planar loops already known from previous studies. For N=5 we obtain non-planar loops, raising the question of characterizing the geometry of complex high-dimensional loops.

physics.flu-dyn↗

arXiv2018

Dynamic Walking on Slippery Surfaces: Demonstrating Stable Bipedal Gaits with Planned Ground Slippage

Dynamic bipedal robot locomotion has achieved remarkable success due in part to recent advances in trajectory generation and nonlinear control for stabilization. A key assumption utilized in both theory and experiments is that the robot's stance foot always makes no-slip contact with the ground, including at impacts. This assumption breaks down on slippery low-friction surfaces, as commonly encountered in outdoor terrains, leading to failure and loss of stability. In this work, we extend the theoretical analysis and trajectory optimization to account for stick-slip transitions at point foot contact using Coulomb's friction law. Using AMBER-3M planar biped robot as an experimental platform, we demonstrate for the first time a slippery walking gait which can be stabilized successfully both on a lubricated surface and on a rough no-slip surface. We also study the influence of foot slippage on reducing the mechanical cost of transport, and compare energy efficiency in both numerical simulations and experimental measurements.

cs.RO↗

arXiv2018

Planar Multi-link Swimmers: Experiments and Theoretical Investigation Using "Perfect Fluid" Model

Robotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer's hydrodynamics in order to optimize its structure and control inputs. In this work, we study a planar snake-like multi-link swimmer by using the `perfect fluid' model that accounts for inertial hydrodynamic forces while neglecting viscous drag effects. The swimmer's dynamic equations of motion are formulated and reduced into a first-order system due to symmetries and conservation of generalized momentum variables. Focusing on oscillatory inputs of joint angles, we study optimal gaits for 3-link and 5-link swimmers via numerical integration. For the 3-link swimmer, we also provide a small-amplitude asymptotic solution which enables obtaining closed-form approximations for optimal gaits. The theoretical results are then corroborated by experiments and motion measurement of untethered robotic prototypes with 3 and 5 links floating in a water pool, showing a reasonable agreement between experiments and the theoretical model.

physics.flu-dyn↗

arXiv2017

Nonlinear parametric excitation effect induces stability transitions in swimming direction of flexible superparamagnetic microswimmers

Microscopic artificial swimmers have recently become highly attractive due to their promising potential for biomedical applications. The pioneering work of Dreyfus et al (2005) has demonstrated the motion of a microswimmer with an undulating chain of superparamagnetic beads, which is actuated by an oscillating external magnetic field. Interestingly, it has also been theoretically predicted that the swimming direction of this swimmer will undergo a $90^\circ$-transition when the magnetic field's oscillations amplitude is increased above a critical value of $\sqrt{2}$. In this work, we further investigate this transition both theoretically and experimentally by using numerical simulations and presenting a novel flexible microswimmer with a superparamagnetic head. We realize the $90^\circ$-transition in swimming direction, prove that this effect depends on both frequency and amplitude of the oscillating magnetic field, and demonstrate the existence of an optimal amplitude, under which, maximal swimming speed can be achieved. By asymptotically analyzing the dynamic motion of microswimmer with a minimal two-link model, we reveal that the stability transitions representing the changes in the swimming direction are induced by the effect of nonlinear parametric excitation.

physics.flu-dyn↗

arXiv2016

Lyapunov stability of a rigid body with two frictional contacts

Lyapunov stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of stability is highly desired in robotic applications that involve multiple unilateral contacts. Nevertheless, Lyapunov stability analysis of such systems is extremely difficult, because even small perturbations may result in hybrid dynamics where the solution involves many nonsmooth transitions between different contact states. This paper concerns with Lyapunov stability analysis of a planar rigid body with two frictional unilateral contacts under inelastic impacts, for a general class of equilibrium configurations under a constant external load. The hybrid dynamics of the system under contact transitions and impacts is formulated, and a \Poincare map at two-contact states is introduced. Using invariance relations, this \Poincare map is reduced into two semi-analytic scalar functions that entirely encode the dynamic behavior of solutions under any small initial perturbation. These two functions enable determination of Lyapunov stability or instability for almost any equilibrium state. The results are demonstrated via simulation examples and by plotting stability and instability regions in two-dimensional parameter spaces that describe the contact geometry and external load.

eess.SY↗

arXiv2016

Optimization and small-amplitude analysis of Purcell's three-link microswimmer model

This work studies the motion of Purcell's three-link microswimmer in viscous flow, by using perturbation expansion of its dynamics under small-amplitude strokes. Leading-order expressions and next-order correction terms for the displacement of the swimmer are obtained for the cases of a square or circular gait in the plane of joint angles. The correction terms demonstrate the reversal in movement direction for large stroke amplitudes, which has previously only been shown numerically. In addition, asymptotic expressions for Lighthill's energetic efficiency are obtained for both gaits. These approximations enable calculating optimal stroke amplitudes and swimmer's geometry (i.e. ratio of links' lengths) for maximizing either the displacement or Lighthill's efficiency.

physics.flu-dyn↗