Related papers: Soap-bubble Optimization of Gaits
This paper presents a comprehensive mathematical model of a servopneumatic system, aimed at its consolidation in literature. The work exploits system's friction forces, temperature and pressure evolution, heat transfer, leakage between…
The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group…
We propose a $\tau$-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional $\tau$-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures…
This paper discusses dynamical systems for disk-covering and sphere-packing problems. We present facility location functions from geometric optimization and characterize their differentiable properties. We design and analyze a collection of…
A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by the wave it produces on impacting the bath. The wave itself is modified by the environment, and thus the interactions of the moving droplet with…
We analyse weak and strong controllability notions for the locomotion of the 3-link Purcell's swimmer, the simplest possible swimmer at low Reynolds number from a geometric framework. After revisiting a purely kinematic form of the…
The non-stationary dynamics of a bouncing ball, comprising of both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signature of self-similarity,…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
Droplets bouncing on a vibrated liquid bath open ways to methods of manipulating droplets, creating double emulsion and performing pilot wave model experiments. In this work, we focus on the role of the droplet deformations in the vertical…
The complete physical understanding of the optimization of the thermodynamic work still is an important open problem in stochastic thermodynamics. We address this issue using the Hamiltonian approach of linear response theory in finite time…
Among the few methods which have been proposed to create small-scale swimmers, those relying on self-phoretic mechanisms present an interesting design challenge in that chemical gradients are required to generate net propulsion. Building on…
We study an ancient problem that in a static or dynamical system, sought an optimal path, which the context always means within an extremal condition. In fact, through those discussions about this theme, we established a universal essential…
We simulate the quasi-static motion of a spherical particle through a stable, horizontal soap film. The soap film subtends a fixed contact angle, in the range $10-135^\circ$, where it meets the particle. The tension and pressure forces…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature, viscous friction with the walls, and includes the transport of surfactant within the films and across…
Miniature-legged robots are constrained by their onboard computation and control, thus motivating the need for simple, first-principles-based geometric models that connect \emph{periodic actuation or gaits} (a universal robot control…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and…
An imbalanced rotor is considered. A system of moving balancing masses is given. We determine the optimal movement of the balancing masses to minimize the imbalance on the rotor. The optimal movement is given by an open-loop control solving…
In this article, a theoretical justification of one type of skew-symmetric optimal translational motion (moving in the minimal acceptable time) of a flexible object carried by a robot from its initial to its final position of absolute…