Related papers: How do we walk? Using hybrid holonomy to approxima…
Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain. Standard control approaches typically assume no-slip contact and therefore degrade when slip occurs. We propose a control framework that…
Animals locomote for various reasons: to search for food, find suitable habitat, pursue prey, escape from predators, or seek a mate. The grand scale of biodiversity contributes to the great locomotory design and mode diversity. Various…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
Symmetry manifests itself in legged locomotion in a variety of ways. No matter where a legged system begins to move periodically, the torso and limbs coordinate with each other's movements in a similar manner. Also, in many gaits observed…
We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…
The study of the movement of flocks, whether biological or technological is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological…
We study a natural construction of a general class of inhomogeneous quantum walks (namely walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
We present a nonlinear stochastic model of the human gait control system in a variety of gait regimes. The stride interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the…
Hybrid systems, such as bipedal walkers, are challenging to control because of discontinuities in their nonlinear dynamics. Little can be predicted about the systems' evolution without modeling the guard conditions that govern transitions…
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the…
A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes…
We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions…
We introduce the notion of a "walk with jumps", which we conceive as an evolving process in which a point moves in a space (for us, typically $\mathbb{H}^2$) over time, in a consistent direction and at a consistent speed except that it is…
Realizing bipedal locomotion on humanoid robots with point feet is especially challenging due to their highly underactuated nature, high degrees of freedom, and hybrid dynamics resulting from impacts. With the goal of addressing this…
We consider a non-homogeneous random walks system on $\bbZ$ in which each active particle performs a nearest neighbor random walk and activates all inactive particles it encounters up to a total amount of $L$ jumps. We present necessary and…