Related papers: Prediction of stable walking for a toy that cannot…
Humans possess a remarkable ability to react to unpredictable perturbations through immediate mechanical responses, which harness the visco-elastic properties of muscles to maintain balance. Inspired by this behaviour, we propose a novel…
We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…
In this paper, we study dynamic stability during running, focusing on the effects of speed and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without…
In the first part of this thesis, we present our efforts on experimental validation of the predictive performance of mechanics-based mathematical models on a physical one-legged hopping robot platform. We extend upon a recently proposed…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…
The paper presents a method to stabilize dynamic gait for a legged robot with embodied compliance. Our approach introduces a unified description for rigid and compliant bodies to approximate their deformation and a formulation for…
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…
Dilaton stabilization may occur in a theory based on a single asymptotically free gauge group with matter due to an interplay between quantum modification of the moduli space and tree-level superpotential. We present a toy model where such…
Snakes can move through almost any terrain. Although their locomotion on flat surfaces using planar gaits is inherently stable, when snakes deform their body out of plane to traverse complex terrain, maintaining stability becomes a…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
Recent studies have shown that many results published in peer-reviewed scientific journals are not reproducible. This raises the following question: why is it so easy to fool myself into believing that a result is reliable when in fact it…
The safety of mobile robots in dynamic environments is predicated on making sure that they do not collide with obstacles. In support of such safety arguments, we analyze and formally verify a series of increasingly powerful safety…
We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating…
In the area of bipedal locomotion, the spring loaded inverted pendulum (SLIP) model has been proposed as a unified framework to explain the dynamics of a wide variety of gaits. In this paper, we present a novel analysis of the mathematical…
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…
Trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. Description of the dynamics by moments is therefore not informative. Instead, we…
Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…
A recent article by Borisov et al. [Regular and Chaotic Dynamics 23.3 (2018): 339-354.] studies the motion of a rigid ball in a rotating-saddle trap. The authors claim that they derive a new equation of motion from the Lagrangian formalism,…
This paper investigates the stability properties and performance of super-twisting sliding-mode control loops subject to periodic perturbations. Although there exist conditions on the control gains that guarantee finite-time stability of…