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This paper studies the $\alpha$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $\alpha$-stability, which is particularly amenable to characterize the ability of…

To reproduce natural standing-up motion, recent studies have emphasized the importance of coordination between the assisting robot and the human. However, many non-wearable assistive devices have struggled to replicate natural motion…

The Cassie bipedal robot designed by Agility Robotics is providing academics a common platform for sharing and comparing algorithms for locomotion, perception, and navigation. This paper focuses on feedback control for standing and walking…

In this paper, we directly design a state feedback controller that stabilizes a class of uncertain nonlinear systems solely based on input-state data collected from a finite-length experiment. Necessary and sufficient conditions are derived…

Maintaining balance while walking is not a simple task for a humanoid robot because of its complex dynamics. The presence of a persistent disturbance makes this task even more challenging, as it can cause a loss of balance and ultimately…

Dynamic/kinematic model is of great significance in decision and control of intelligent vehicles. However, due to the singularity of dynamic models at low speed, kinematic models have been the only choice under many driving scenarios. This…

We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…

Soft machines typically exhibit slow locomotion speed and low manipulation strength because of intrinsic limitations of soft materials. Here, we present a generic design principle that harnesses mechanical instability for a variety of…

For systems that are not observable at the very equilibrium of interest to be stabilized, output-feedback stabilization is considerably challenging. In this paper we solve this control problem for the case-study of a second-order system…

Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…

If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…

In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots…

During the steady gait, humans stabilize their head around the vertical orientation. While there are sensori-cognitive explanations for this phenomenon, its mechanical e fect on the body dynamics remains un-explored. In this study, we take…

We derive and analyze a three dimensional model of a figure skater. We model the skater as a three-dimensional body moving in space subject to a non-holonomic constraint enforcing movement along the skate's direction and holonomic…

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…

We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to…

We present a locomotion mechanism that uses the stick-slip transition of a soft passive structure with an internal mechanical resonance. The structure is harmonically driven by a global vertical shaking and, because of its resonance…

Some dynamical properties of non interacting particles in a bouncer model are described. They move under gravity experiencing collisions with a moving platform. The evolution to steady state is described in two cases for dissipative…

Mechanisms of locomotion in microscopic systems are of great interest not only for technological applications, but also for the sake of understanding, and potentially harnessing, processes far from thermal equilibrium. Down-scaling is a…

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…