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This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel…
One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of…
Two-component mixtures in optical lattices reveal a rich variety of different phases. We employ an exact diagonalization method to obtain the relevant correlation functions in hexagonal optical lattices to characterize those phases. We…
This paper presents the accessibility and small-time local controllability (STLC) results for $N$-link horizontal planar manipulators with only one unactuated joint. STLC is important in controls, both for design considerations and because…
Generalizable manipulation requires that robots be able to interact with novel objects and environment. This requirement makes manipulation extremely challenging as a robot has to reason about complex frictional interactions with…
We present a novel 6 DOF robotic mechanism for reaching high ceilings and positioning an end-effector. The end-effector is supported with three scissor mechanisms that extend towards the ceiling with 6 independent linear actuators moving…
This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are…
Optical lattice systems offer the possibility of creating and tuning Dirac points which are present in the tight-binding lattice dispersions. For example, such a behavior can be achieved in the staggered flux lattice or honeycomb type of…
Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed…
We study jumping lines loci of logarithmic bundles associated with finite sets of points in the projective plane. Using the interpolation matrix introduced in [DMTG25], we describe these loci as the zero sets of explicit determinants…
We study the radiative dynamics of coupled electric dipoles, modelled as Lorentz oscillators (LOs), in the presence of real-time mechanical oscillations. The dipoles are treated in a self-consistent way through a direct electromagnetic…
The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of…
We study two-dimensional (2D) solitons in the mean-field models of ultracold gases with long-range quadrupole-quadrupole interaction (QQI) between particles. The condensate is loaded into a deep optical-lattice (OL) potential, therefore the…
On the space of $\pm 1$ spin configurations on the 3$d$-square lattice, we consider the \emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities…
This chapter is about the fundamentals of fabrication, control, and human-robot interaction of a new type of collaborative robotic manipulators, called malleable robots, which are based on adjustable architectures of varying stiffness for…
We investigate the Josephson effect through a two-level quantum dot with an exchange coupling between two dot electrons. We compute the superconducting phase relationship and construct the phase diagram in the superconducting gap--exchange…
We introduce a canonical operator-theoretic construction associated to a finite geometric lattice, in which a simple nonassociative ``diamond product'' on the lattice basis gives rise to a family of creation operators indexed by atoms and a…
Closed kinematic chains are created whenever multiple robot arms concurrently manipulate a single object. The closed-chain constraint, when coupled with robot joint limits, dramatically changes the connectivity of the configuration space.…
We introduce a renormalization model which explains how the behavior of a discrete-time continuous dynamical system changes as the dimension of the system varies. The model applies to some two-dimensional systems, including H\'enon and Lozi…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…