19,266 research outputs found
A modal approach to hyper-redundant manipulator kinematics
This paper presents novel and efficient kinematic modeling techniques for “hyper-redundant” robots. This approach is based on a “backbone curve” that captures the robot's macroscopic geometric features. The inverse kinematic, or “hyper-redundancy resolution,” problem reduces to determining the time varying backbone curve behavior. To efficiently solve the inverse kinematics problem, the authors introduce a “modal” approach, in which a set of intrinsic backbone curve shape functions are restricted to a modal form. The singularities of the modal approach, modal non-degeneracy conditions, and modal switching are considered. For discretely segmented morphologies, the authors introduce “fitting” algorithms that determine the actuator displacements that cause the discrete manipulator to adhere to the backbone curve. These techniques are demonstrated with planar and spatial mechanism examples. They have also been implemented on a 30 degree-of-freedom robot prototype
Stability criteria for planar linear systems with state reset
In this work we perform a stability analysis for a class of switched linear systems, modeled as hybrid automata. We deal with a switched linear planar system, modeled by a hybrid automaton with one discrete state. We assume the guard on the transition is a line in the state space and the reset map is a linear projection onto the x-axis. We define necessary and sufficient conditions for stability of the switched linear system with fixed and arbitrary dynamics in the location. \u
Interfacial motion in flexo- and order-electric switching between nematic filled states
We consider a nematic liquid crystal, in coexistence with its isotropic
phase, in contact with a substrate patterned with rectangular grooves. In such
a system, the nematic phase may fill the grooves without the occurrence of
complete wetting. There may exist multiple (meta)stable filled states, each
characterised by the type of distortion (bend or splay) in each corner of the
groove and by the shape of the nematic-isotropic interface, and additionally
the plateaux that separate the grooves may be either dry or wet with a thin
layer of nematic. Using numerical simulations, we analyse the dynamical
response of the system to an externally- applied electric field, with the aim
of identifying switching transitions between these filled states. We find that
order-electric coupling between the fluid and the field provides a means of
switching between states where the plateaux between grooves are dry and states
where they are wet by a nematic layer, without affecting the configuration of
the nematic within the groove. We find that flexoelectric coupling may change
the nematic texture in the groove, provided that the flexoelectric coupling
differentiates between the types of distortion at the corners of the substrate.
We identify intermediate stages of the transitions, and the role played by the
motion of the nematic-isotropic interface. We determine quantitatively the
field magnitudes and orientations required to effect each type of transition.Comment: 14 pages, 12 fig
On feedback stabilization of linear switched systems via switching signal control
Motivated by recent applications in control theory, we study the feedback
stabilizability of switched systems, where one is allowed to chose the
switching signal as a function of in order to stabilize the system. We
propose new algorithms and analyze several mathematical features of the problem
which were unnoticed up to now, to our knowledge. We prove complexity results,
(in-)equivalence between various notions of stabilizability, existence of
Lyapunov functions, and provide a case study for a paradigmatic example
introduced by Stanford and Urbano.Comment: 19 pages, 3 figure
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