152 research outputs found
Dynamics and Control of Humanoid Robots: A Geometrical Approach
his paper reviews modern geometrical dynamics and control of humanoid robots.
This general Lagrangian and Hamiltonian formalism starts with a proper
definition of humanoid's configuration manifold, which is a set of all robot's
active joint angles. Based on the `covariant force law', the general humanoid's
dynamics and control are developed. Autonomous Lagrangian dynamics is
formulated on the associated `humanoid velocity phase space', while autonomous
Hamiltonian dynamics is formulated on the associated `humanoid momentum phase
space'. Neural-like hierarchical humanoid control naturally follows this
geometrical prescription. This purely rotational and autonomous dynamics and
control is then generalized into the framework of modern non-autonomous
biomechanics, defining the Hamiltonian fitness function. The paper concludes
with several simulation examples.
Keywords: Humanoid robots, Lagrangian and Hamiltonian formalisms, neural-like
humanoid control, time-dependent biodynamicsComment: 27 pages, 9 figures, Late
Jet Methods in Time-Dependent Lagrangian Biomechanics
In this paper we propose the time-dependent generalization of an `ordinary'
autonomous human biomechanics, in which total mechanical + biochemical energy
is not conserved. We introduce a general framework for time-dependent
biomechanics in terms of jet manifolds associated to the extended
musculo-skeletal configuration manifold, called the configuration bundle. We
start with an ordinary configuration manifold of human body motion, given as a
set of its all active degrees of freedom (DOF) for a particular movement. This
is a Riemannian manifold with a material metric tensor given by the total
mass-inertia matrix of the human body segments. This is the base manifold for
standard autonomous biomechanics. To make its time-dependent generalization, we
need to extend it with a real time axis. By this extension, using techniques
from fibre bundles, we defined the biomechanical configuration bundle. On the
biomechanical bundle we define vector-fields, differential forms and affine
connections, as well as the associated jet manifolds. Using the formalism of
jet manifolds of velocities and accelerations, we develop the time-dependent
Lagrangian biomechanics. Its underlying geometric evolution is given by the
Ricci flow equation.
Keywords: Human time-dependent biomechanics, configuration bundle, jet
spaces, Ricci flowComment: 13 pages, 3 figure
Jet Spaces in Modern Hamiltonian Biomechanics
In this paper we propose the time-dependent Hamiltonian form of human
biomechanics, as a sequel to our previous work in time-dependent Lagrangian
biomechanics [1]. Starting with the Covariant Force Law, we first develop
autonomous Hamiltonian biomechanics. Then we extend it using a powerful
geometrical machinery consisting of fibre bundles and jet manifolds associated
to the biomechanical configuration manifold. We derive time-dependent,
dissipative, Hamiltonian equations and the fitness evolution equation for the
general time-dependent human biomechanical system.
Keywords: Human biomechanics, covariant force law, configuration manifold,
jet manifolds, time-dependent Hamiltonian dynamicsComment: 16 pages, 3 figure
New Mechanics of Spinal Injury
The prediction and prevention of spinal injury is an important aspect of
preventive health science. The spine, or vertebral column, represents a chain
of 26 movable vertebral bodies, joint together by transversal viscoelastic
intervertebral discs and longitudinal elastic tendons. This paper proposes a
new locally-coupled loading-rate hypothesis}, which states that the main cause
of both soft- and hard-tissue spinal injury is a localized Euclidean jolt, or
SE(3)-jolt, an impulsive loading that strikes a localized spine in several
coupled degrees-of-freedom simultaneously. To show this, based on the
previously defined covariant force law, we formulate the coupled Newton-Euler
dynamics of the local spinal motions and derive from it the corresponding
coupled SE(3)-jolt dynamics. The SE(3)-jolt is the main cause of two basic
forms of spinal injury: (i) hard-tissue injury of local translational
dislocations; and (ii) soft-tissue injury of local rotational disclinations.
Both the spinal dislocations and disclinations, as caused by the SE(3)-jolt,
are described using the Cosserat multipolar viscoelastic continuum model.
Keywords: localized spinal injury, coupled loading-rate hypothesis, coupled
Newton-Euler dynamics, Euclidean jolt dynamics, spinal dislocations and
disclinationsComment: 14 pages, 1 figure, Late
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