20,402 research outputs found
A Discrete Geometric Optimal Control Framework for Systems with Symmetries
This paper studies the optimal motion control of
mechanical systems through a discrete geometric approach. At
the core of our formulation is a discrete Lagrange-dâAlembert-
Pontryagin variational principle, from which are derived discrete
equations of motion that serve as constraints in our optimization
framework. We apply this discrete mechanical approach to
holonomic systems with symmetries and, as a result, geometric
structure and motion invariants are preserved. We illustrate our
method by computing optimal trajectories for a simple model of
an air vehicle flying through a digital terrain elevation map, and
point out some of the numerical benefits that ensue
Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion
Elastic network models (ENM) and constraint-based, topological rigidity
analysis are two distinct, coarse-grained approaches to study conformational
flexibility of macromolecules. In the two decades since their introduction,
both have contributed significantly to insights into protein molecular
mechanisms and function. However, despite a shared purpose of these approaches,
the topological nature of rigidity analysis, and thereby the absence of motion
modes, has impeded a direct comparison. Here, we present an alternative,
kinematic approach to rigidity analysis, which circumvents these drawbacks. We
introduce a novel protein hydrogen bond network spectral decomposition, which
provides an orthonormal basis for collective motions modulated by non-covalent
interactions, analogous to the eigenspectrum of normal modes, and decomposes
proteins into rigid clusters identical to those from topological rigidity. Our
kinematic flexibility analysis bridges topological rigidity theory and ENM, and
enables a detailed analysis of motion modes obtained from both approaches. Our
analysis reveals that collectivity of protein motions, reported by the Shannon
entropy, is significantly lower for rigidity theory versus normal mode
approaches. Strikingly, kinematic flexibility analysis suggests that the
hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of
motions, which goes nearly undetected in ENM. This hierarchy reveals distinct
motion regimes that rationalize protein stiffness changes observed from
experiment and molecular dynamics simulations. A formal expression for changes
in free energy derived from the spectral decomposition indicates that motions
across nearly 40% of modes obey enthalpy-entropy compensation. Taken together,
our analysis suggests that hydrogen bond networks have evolved to modulate
protein structure and dynamics
Endoscopic Camera Control by Head Movements for Thoracic Surgery
In current video-assisted thoracic surgery, the endoscopic camera is operated by an assistant of the surgeon, which has several disadvantages. This paper describes a system which enables the surgeon to control the endoscopic camera without the help of an assistant. The system is controlled using head movements, so the surgeon can use his/her hands to oper- ate the instruments. The system is based on a flexible endoscope, which leaves more space for the surgeon to operate his/her instruments compared to a rigid endoscope. The endoscopic image is shown either on a monitor or by means of a head- mounted display. Several trial sessions were performed with an anatomical model. Results indicate that the developed concept may provide a solution to some of the problems currently encountered in video-assisted thoracic surgery. The use of a head-mounted display turned out to be a valuable addition since it ensures the image is always in front of the surgeonâs eyes
Recommended from our members
Construction of periodic adapted orthonormal frames on closed space curves
The construction of continuous adapted orthonormal frames along C1 closedâloop spatial curves is addressed. Such frames are important in the design of periodic spatial rigidâbody motions along smooth closed paths. The construction is illustrated through the simplest nonâtrivial context â namely, C1 closed loops defined by a single Pythagoreanâhodograph (PH) quintic space curve of a prescribed total arc length. It is shown that such curves comprise a twoâparameter family, dependent on two angular variables, and they degenerate to planar curves when these parameters differ by an integer multiple of Ď. The desired frame is constructed through a rotation applied to the normalâplane vectors of the EulerâRodrigues frame, so as to interpolate a given initial/final frame orientation. A general solution for periodic adapted frames of minimal twist on C1 closedâloop PH curves is possible, although this incurs transcendental terms. However, the C1 closedâloop PH quintics admit particularly simple rational periodic adapted frames
- âŚ