84,816 research outputs found
Physical problem solving: Joint planning with symbolic, geometric, and dynamic constraints
In this paper, we present a new task that investigates how people interact
with and make judgments about towers of blocks. In Experiment~1, participants
in the lab solved a series of problems in which they had to re-configure three
blocks from an initial to a final configuration. We recorded whether they used
one hand or two hands to do so. In Experiment~2, we asked participants online
to judge whether they think the person in the lab used one or two hands. The
results revealed a close correspondence between participants' actions in the
lab, and the mental simulations of participants online. To explain
participants' actions and mental simulations, we develop a model that plans
over a symbolic representation of the situation, executes the plan using a
geometric solver, and checks the plan's feasibility by taking into account the
physical constraints of the scene. Our model explains participants' actions and
judgments to a high degree of quantitative accuracy
Explaining intuitive difficulty judgments by modeling physical effort and risk
The ability to estimate task difficulty is critical for many real-world
decisions such as setting appropriate goals for ourselves or appreciating
others' accomplishments. Here we give a computational account of how humans
judge the difficulty of a range of physical construction tasks (e.g., moving 10
loose blocks from their initial configuration to their target configuration,
such as a vertical tower) by quantifying two key factors that influence
construction difficulty: physical effort and physical risk. Physical effort
captures the minimal work needed to transport all objects to their final
positions, and is computed using a hybrid task-and-motion planner. Physical
risk corresponds to stability of the structure, and is computed using noisy
physics simulations to capture the costs for precision (e.g., attention,
coordination, fine motor movements) required for success. We show that the full
effort-risk model captures human estimates of difficulty and construction time
better than either component alone
Automatic Differentiation of Algorithms for Machine Learning
Automatic differentiation---the mechanical transformation of numeric computer
programs to calculate derivatives efficiently and accurately---dates to the
origin of the computer age. Reverse mode automatic differentiation both
antedates and generalizes the method of backwards propagation of errors used in
machine learning. Despite this, practitioners in a variety of fields, including
machine learning, have been little influenced by automatic differentiation, and
make scant use of available tools. Here we review the technique of automatic
differentiation, describe its two main modes, and explain how it can benefit
machine learning practitioners. To reach the widest possible audience our
treatment assumes only elementary differential calculus, and does not assume
any knowledge of linear algebra.Comment: 7 pages, 1 figur
Enhanced LFR-toolbox for MATLAB and LFT-based gain scheduling
We describe recent developments and enhancements of the LFR-Toolbox for MATLAB for building LFT-based uncertainty models and for LFT-based gain scheduling. A major development is the new LFT-object definition supporting a large class of uncertainty descriptions: continuous- and discrete-time uncertain models, regular and singular parametric expressions, more general uncertainty blocks (nonlinear, time-varying, etc.). By associating names to uncertainty blocks the reusability of generated LFT-models and the user friendliness of manipulation of LFR-descriptions have been highly increased. Significant enhancements of the computational efficiency and of numerical accuracy have been achieved by employing efficient and numerically robust Fortran implementations of order reduction tools via mex-function interfaces. The new enhancements in conjunction with improved symbolical preprocessing lead generally to a faster generation of LFT-models with significantly lower orders. Scheduled gains can be viewed as LFT-objects. Two techniques for designing such gains are presented. Analysis tools are also considered
Flap-lag-torsional dynamics of helicopter rotor blades in forward flight
A perturbation/numerical methodology to analyze the flap-lead/lag motion of a centrally hinged spring restrained rotor blade that is valid for both hover and for forward flight was developed. The derivation of the nonlinear differential equations of motion and the analysis of the stability of the steady state response of the blade were conducted entirely in a Symbolics 3670 Machine using MACSYMA to perform all the lengthy symbolic manipulations. It also includes generation of the fortran codes and plots of the results. The Floquet theory was also applied to the differential equations of motion in order to compare results with those obtained from the perturbation analysis. The results obtained from the perturbation methodology and from Floquet theory were found to be very close to each other, which demonstrates the usefullness of the perturbation methodology. Another problem under study consisted in the analysis of the influence of higher order terms in the response and stability of a flexible rotor blade in forward flight using Computerized Symbolic Manipulation and a perturbation technique to bypass the Floquet theory. The derivation of the partial differential equations of motion is presented
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