Several years ago, CenterSpace kindly lent us its .NET mathematical library, NMath, for purely academic research purposes in the area of evolutionary robotics and robot navigation. The global robot localization task in a known environment was solved using 2D Laser SickPLS100 and point-to-point metrics. Navigation algorithms use powerful metaheuristic optimizers such as Differential Evolution, Particle Swarm Optimization, Repulsive Particle Swarm Optimization and CMA-Evolutionary Strategy. NMath library is used for all matrix computations i.e. multiplication, addition, subtraction, matrix inversion and matrix transposition etc. NMath is further used for eigenvalue computation at CMAES processing and for generation of random numbers with multivariable distributions (normal, Cauchy and uniform). Optimizers that use NMath library solve two, three or six dimensional optimization problems, that are in this case nonlinear, nonseparable, non-continuous, constrained, strongly multimodal and well conditioned. All computations were conducted in a common office environment under normal and also under heavy-duty operation conditions where the sensor data were loaded by various types of a noise. NMath library was also applied for so called N-dimensional (non-scalable) optimizer construction that uses more than 65 standard benchmark functions. see e.g. http://en.wikipedia.org/wiki/Test_functions_for_optimization.

All development work was done using purely MS Visual Studio C++/CLI 2008/2012 .NET 3.x,4.x for Windows XP,7,8 x32,x64. The research was a very demanding task.

NMath library was strong, fast and, above all, stable in the .NET environment and provides accurate results even if the numerical expression (reconing) is at the edge of the used programming language C++/CLI and especially for used processors of iAPX series.

All results of this many years-long-research were published in the prestigious journal,

Applied Artificial Intelligence, Taylor & Francis Eds., see DOI:10.1080/08839514.2014.875684, vol. 28, no. 4, 2014,

All created algorithms were included into OpenSlam.Org, University Freiburg project and are used by various researchers from around the world and, of course by our parent university Czech Technical University in Prague, for practical experiments and theoretical research. A WEB page of this project is at http://robomap.4fan.cz/.

We would like to express our cordial thanks to Trevor Misfeldt, CEO of CenterSpace Software for his willingness to help and perfect technical support.

Jaroslav Moravec and Petr Pošík (http://labe.felk.cvut.cz/~posik/)

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Jaroslav says:

I use NMath in RobomapStudio for evolutionary computations and robot pose estimation for navigation in known and partially known environments using 2D laser data. My  Covariance Matrix Adaptation Evolution Strategy (CMAES) implementation is completely built on NMath. I also use NMath in a variety of other ways–for example, for various types of statistical distribution generating (Cauchy, Gauss etc.). NMath provides significantly better results (accuracy) and stability in comparison to the Iridium (Math.NET) library, for example. NMath is a great tool to solve, simply and easily, many numerical problems in MS VS C++/CLI .NET language.

RobomapStudio is part of the international OpenSLAM project of the University of Freiburg. Results of the RobomapStudio are used in several research groups at the Czech Technical University in Prague (for example, here and here), and by many other research centers around the world.

For more information on Jaroslav’s work using NMath, see his recent publication in the journal Evolutionary Intelligence (Sept. 2013).

How are you using NMath? We’re always interested in hearing about interesting applications of NMath “in the wild,” and in receiving suggestions for how NMath can be improved. Let us know at info@centerspace.net.

Ken

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