New algebra speeds simulation software on Mars Pathfinder

PASADENA, Calif. - A new form of mathematics known as spatial operator algebra is at the heart of improvements to a design and development software package that helped NASA engineers craft hardware and software for the Mars Pathfinder mission.

By John McHale

PASADENA, Calif. - A new form of mathematics known as spatial operator algebra is at the heart of improvements to a design and development software package that helped NASA engineers craft hardware and software for the Mars Pathfinder mission.

The Dynamics Algorithms for Real-Time Simulation (DARTS) software is a multi-body dynamics simulator that can help users test and verify flight software and hardware for a variety of spacecraft. Its underlying algorithms provide the fastest possible solution technique to multidimensional analysis, its developers claim.

DARTS enables the use of high-fidelity spacecraft dynamics models without sacrificing simulation speed, and helps engineers reliably design and test flight software and reduce development costs and mission risks.

The spatial operator algebra, developed by Abhinandan Jain, Guillermo Rodriguez, and Guy K. Man of the NASA Jet Propulsion Laboratory (JPL) in Pasadena, Calif., is a mathematical approach for modeling the dynamic behavior of complex, articulated collections of bodies interacting with each other in free-space or in contact with the environment.

"It gives us more insight into behavior of dynamic bodies," Jain explains. The software can analyze many variables at once to increase the accuracy of predictions.

"Previously, algorithms increased the number of bodies cubically; our algebra increases them linearly," Rodriguez says. The JPL scientists accomplished this by embedding a filter into the software that enabled the computations to achieve linear growth.

The architecture enhanced software development by positioning design models during the development of the software itself, Rodriguez explains. It used operator algebra, a high-level symbology, which matches each symbol to many detailed operations.

The spatial algebra retrieves large and complex spatial data sets and their relation to one another, Rodriguez says. For example, something pushes the spaceship at point A, the algorithm will analyze how it is affected at points B, C, etc.

NASA officials consider DARTS to be an enabling technology in dynamics simulation, which has saved more than $10 million to date on NASA missions. NASA officials attribute the savings to streamlining the software development process by using the same software for all parts of spacecraft design.

NASA engineers calculate the software has been responsible for improvements in simulation speed and fidelity by as much as 100 times in flight applications.

Fidelity is the number of bodies that scientists can analyze using the software. For example, engineers can now examine the results of vibrations in parts of the spacecraft that previous algorithms were unable to detect. The team received an award for developing of the new algebra three years ago.

Rodriguez sees the software`s ability to analyze a large amount of information in a short time contributing to the engineering of complex mechanical systems in many fields.

It has been used on NASA`s Cassini, Galileo, Mars Pathfinder, Stardust, New Millennium, and Neptune Orbiter missions. DARTS also has been adapted to develop the NEIMO software for the molecular dynamics simulation of large-scale molecular systems.

As part of a National Science Foundation Grand Challenge Project, NEIMO is in use at the California Institute of Technology in Pasadena, Calif., for the simulation and analysis of protein folding, drug design, catalysts, virus mechanisms, and other applications.

NASA`s inventions and contributions board will present the software award at the Technology 2007 Conference in Boston Sept. 23.

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