The Lariat Online

3 Baylor professors head research group on $300,000 grant

Oct. 14, 2004


It isn't often that mathematical theories change. However, great strides are being made in a relatively new field of math called time scales. These strides are being taken with the help of a three-year $300,000 grant from the National Science Foundation to a research group of three Baylor professors.

Dr. Ian Gravagne, assistant professor of electrical and computer engineering; Dr. John Davis, assistant professor of mathematics; and Dr. Robert Marks, distinguished professor of electrical and computer engineering, are heading up the research group.

Three years ago, Gravagne was working on robotics in the engineering department when he came across a problem. Most robots as we know them today can only function in one of two ways -- discreet or continuous.

According to Gravagne and Davis, discreet robotics work like an elbow, moving at certain points. Continuous robotics are more like snakes, moving continuously at multiple and indistinguishable points. Time scales are a mathematical theory to describe how both discreet and continuous systems work together.

Gravagne wanted to combine these two functions and use a hybrid of the systems, but didn't have the math in order to complete the operation. Through an e-mail to the mathematics department, Davis and Gravagne started working to develop the math theory to do the engineering work. This robotics question spawned the beginning of the development of the time scales, or hybrid theories, that can be used for many applications in various fields.

"Time scales are a wide-open field," Davis said. "The theory has only been around for about 10 years and have never been used in applications."

Davis and Gravagne worked for a year with two graduate students working on the theories involved. Marks came to Baylor after that first year and quickly joined the research group.

"Time scales is mathematics that can be applied to a number of different disciplines, a tool that can be used in various areas and we are just beginning to scratch the surface with applications for this new area of ideas," Marks said.

There is very little research on either the math or engineering functions of time scales. Baylor is one of the few places nationwide where any work is being done with the new theory, and the first university to publish any papers on the subject.

"This research is a cooperative effort, combining both the mathematics and engineering departments," Davis said. "It really fits with Baylor's philosophy of interdisciplinary work that breaks down artificial boundaries between departments."

Marks agrees with Davis, adding that engineering working with mathematics is a synergistic relationship that fits very well with the goals of Baylor 2012 in opening a new paradigm in the way people look at engineering problems.

The research group is using the National Science Foundation grant to explore time scale applications in distributed control networks.

"There is a tiny Internet in every modern car that hooks together the sensors, actuators, motors, hydraulics and moving parts, and computers. In certain situations, there becomes so much information in the network that things start not working," Gravagne said.

According to Gravagne, the best way to control the network from freezing right now is to control the amount of information trying to go through the network that can crash the system. Research conducted by the group will use time scales to help change the timing of the functions so that manufacturers can put more peripherals on each network. Distributed control networks also appear in manufacturing and medical technology fields.

According to Marks, time scales can be used to help distributed control networks because in most cases where computers are being used to control physical things the computer operates at a steady, pre-defined pace.

"Part of the solution to the distributed control networks problem is to allow the computer to change its timing. Time scales math can handle situations with nonuniform timing, such as is involved in the automobile systems," Marks said.

According to Davis, the money from the National Science Foundation primarily goes to the graduate students hired to do part of the research. Two engineering graduate students have been hired to work on building computer simulations and hardware for communications networks. A mathematics doctoral candidate will be hired to help work on the theory. Gravagne said he also hopes to use undergraduates in the research and has applied for an amendment to their National Science Foundation grant to be used for an undergraduate program.

The research group meets twice a week during the academic year, and more frequently during the summer. For the first two years, the work is highly theoretical. The group will transition to testing and refining their theories during the third year.

"Baylor is the epicenter for this research in the country, drawing talent, research money and prestige to Baylor," Davis said. "This will benefit people from the Army to the general good of the scientific community."