In the past, when researchers modeled quadruped gaits — how four-legged organisms walk, run and move — gaits have been modeled with separate neural networks, according to Professor and Associate Chair of the Department of Mathematical Sciences at the University of Northern Colorado Katherine Morrison.
Alongside Morrison, Brown researchers recently developed a neural network that can model five distinctive gait patterns in four-legged animals: bounding, pacing, trotting, walking and pronking.
“The big contribution here was then being able to understand how to get all of those different networks that could produce the individual gaits to coexist, or merge, or glue them together in such a way that you could still produce all five gaits in a single network,” Morrison, an author of the study, told The Herald.
Professor of Applied Mathematics Carina Curto and postdoctoral research associate Juliana Londono Alvarez are co-authors on the study.
The project was designed to “develop a network model” to represent neural activity generating particular gaits in quadrupeds, Morrison explained. “The idea is that we have neurons that are representing the activity for those limb nodes, and then we have a network that is collecting these neurons, representing the synapses between them,” she added.
Modeling this connectivity allowed the researchers to observe different activity patterns, with particular firing sequences representing distinct gaits.
“The idea that inspired the engineering was based on mathematical theory and mathematical models of how these neurons would interact in the network,” Morrison said.
According to Morrison, the researcher simulated equations that represented neurons’ behavior over time, such as how often they fire “based on the inputs that they’re getting from other nodes in the network.”
Assessing a given network in a given initial conditions, the researchers are able to simulate which neurons will fire over time. The researchers then used the simulation data to produce plots of what the patterns of firing look like, which was used to verify whether this pattern reflected the desired limb movements.
According to Morrison, the study began when Alvarez started working with the research team as a Ph.D. student at Pennsylvania State University.
Alvarez was “particularly interested in this question about quadruped gaits,” after reading a paper that had a “rather complicated model of quadruped gaits in one of her classes.” She wanted to identify a simpler yet biologically plausible model, Morrison said.
One of the study’s long-term goals is to use its work in circuitry to enable robots to perform functions like transitioning “between (walking) and trotting or a bound gait,” according to Morrison.
James Anderson, who was part of one of the early groups of researchers working on neural networks and is professor emeritus of cognitive and psychological sciences, said that these networks have many different applications.
“They’re really marvelously versatile things, and some of the stuff, like the various (artificial intelligence) systems, are extremely clever,” he said.
