A milestone in the study of octopus arms

The model is in turn used to explain how structural mechanics dramatically simplify the control of the arm by automatically orchestrating complex three-dimensional recurrent motions out of simple muscle contraction patterns. The researchers have been collaborating on this work since 2019 with the overarching goal of developing "cyberoctopus" capability -- in other words, creating robotic control systems that can replicate the complex movements of octopus arms.

In many animals including humans, a centralized brain serves as the decision-making hub, or controller, for the rest of the body. In contrast, octopus "brains" are distributed along the eight arms such that each arm can operate independently. Furthermore, the octopus's physiology allows each arm to achieve a range of motion described by nearly infinite degrees of freedom, making computation extremely complex.

"The general motivation is to figure out how to control a complex system with many degrees of freedom and find an alternative to running expensive computations," Gazzola said. "The octopus is an interesting animal model that has been studied since the 1980s. [Researchers] want to know the 'secret' to its abilities."

"I find it very interesting to learn from live animals and translate some of the insights into ideas for soft robotic design," Tekinalp said of his motivation for the study.

In previous efforts, the researchers worked with an interdisciplinary team to develop a theoretical approach to controlling a simplified octopus arm model. In this work, the team employed MRI and histological and biomechanical data to simulate a realistic arm comprised of nearly 200 intertwined muscle groups.

They also used image tracking to record the movements of a live octopus as it performed tasks in a tank. The octopus was placed on one side of a Plexiglas sheet with a hole through which only one arm could reach. In the experiments, a tempting object was placed on the opposite side of the sheet. The researchers could then video-capture the octopus reaching for and manipulating the object.

"It was almost like working with a little kid," Gazzola recalled of observing the octopus. "You have to know how to approach [the octopus] and keep it engaged."

From the imaging, the team extracted motion data and showed in simulation that their control approach could replicate the complex motions exhibited by the octopus arm. "We used topology and differential geometry to apply a set of fundamental theoretical results to the arm to describe its shape and control it via muscle actuation," Gazzola said.

To describe the arm's motion, the team developed simple muscle activation templates that could achieve complex 3D motion. "Instead of working with thousands of degrees of freedom, we related two topological quantities -- writhe and twist -- to muscle dynamics," Gazzola said. "These two quantities are each controlled by different muscle groups whose coactivation gives rise to a third topological quantity, that describe the arm's 3D morphological changes -- that is, its motion."

Their high-fidelity computational model is a milestone both in biology, where it can help explain the octopus's impressive capability, and engineering. "The computational model is a useful testbed for roboticists to test their algorithms," Mehta said.

The long-term study represents interdisciplinary efforts from multiple research groups and several students on campus over the years. Indeed, the team continues to change -- Tekinalp, who will graduate in December 2024, will be going on to a postdoctoral position at the University of Maryland, College Park.

"For both Mattia and I, it was heartening to see the close cooperation between the students from our two research groups," Mehta said.

Among the many next steps for this work, the researchers anticipate expanding their simulation techniques to investigate methods of controlling all eight arms in a collaborative fashion (e.g., mimicking how an octopus might work with multiple objects at once). They also hope to translate their findings into robotic prototypes for experimental testing.

"Our theoretical understanding is still an intuitive approach," Gazzola said of additional next steps. "We want to develop an automated framework so that our octopus model can learn to perform tasks on its own."