Robotic Motion In Curved Space Defies Common Laws of Physics

When humans, animals, also machines move throughout the world, they always press against something, whether it is the ground, air, or water. Until currently, physicists thought this to be a constant, following the law of conservation momentum. Currently, scientists from the Georgia Institute of Technology have proven the opposite– when bodies exist in curved spaces, it turns out that they could, in fact, move without pressing against something.

The findings were released in Proceedings of the National Academy of Sciences on July 28th, 2022. In the paper, a group of scientists led by Zeb Rocklin, assistant professor in the College of Physics at Georgia Tech, created a robotic confined to a spherical surface with unprecedented degrees of isolation from its environment so that these curvature-induced effects would predominate.

“We allow our shape-changing object move on the simplest curved space, a sphere, to systematically study the motion in curved space,” said Rocklin. “We learnt that the predicted effect, which was so counter-intuitive some physicists dismissed it, indeed occurred: as the robotic changed its shape, it inched forward around the sphere in a manner that might not be attributed to environmental interactions.”

Creating a curved path

The research scientists set out to study how an object moved within a curved space. To confine the thing on the sphere with minimal interaction or exchange of momentum with the environment in the curved space, they permitted a set of motors drive on curved tracks as moving masses.

They then linked this system holistically to a rotating shaft so that the motors always move on a sphere. The shaft was supported by air bearings and also bushings to minimize the friction, and the alignment of the shaft was adjusted with the Globe’s gravity to minimize the residual force of gravity.

From there, as the robotic kept moving, gravity and friction exerted mild forces on it. These pressures hybridized with the curvature effects to produce a strange dynamic with properties neither might induce on their own. The research provides a crucial demo of how curved spaces could be attained and how it fundamentally challenges physical laws and intuition created for flat space. Rocklin wishes the experimental techniques developed will allow other researchers to explore these curved spaces.

Applications in space and beyond

While the results are small, as robotics becomes increasingly precise, understanding this curvature-induced effect might be of functional value, equally as the slight frequency shift induced by gravity became important to enable GPS systems to accurately share their positions to orbital satellites. Ultimately, the concepts of how a space’s curvature can be utilized for locomotion may enable spacecraft to navigate the greatly curved space around a black hole.

“This study additionally relates to the ‘Difficult Engine’ study,” said Rocklin. “Its designer claimed that it could move forward without any propellant. That engine was indeed impossible, but since spacetime is very slightly curved, a tool could really move forward with no any external forces or emitting a propellant– a novel discovery.”

More information:

Shengkai Li et al, Robotic swimming in curved space via geometric phase, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.2200924119

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