2022-08-08 ジョージア工科大学
Experimental realization of a swimmer on a sphere with actuated motors on a freely rotating boom arm.
研究チームは、こうした曲率に起因する効果が優勢になるように、環境から前例のないレベルで隔離された球面に閉じ込められたロボットを作成しました。
研究者たちは、曲がった空間の中で物体がどのように動くかを研究しようとした。球体上に物体を閉じ込め、湾曲した空間における環境との相互作用や運動量の交換を最小限に抑えるため、一連のモーターを移動質量として湾曲した軌道上で駆動させた。そして、このシステムを回転軸に全体的に接続し、モーターが常に球面上を移動するようにした。軸はエアベアリングとブッシュで支え、摩擦を最小限に抑え、地球の重力に合わせて軸のアライメントを調整し、重力の残留力を最小にした。
そこからロボットが動き続けると、重力と摩擦でわずかな力が働く。この力が曲率の効果と混ざり合い、どちらか一方だけでは実現できない不思議な力学を生み出しているのです。この研究は、曲がった空間がどのようにして実現されるのか、また、平らな空間を想定した物理法則や直観に根本的に疑問を投げかける重要な実証となりました。
＜関連情報＞
- https://research.gatech.edu/robotic-motion-curved-space-defies-standard-laws-physics
- https://www.pnas.org/doi/10.1073/pnas.2200924119
幾何学的位相による湾曲空間でのロボット遊泳 Robotic swimming in curved space via geometric phase
Shengkai Li, Tianyu Wang, Velin H. Kojouharov, James McInerney, Enes Aydin, Yasemin Ozkan-Aydin, Daniel I. Goldman , and D. Zeb Rocklin
Proceedings of the National Academy of Science Published:July 28, 2022
DOI:https://doi.org/10.1073/pnas.2200924119
Significance
In Newtonian dynamics, acceleration requires force, which is taken to imply that a stationary object cannot move without exchanging momentum with its environment. Here, we realize a system that defies this requirement: a robot confined to a sphere. As the device actively changes its shape, the noncommutativity of “translations” in curved spaces allows it to advance without frictional or gravitational forces, akin to how a falling cat can use shape changes to control its orientation but not its position. Under controlled frictional forces, the robot can achieve a state with finite momentum that nevertheless does not move forward. Our work demonstrates how the interaction between environmental curvature, active driving, and geometric phases yields rich, exotic phenomena.
Abstract
Locomotion by shape changes or gas expulsion is assumed to require environmental interaction, due to conservation of momentum. However, as first noted in [J. Wisdom, Science 299, 1865-1869 (2003)] and later in [E. Guéron, Sci. Am. 301, 38-45 (2009)] and [J. Avron, O. Kenneth, New J. Phys, 8, 68 (2006)], the noncommutativity of translations permits translation without momentum exchange in either gravitationally curved spacetime or the curved surfaces encountered by locomotors in real-world environments. To realize this idea which remained unvalidated in experiments for almost 20 y, we show that a precision robophysical apparatus consisting of motors driven on curved tracks (and thereby confined to a spherical surface without a solid substrate) can self-propel without environmental momentum exchange. It produces shape changes comparable to the environment’s inverse curvatures and generates movement of 10−1<?XML:NAMESPACE PREFIX = “[default] http://www.w3.org/1998/Math/MathML” NS = “http://www.w3.org/1998/Math/MathML” />10−1 cm per gait. While this simple geometric effect predominates over short time, eventually the dissipative (frictional) and conservative forces, ubiquitous in real systems, couple to it to generate an emergent dynamics in which the swimming motion produces a force that is counter-balanced against residual gravitational forces. In this way, the robot both swims forward without momentum and becomes fixed in place with a finite momentum that can be released by ceasing the swimming motion. We envision that our work will be of use in a broad variety of contexts, such as active matter in curved space and robots navigating real-world environments with curved surfaces.
