Limit cycles turn active matter into robots

Abstract

Active matter composed of energy-generating microscopic constituents is a promising platform to create autonomous functional materials. However, the very presence of these microscopic energy sources is what makes active matter prone to dynamical instabilities and hence hard to control. Here, we show that these instabilities can be coaxed into work-generating limit cycles that turn active matter into robots. We illustrate this general principle in odd active media, model systems whose interaction forces are as simple as textbook molecular bonds yet not constrained to be the gradient of a potential. These emergent robotic functionalities are demonstrated by revisiting what is arguably the oldest of inventions: the wheel. Unlike common wheels that are driven by external torques, an odd wheel undergoes work-generating limit cycles that allow it to roll autonomously uphill by virtue of its own deformation, as demonstrated by our prototypes. Similarly, familiar scattering phenomena, like a ball bouncing off a wall, turn into basic robotic manipulations when either the ball or the wall is odd. Using continuum mechanics, we reveal collective robotic mechanisms that steer the outcome of collisions or influence the absorption of impacts in experiments. Beyond robotics, work-generating limit cycles can also control the non-linear dynamics of active soft materials, biological systems and driven nanomechanical devices.

4 Figures, Methods and SI. Supplemental videos at https://home.uchicago.edu/~vitelli/videos.html

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• Symmetry-driven Phononic Metamaterials
• Mechanical inhibition of dissipation in a thermodynamically consistent active solid
• Mechanochemical feedback drives complex inertial dynamics in active solids
• More is less in unpercolated active solids
• Reentrant transition to collective actuation in active solids with a polarizing field
• Collective actuation in active solids in the presence of a polarizing field: a systematic analysis of the dynamical regimes
• Odd elasticity in disordered chiral active materials
• From Active to Odd to Smart Matter
• Dispersion Relations for Active Undulators in Overdamped Environments
• Pattern Formation in Robotic Mechanical Metamaterial
• Screw Symmetry, Chiral Hydrodynamics and Odd Instability in Active Cholesterics