  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.
