  Non-reciprocal transmission of motion is potentially highly beneficial to a
wide range of applications, ranging from wave guiding, to shock and vibration
damping and energy harvesting. To date, large levels of non-reciprocity have
been realized using broken spatial or temporal symmetries, yet only in the
vicinity of resonances or using nonlinearities, thereby nonreciprocal
transmission remains limited to narrow ranges of frequencies or input
magnitudes and sensitive to attenuation. Here, we devise a novel type of
robotic mechanical metamaterials wherein we use local control loops to break
reciprocity at the level of the interactions between the unit cells. We show
theoretically that first-of-their-kind asymmetric standing waves at all
frequencies and unidirectionally amplified propagating waves emerge. We
demonstrate experimentally and numerically that this property leads to tunable,
giant, broadband and attenuation-free non-reciprocal performances, namely a
level of 50dB non-reciprocal isolation over 3.5 decades in frequency, as well
as one-way amplification of pulses.
