Non-reciprocal kinks in frustrated active metamaterials

Reciprocity is a fundamental principle governing most physical systems. In recent years, large levels of non-reciprocity have been realized by breaking local spatial symmetries. Here we break local and global symmetries as the same time by combining non-reciprocity and the non-orientable topology. We use local control loops to break reciprocity at the level of interactions between robotic unit cells. The non-orientable topology is realized by global geometrical frustration, which breaks global translation symmetry. We show theoretically and experimentally that unidirectionally propagating kinks emerge in this active system. These reciprocal kinks are topological protected. Based on the non-reciprocal kinks, we build a soft robot, which has various topologically protected motions. We anticipate non-reciprocal kinks will open avenues for energy absorption and harvesting, soft robotics, wave propagations and topological metamaterials.