  Multi-step pathways, constituted of a sequence of reconfigurations, are
central to a wide variety of natural and man-made systems. Such pathways
autonomously execute in self-guided processes such as protein folding and
self-assembly, but require external control in macroscopic mechanical systems,
provided by, e.g., actuators in robotics or manual folding in origami. Here we
introduce shape-changing mechanical metamaterials, that exhibit self-guided
multi-step pathways in response to global uniform compression. Their design
combines strongly nonlinear mechanical elements with a multimodal architecture
that allows for a sequence of topological reconfigurations, i.e., modifications
of the topology caused by the formation of internal self-contacts. We realized
such metamaterials by digital manufacturing, and show that the pathway and
final configuration can be controlled by rational design of the nonlinear
mechanical elements. We furthermore demonstrate that self-contacts suppress
pathway errors. Finally, we demonstrate how hierarchical architectures allow to
extend the number of distinct reconfiguration steps. Our work establishes
general principles for designing mechanical pathways, opening new avenues for
self-folding media, pluripotent materials, and pliable devices in, e.g.,
stretchable electronics and soft robotics.
