The vision of robotic materials—cohesive collectives of robotic units that can arrange into virtually any form with any physical properties—has long intrigued both science and fiction. Yet, this vision requires a fundamental physical challenge to be overcome: The collective must be strong, to support loads, yet flow, to take new forms. We achieve this in a material-like robotic collective by modulating the interunit tangential forces to control topological rearrangements of units within a tightly packed structure. This allows local control of rigidity transitions between solid and fluid-like states in the collective and enables spatiotemporal control of shape and strength. We demonstrate structure-forming and healing and show the collective supporting 700 newtons (500 times the weight of a robot) before “melting” under its own weight.