Current research in human–robot interaction often focuses on rendering communication between humans and robots more ‘natural’ by designing machines that appear and behave humanlike. Communication, in this human-centric approach, is often understood as a process of successfully transmitting information in the form of predefined messages and gestures. This article introduces an alternative arts-led, movement-centric approach, which embraces the differences of machinelike robotic artefacts and, instead, investigates how meaning is dynamically enacted in the encounter of humans and machines. Our design approach revolves around a novel embodied mapping methodology, which serves to bridge between human–machine asymmetries and socioculturally situate abstract robotic artefacts. Building on concepts from performativity, material agency, enactive sense-making and kinaesthetic empathy, our Machine Movement Lab project opens up a performative-relational model of human–machine communication, where meaning is generated through relational dynamics in the interaction itself.