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The transition from sessile suspension to active mobile detritus feeding in early echinoderms (c.a. 500 Mya) required sophisticated locomotion strategies. However, understanding locomotion adopted by extinct animals in the absence of trace fossils and modern analogues is extremely challenging. Here, we develop a biomimetic soft robot testbed with accompanying computational simulation to understand fundamental principles of locomotion in one of the most enigmatic mobile groups of early stalked echinoderms—pleurocystitids. We show that these Paleozoic echinoderms were likely able to move over the sea bottom by means of a muscular stem that pushed the animal forward (anteriorly). We also demonstrate that wide, sweeping gaits could have been the most effective for these echinoderms and that increasing stem length might have significantly increased velocity with minimal additional energy cost. The overall approach followed here, which we call “Paleobionics,” is a nascent but rapidly developing research agenda in which robots are designed based on extinct organisms to generate insights in engineering and evolution.