Measuring the ever-changing 3-dimensional (3D) motions of the ocean requires simultaneous sampling at multiple locations. In particular, sampling the complex, nonlinear dynamics associated with submesoscales (<1-10 km) requires new technologies and approaches. Here we introduce the Mini-Autonomous Underwater Explorer (M-AUE), deployed as a swarm of 16 independent vehicles whose 3D trajectories are measured near-continuously, underwater. As the vehicles drift with the ambient flow or execute preprogrammed vertical behaviours, the simultaneous measurements at multiple, known locations resolve the details of the flow within the swarm. We describe the design, construction, control and underwater navigation of the M-AUE. A field programme in the coastal ocean using a swarm of these robots programmed with a depth-holding behaviour provides a unique test of a physical-biological interaction leading to plankton patch formation in internal waves. The performance of the M-AUE vehicles illustrates their novel capability for measuring submesoscale dynamics.