Expanding our global testing capacity is critical to preventing and containing pandemics. Accordingly, accessible and adaptable automated platforms that in decentralized settings perform nucleic acid amplification tests resource-efficiently are required. Pooled testing can be extremely efficient if the pooling strategy is based on local viral prevalence; however, it requires automation, small sample volume handling and feedback not available in current bulky, capital-intensive liquid handling technologies. Here we use a swarm of millimetre-sized magnets as mobile robotic agents ('ferrobots') for precise and robust handling of magnetized sample droplets and high-fidelity delivery of flexible workflows based on nucleic acid amplification tests to overcome these limitations. Within a palm-sized printed circuit board-based programmable platform, we demonstrated the myriad of laboratory-equivalent operations involved in pooled testing. These operations were guided by an introduced square matrix pooled testing algorithm to identify the samples from infected patients, while maximizing the testing efficiency. We applied this automated technology for the loop-mediated isothermal amplification and detection of the SARS-CoV-2 virus in clinical samples, in which the test results completely matched those obtained off-chip. This technology is easily manufacturable and distributable, and its adoption for viral testing could lead to a 10-300-fold reduction in reagent costs (depending on the viral prevalence) and three orders of magnitude reduction in instrumentation cost. Therefore, it is a promising solution to expand our testing capacity for pandemic preparedness and to reimagine the automated clinical laboratory of the future.