Industrial robots cannot be reconfigured to optimally fulfill a given task and often have to be caged to guarantee human safety. Consequently, production processes are meticulously planned so that they last for long periods to make automation affordable. However, the ongoing trend toward mass customization and small-scale manufacturing requires purchasing new robots on a regular basis to cope with frequently changing production. Modular robots are a natural answer: Robots composed of standardized modules can be easily reassembled for new tasks, can be quickly repaired by exchanging broken modules, and are cost-effective by mass-producing standard modules usable for a large variety of robot types. Despite these advantages, modular robots have not yet left research laboratories because an expert must reprogram each new robot after assembly, rendering reassembly impractical. This work presents our set of interconnectable modules (IMPROV), which programs and verifies the safety of assembled robots themselves. Experiments show that IMPROV robots retained the same control performance as nonmodular robots, despite their reconfigurability. With respect to human-robot coexistence, our user study shows a reduction of robot idle time by 36% without compromising on safety using our self-verification concept compared with current safety standards. We believe that by using self-programming and self-verification, modular robots can transform current automation practices.