We present NeRTA (Next Release Time Analysis), a technique to enable dynamic software updates for lowlevel control software of mobile robots. Dynamic software updates enable software correction and evolution during system operation. In mobile robotics, they are crucial to resolve software defects without interrupting system operation or to enable on-the-fly extensions. Low-level control software for mobile robots, however, is time sensitive and runs on resource-constrained hardware with no operating system support. To minimize the impact of the update process, NeRTA safely schedules updates during times when the computing unit would otherwise be idle. It does so by utilizing information from the existing scheduling algorithm without impacting its operation. As such, NeRTA works orthogonal to the existing scheduler, retaining the existing platform-specific optimizations and fine-tuning, and may simply operate as a plug-in component. To enable larger dynamic updates, we further conceive an additional mechanism called bounded reactive control and apply mixed-criticality concepts. The former cautiously reduces the overall control frequency, whereas the latter excludes less critical tasks from NeRTA processing. Their use increases the available idle times. We combine real-world experiments on embedded hardware with simulations to evaluate NeRTA. Our experimental evaluation shows that the difference between NeRTA's estimated idle times and the measured idle times is less than 15% in more than three-quarters of the samples. The combined effect of bounded reactive control and mixed-criticality concepts results in a 150+% increase in available idle times. We also show that the processing overhead of NeRTA and of the additional mechanisms is essentially negligible.