There is some interest in using battery power for devices that need very low noise levels (like high-precision phono preamps for archiving purposes). While ESP have a circuit for an automatic charger, that doesn't allow for continuous operation.
You could instead use two batteries and swap between them, charging whichever one isn't currently in use. To avoid a voltage discontinuity when switching, they could both be used temporarily, "fading" from the low voltage to the high voltage, then switching the low one out to be charged once the target voltage is reached (the output would presumably be regulated anyway, so the actual output voltage from the PSU wouldn't matter). This would probably need some sort of microprocessor control (and it'd be awfully cute to have a display of battery voltages, etc.).