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Boncuk,
I have several rechargeable Nickel-metal hydride batteries. My workplace encourages us to use them as a gesture for the environment. They produce 1.2 volts when fully charged. If you want to allow the end user to use rechargeables, you couldn't use the voltage as an indicator of charge status. Really, the cell is depleted when it produces 0 volts. It is useless when the combined output is less than the requirements of your components (in this case, 1.8 volts total). Assuming the microcontroller and all other components still work acceptably at 1.8 volts, then that's all you need the cells to produce.
Richard
Well, look, I guess engineering is all about compromise. Ultimately, you can accept a widely varying input voltage if your components can tolerate it, and you might get identical function from your components or tolerably different behaviour given different input voltages. Or you could try to fix the voltage and accept loss of power as heat. A low drop out regulator limits your margin for error so that you may not be able to use rechargeables at all. One way or another, you're taking the worst of it somewhere.