Thank you for this very comprehensive and informative response.
I use a NOCO GENIUS 5 Output 12V 5000mA charger. So I think the problem is not with the charger. I'm interested to learn that it takes an average of 12 hours for a full charge and should read more than 13V !
I also bought 2 other new batteries: Optima Blue top BT DC 4.2 55 Ah. I noticed that with these new batteries, the autonomy of the robot was very short: +/- 30 minutes. One of the 2 batteries was discharging very fast. I sent it back to the supplier who confirmed that it had discharged too much and that it was out of service.
So I'm wondering if I should buy just one that won't be the same age as the other or I should buy 2 new batteries
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It seems to me that the batteries which are connected in serial, must be identical (type, age and so on...).
The second one seems to discharge normally but I will make the test you suggested : a converter 12V to 220V and a lamp. Then I will measure the time it takes to recharge it.
How low can I let it go ? In other words at which voltage can I consider that the battery is discharged ?
Thanks again for your time