Mining robots are what mine for you. They will mine day and night non-stop as long as your batteries are running. Your mining robots can only mine three mines at one time (a fourth can be obtained by using the remote control gadget), and mine at 25BPH (buckets per hour).
Your batteries are what run your mining robots, if they run out, your bots will stop mining and you'll stop finding things. Your batteries can be recharged simply by clicking the "findings" tab while not over inventory limit. At first, your maximum battery life is 20 hours, meaning your going to have to check at least once a day to keep them running. This time can be increased by getting more melds, which will increase your battery life by 1 hour per meld. You can also buy temporary battery extensions in the shop that will give you 10 days of battery life each. These are only temporary, but can be helpful if your going on vacation or will be away from a computer for a long period of time, allowing your mining robots to keep mining despite you not being there to recharge them. Each extension costs 9 credits.
These mining robots are special robots built by manufacturers in factories. They come in varieties labeled MR 05, MR 06, etc. The level of the robot is determined by the number of melds owned by the Manufacturer: 50-59 gives MR 05, 60-69 gives MR 06, etc. Since you cannot be a Manufacturer with less than 50 melds there is no MR 01 or MR 02 - it is possible to buy (but no longer produce) MR 03 and 04 on the older servers because the meld limit on manufacturing was once 30.
Mining robots replace your standard mining robot and have the ability to find damaged versions of normal items as they process buckets in your mine. The damaged items that are found will be blue, red, purple or orange rarity. Damaged items cannot be used or sold but they can be repaired in a factory with 1 Ore and 1000 components. Mining Robots can be bought and sold on the free market. Damaged items can be shipped.
Mining with an MR does NOT improve your ability to find normal items. When the buckets you have mined are being sifted for items, there is just the additional chance that a Damaged item is found.
Bigrig73 made the first miner robot, an MR 12, with the first Damaged Item being Damaged TNT.
There is no concrete data on MR bot find rate available.