I am trying to control a robotic arm with an Arduino Mega. There are six MG996R servos, the power
supply is 2 ICR18650 2600mAh 3.7V batteries, I am using two L7806 6V 1A voltage regulators to reduce the voltage for the servos with 3 servos per voltage regulator. Are there any problems with this circuit that could damage anything? Also after about a minute one of the servos make a high noise, is that a problem? I just want to be careful so I don't have to order parts again.
Your proposed servo power supply is totally inadequate. Budget AT LEAST 1 Amp per servo in all cases, the MG996R requires 1.4 A every time it starts to move.
Stall current of a MG996R is 2.5Amp@6volt.
One 1Amp regulator for three servos?..
Leo..
I stand corrected. The servo power supply has to be able to provide at least 3A (with safety margin) per moving servo.
You will probably need higher capacity batteries as well.
This isn't going to be easy!
Also after about a minute one of the servos make a high noise
Without the proper caps on the voltage regulators it could be the regulator that is oscillating.
Is there any way that I could limit the amount of amperage that the servos draw? Also, would it work to get another battery putting it up to 11.1 volts and I could put the servos in series instead of using voltage regulators, so each gets servo gets about 5.6V? And what is the main problem with the amperage being too high?
Nicholas_Robot:
Is there any way that I could limit the amount of amperage that the servos draw?
Only by reducing the voltage you use to power them, but that reduces their torque and speed in proportion. 
Nicholas_Robot:
Also, would it work to get another battery putting it up to 11.1 volts and I could put the servos in series, so each gets servo gets about 5.6V?
It certainly would not. 
Nicholas_Robot:
And what is the main problem with the amperage being too high?
If you draw too much current, the power supply (not so much the batteries if using lithiums, but the regulator) will not be able to maintain the voltage which will fall and the servo will not work. And if the regulator is not designed to "fail safe" on excessive current draw, it may burn out.
However, powering with 11.1 (nominal) volts and using a swithhmode "buck" converter specifically designed to cope with the maximum current draw would be quite efficient.
At present, you lack too much basic circuit theory to be designing your own.
RC suppliers sell "BEC" (battery eliminator) modules for powering servos from higher voltage battery packs. 3 Amps per servo!
I really don't want to buy anything online because it would take a month to arrive. If I bought six 5V 2A voltage regulators from an electronics store, one for each servo, it should work out. The stall current would be 2.08A though, but it is just a robotic arm, nothing crazy. Also, I only run one servo at a time it would be less of a concern for the batteries.
Aren't these servos designed for direct power from batteries?
I'd drop the regulators and power the servos directly from the batteries. If the difference between nominal 7.2V and 7.4V is not acceptable, insert a fat diode to reduce the voltage a bit.