Would this schematic work?

I’m making a model of the Curiosity rover.

It has 15 servo’s. Some operating at 7.4 V, others at 6 V. I use a voltage regulator to go from the 7.4 V the 2S2P LiPo provides to 6 V. The servo’s are controlled by an Arduino Mega 2560. There’s also some fans. Some work at 12 V, others at 5 V. They’re always on, unless I switch the battery off with the mechanical switch. There’s also a LASER diode. The driver of this LASER diode is made for 1S batteries, so I have a small 1S1P LiPo battery for the LASER. The LASER diode uses a 5V digital signal from the Arduino to turn on/off (NC). The Arduino itself is powered directly from the 2S2P. Everything is radio controlled.

Would this schematic work? The one thing I’m not so confident about is the ground of the Arduino. I don’t know if I can just connect two grounds of two different batteries on 2 different voltages like that.

Well, techically speaking, that is not a schematic. It is a block diagram. There is only ONE schematic symbol there (the laser diode). A 2S2P Lipo battery has a charged voltage of 8.4V, and should NOT be discharged below 6.4 V.

It has 15 servo's. Some operating at 7.4 V, others at 6 V. I use a voltage regulator to go from the 7.4 V the 2S2P LiPo provides to 6 V. The servo's are controlled by an Arduino Mega 2560. There's also some fans. Some work at 12 V, others at 5 V. They're always on, unless I switch the battery off with the mechanical switch. There's also a LASER diode. The driver of this LASER diode is made for 1S batteries, so I have a small 1S1P LiPo battery for the LASER. The LASER diode uses a 5V digital signal from the Arduino to turn on/off (NC). The Arduino itself is powered directly from the 2S2P. Everything is radio controlled.

Would this schematic work? The one thing I'm not so confident about is the ground of the Arduino. I don't know if I can just connect two grounds of two different batteries on 2 different voltages like that.

since there is no schematic and no indication of where the wires are connected to the receiver and why it is connected to a digital in and an analog in. Where does it explain the receiver connections ? Why is the receiver connected to the arduino ?

The receiver is connected to the Arduino because there's too many servo's to control everything directly. I'd use the switches on the radio controller to choose which set of servo's are being controlled.

For instance, switch 1 and switch 2 are off: now I can drive.
Switch 1 is on and switch 2 is off: now I can move the arm.
Switch 1 is off and switch 2 is on: now I can point the LASER.
Switch 1 is on and switch 2 is on: now the LASER turns on and I can point the LASER.

This could also be done with transistors or so, but there's another reason. The movement of certain servo's isn't so simple. Some will be limited in the angle they can travel so that they can't cause damage. The servo speed must be controllable. I don't see how I can do that without an Arduino.

I'm not saying that your approach is wrong, but FYI, this is NOT how to best utilize the forum.
The BEST way to utilize the forum, is NOT to propose YOUR solution (and ask us if it will work).
The BEST way to utilize the forum is ASSUME that WHATEVER you THOUGHT would be a good solution
is , in fact NOT (good) and simply begin your post with a comprehensive summary of your project objective and a list of the items (components) you have at your disposal, and simply ask the question:

WHAT IS THE BEST WAY TO UTILIZE MY RESOURCES TO ACCOMPLISH THE FOLLOWING MISSION OBJECTIVE:

Control yada yada yada ....

So WHY am I saying this ?

WHAT are the odds that YOU know MORE about how to do it than 100 + experts all over the world, most with 20+ years experience ?

Why not just start out by saying:
"If I knew how to do this I wouldn't be posting, so how should I do this ?"

If you have that many servos then why don't you use them to input binary numbers and use the arduino to look up the funtion of each number. How difficult is it to use a servo to interrupt an optical interrupter
, the output of which is a TTL 1 or 0 input to the arduino ?
how many combinations are possible with 4 servos ?

Why not add ONE or MORE of THESE

Are you aware of the SERVO FUNCTION ?

Why not use the arduino to control the servos ?
If you make an optical array , you could you a servo to select one of 'n' sensors to input number .

As a block diagram yes it will work. You need to connect all the GNDs together to make then a common reference point for the components. It may be simpler to use a proper RC Transmitter and Receiver to control the servos and control the laser via an RC switch. HobbyKing do some fairly cheap sets that would suffice

If some servos will run at 7.2V nominal - Futaba HV? they will also run on 6V but with a little less torque and speed

If you provide a complete circuit diagram for the servos ie are they on separate channels or are some on the same channel etc it would help

So the question is: what is a good way to control 15 servos with an arduino?

You will probably have power problems. Budget at least 1 Ampere per moving servo, so your servo power supply will need to be very beefy. If using batteries, you will need high discharge RC types (10 to 15 Amperes).

Due to electrical noise induced by the servos, the Arduino and radio will probably have to use a separate battery.

I don't know if I can just connect two grounds of two different batteries on 2 different voltages like that.

Grounds must always be connected together.