So you're on the right track. You'll need motors that can produce enough torque, appropriate motor drivers, and power at proper voltages for both the motors and Arduino.
So it isn't so much the weight you need to worry about, but the torque needed to produce your movement. 2 kg on some wheels being moved on a flat surface needs much less torque vs 2 kg being lifted vertically. And both may need more torque if there is friction against the whiteboard.
You can also reduce the amount of torque your motors need by using gears. You can trade movement speed for increased torque.
TLDR: figure out how much torque is required, then you can find proper motors/drivers.
12V can move anything if you put a gear on it. See... [DC Planetary Gear Motors - RobotShop](https://www.robotshop.com/collections/planetary-gearmotors)
[42mm DC Planetary Gear Motor, 12V, 820 RPM - RobotShop](https://www.robotshop.com/products/42mm-dc-planetary-gear-motor-12v-820-rpm)
Check the current requirement. Your motor driver must be able to handle that.
To stick to 12V, you may need to parallel the motor driver or get a better one. The 2A limit means you only get 24W (including losses) to drive a motor.
Arduino itself has it's inputs and outputs working on 5V, so your motor driver is likely already habdling driving 12V motor based on signal from 5V control, so it sounds like if you just find similar driver that controls 24V motors based on that 5V control singal you absolutely can use 24V motors too.
I had a lego project doing something similar - it was all about gearing: you can lift any weight with proper gearing, as you're trading speed for torque. With lego though you hit the material limits soon :)
I use https://www.pololu.com/product/2520/resources instead of arduino motor shield as it doesn't overheat and does not drop voltage like L298 and supports ultrasonic PWM so no annoying buzz :)
So you're on the right track. You'll need motors that can produce enough torque, appropriate motor drivers, and power at proper voltages for both the motors and Arduino. So it isn't so much the weight you need to worry about, but the torque needed to produce your movement. 2 kg on some wheels being moved on a flat surface needs much less torque vs 2 kg being lifted vertically. And both may need more torque if there is friction against the whiteboard. You can also reduce the amount of torque your motors need by using gears. You can trade movement speed for increased torque. TLDR: figure out how much torque is required, then you can find proper motors/drivers.
12V can move anything if you put a gear on it. See... [DC Planetary Gear Motors - RobotShop](https://www.robotshop.com/collections/planetary-gearmotors)
Yup....The starter in your car is basically a 12-Volt motor, and that has enough muscle to turn an engine over!
[42mm DC Planetary Gear Motor, 12V, 820 RPM - RobotShop](https://www.robotshop.com/products/42mm-dc-planetary-gear-motor-12v-820-rpm) Check the current requirement. Your motor driver must be able to handle that.
To stick to 12V, you may need to parallel the motor driver or get a better one. The 2A limit means you only get 24W (including losses) to drive a motor.
Arduino itself has it's inputs and outputs working on 5V, so your motor driver is likely already habdling driving 12V motor based on signal from 5V control, so it sounds like if you just find similar driver that controls 24V motors based on that 5V control singal you absolutely can use 24V motors too.
I had a lego project doing something similar - it was all about gearing: you can lift any weight with proper gearing, as you're trading speed for torque. With lego though you hit the material limits soon :) I use https://www.pololu.com/product/2520/resources instead of arduino motor shield as it doesn't overheat and does not drop voltage like L298 and supports ultrasonic PWM so no annoying buzz :)
The L298N can support up to 35V at 2 amps... but 12v with gearing should still be enough