On my quad, one of the motors starts just a little later than the other 3.
First I thought that the problem is the motor, so I changed it with a brand new one, but the problem didn't go away. Now I see that the ESC connected to that motor get warm - not hot - just warm while the rest stay cold. I'm powering the APM with the power module, and the V+ of the build in BECs are unconnected.
I tried calibrating the ESCs few times, but that motor still starts a little later.
Could the ESC be bad?