1. PID controller. We try Mellinger controller today it does work, but why PID cant?

2. • Rate is the logging frequency. Use count just to confirms cmdFullState work.
   • Yes, we update like you said expect case 2 and the former part of case 3. p,v is the estimated pos and vel from logging, v' = v+a*dt, p' = p+v*dt, p',v' are those passed to the cmdFullState.

3. I think double integrator model, since velocity is part of our model function and the model outputs acceleration.

PID has low gains - generally it's more robust, but also doesn't track as well.

I am not sure why you use p and v from the odometry - that creates a strange feedback loop. Ideally you keep the state (=odometry) and setpoint separate. That is, store on the host-side the previous desired velocity for propagating the state, rather than using the current velocity. Make sure that the setpoint itself follows consistent double integrator dynamics (which is not the case when you mix setpoint and state), e.g., by plotting the desired states you sent via cmdFullState over time.

What we want to do is kind of "decentralized", each crazyflie acts based on current own and neighbors' state estimate. With this prerequisite, the setpoint has to rely on the state, or maybe it is something else not setpoint? I know not much about control, no more than fixed setpoint like the simplest PID, is there wiki or blog to introduce the control method you said?