rholt:
So far, not a very helpful thread...
I find it a good general policy NOT to ask my questions in unhelpful Threads. I suggest you ask the moderator (click report to in my Post, not yours) to move your question to a new Thread with a title that reflects your robot balancing project.
I am not very familiar with AccelStepper but it seems to be designed to move a motor X number of steps ramping up and down the speed on the way. I can imagine that changing the speed in the middle of that will throw off all the acceleration calculations. For example what happens if you ask it to change speed just before it was due to start decelerating? I don't think there is any way to know which phase it is in.
It is pretty easy to write code to drive a stepper motor and, hence, it should be easy enough to build in acceleration.
I wonder if your application needs to accelerate up (or down) to a speed and then hold the speed indefinitely until another change-speed command comes along.
Have you seen this Segway Thread
...R