I plan to buy several 3pi robots that I want to control the speed.
I have read about speed control here https://www.pololu.com/docs/0J21/5.c, and I would like to know what is the response time for the speed control. If I set a new speed for a wheel through set_motors(), how long doest it need to take effect .
The duty cycle of the motor driver PWM updates at the start of the next PWM cycle after the set_motors() function is called, so it is pretty much as fast of a change as possible when using PWM-based speed control. The limiting factor in speed updates is going to be the inertia of the robot or the time it takes to do all the other calculations in your main loop, not the response time of the set_motors() function.