During experiments with Java version of Lego motor controller and built-in LeJOS motor controller I found that they use different approaches to implement smooth acceleration. Lego controller uses integer arithmetics and implements non-linear acceleration algorithm. It divides the acceleration distance to the speed delta and gets the interval to increase speed for 1 degree/sec. Each time when the motor covers the interval, the controller increases its speed for 1 degree/sec. This algorithms is simple but acceleration is non-linear. LeJOS uses different approach. The version I tested had problems with smooth acceleration. But LeJOS team has published an updated version of motor controller that works well. This version implements linear acceleration approach using floating point arithmetic. Also LeJOS controller uses much smalled discretization interval (interval between regulation cycles). Lego controller uses 100ms interval, LeJOS controller uses 4ms interval. This small regulation interval has some advantages and disadvantages: it provides more fast reaction to change of external load but requires more CPU time, especially being implemented in Java. Lego controller is implemented in native ARM code and works faster.
I wanted to make a controller that has best qualities of LeJOS controller but requires less CPU time. I tried to increase discretization interval but found that this controller has problems with rotation to a specified angle. It could not reach the target position with zero speed and requires additional time to reach the target point.
