As the title suggests, what is a good tool path generation algorithm for moving from point A at PA(x, y) with velocity VA(x, y) to point B at PB(x, y) with velocity VB(x, y)?

Naively, one may think just find the acceleration A(x, y) so that by the time the object reaches PB(x, y), the velocity reaches VB(x, y).

However, this does not work all the time, as in the real world the system has a maximum motor winding current, thus a maximum force, thus a maximum acceleration, so the acceleration must be capped at Amax.

Furthermore, for power supply stability reasons, I would prefer the acceleration to be kept constant at +-Amax or zero, so for each axis, only 3 possible acceleration values can be used, +Amax, 0 or -Amax.

Given the constraints, what is a good strategy for this problem?

I do have a naive solution that I will post later, but I'd like to know if there are other solutions.

Regards,

B.G.