Algorithm to control acceleration until a position is reached

Question

I have a point that moves (in one dimension), and I need it to move smoothly. So I think that it\'s velocity has to be a continuous function and I need to control the accelerati

Answer 1

I'd do something like Alex Deem's answer for trajectory planning, but with limits on force and velocity:

In pseudocode:

xtarget:  target position
vtarget:  target velocity*
x: object position
v: object velocity
dt: timestep

F = Ki * (xtarget-x) + Kp * (vtarget-v);
F = clipMagnitude(F, Fmax);
v = v + F * dt;
v = clipMagnitude(v, vmax);
x = x + v * dt;

clipMagnitude(y, ymax):
   r = magnitude(y) / ymax
   if (r <= 1)
       return y;
   else
       return y * (1/r);

where Ki and Kp are tuning constants, Fmax and vmax are maximum force and velocity. This should work for 1-D, 2-D, or 3-D situations (magnitude(y) = abs(y) in 1-D, otherwise use vector magnitude).