I would like to calculate the 3D discrete trajectory from a initial point $P_0$ to a variable point that changes each sample time $T_s$. The maximum absolute acceleration is $a_{max}$ and the initial velocity $v_0 = (0,0,0)$.
The final destination point changes each time, for instance imagine at time $T_s = 1$ ms the final point $P_f = (3,1)$ then at the time $T_s = 2$ ms, $P_f = (3,3)$ and so on. This changes won't be so big, but the numbers were to understand the point.
This might be a difficult matter so if someone knows how to adress atleast the first stage of the trajectory when we are accelerating towards the final point from the starting point it would be so good for me, the smooth approach once we are closer I do not care much.
Thanks in advance!