%*** CHAPTER 9: TRAJECTORY GENERATION ***

function s = QuinticTimeScaling(Tf, t)
% Takes Tf: Total time of the motion in seconds from rest to rest,
%       t: The current time t satisfying 0 < t < Tf.
% Returns s: The path parameter s(t) corresponding to a fifth-order
%            polynomial motion that begins and ends at zero velocity and 
%            zero acceleration.
% Example Input: 
%{
  clear; clc;
  Tf = 2;
  t = 0.6;
  s = QuinticTimeScaling(Tf,t)
%}
% Output:
% s =
%    0.1631

s = 10 * (t / Tf) ^ 3 - 15 * (t / Tf) ^ 4 + 6 * (t / Tf) ^ 5;
end