function[tme,r,v,a]=minjerk(ro,rf,tm,dt)

% MINJERK Usage: minjerk(ro,rf,tm,dt) ro,rf are (x,y)

% initial and final positions

% tm is the movement time dt is time increment.

% Returns (x,y) positions through trajectory in r,

% velocities in v, acceleration in a 

% and time in tme





tme=[0:dt:tm];

ts=tme/tm;

xo=ro(1,1);

yo=ro(1,2);

xf=rf(1,1);

yf=rf(1,2);



t2=ts.*ts;

t3=t2.*ts;

t4=t3.*ts;

t5=t4.*ts;





r=ones(size(ts'))*ro+(15*t4-6*t5-10*t3)'*(ro-rf);

v=((60*t3-30*t4-30*t2)/tm)'*(ro-rf);

a=((180*t2-120*t3-60*ts)/(tm*tm))'*(ro-rf);

tme=tme';