[t,q]=ode45( @robot, 0:0.01:10, [4;5;pi/3;1] )
plot( q(:,1), q(:,2) )

function dq = robot( t, q )
x = q(1);
y = q(2);
theta = q(3);
v = q(4);
% trajektoria
xr = sin(t);
yr = cos(t);
dxr = cos(t);
dyr = -sin(t);
ddxr = -sin(t);
ddyr = -cos(t);

 % robot:
dx = v*cos(theta);
dy = v*sin(theta);
% opis celu sterowania
e = [xr;yr] - [x;y];
de = [dxr;dyr] - [dx;dy];
dde = -10*de-25*e;
% sterowanie
A = [ cos(theta), -v*sin(theta) ; ...
sin(theta), v*cos(theta) ];
aw = inv(A)*(-dde + [ddxr;ddyr] );
a = aw(1);
w = aw(2);
% model układu - kinematyka / dynamika
dq = [ v*cos(theta) ; ...
v*sin(theta) ; ...
w ; ...
a ];
end