why does ode45 happen this index error?

I've been struggling with this program for a long time.

Is this ode45 being used incorrectly?

global d;
d=1;
tspan=[0;0.05];
xi=[1;2;pi];
vk=[3;5];
func=@(xi,vk) TwoWheel2(xi,vk);
[t,y]=ode45(func,tspan,0);
function dxi = TwoWheel2(xi,vk)
    v1=speed(vk);
    wk=toRadian(vk);
    dxi = zeros(3,1);
    dxi(1) = cos(xi(3)) * v1;
    dxi(2) = sin(xi(3)) * v1;
    dxi(3) = wk;
end
function u0=toRadian(vk)
    global d;
    vr=vk(1);
    vl=vk(2);
    u0=(vr-vl)/(2*d);
end
function v1=speed(vk)
    vr=vk(1);
    vl=vk(2);
    v1=(vr+vl)/2;
end

>> testode
The index exceeds the number of array elements (1).

error: testode>speed (line 22)
    vl=vk(2);
error: testode>TwoWheel2 (line 7)
    v1=speed(vk);
error: testode>@(xi,vk)TwoWheel2(xi,vk) (line 4)
func=@(xi,vk) TwoWheel2(xi,vk);
error: odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.
error: ode45 (line 115)
  odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
error: testode (line 5)
[t,y]=ode45(func,tspan,0);

Answer 1

[Alan Stevens]

See the following:

global d;
d=1;
tspan=[0;0.05];
xi=[1;2;pi];
vk=[3;5];
[t,y]=ode45(@TwoWheel2,tspan,xi,[],vk);
function dxi = TwoWheel2(~,xi,vk)
    v1=speed(vk);
    wk=toRadian(vk);
    dxi = zeros(3,1);
    dxi(1) = cos(xi(3)) * v1;
    dxi(2) = sin(xi(3)) * v1;
    dxi(3) = wk;
end
function u0=toRadian(vk)
    global d;
    vr=vk(1);
    vl=vk(2);
    u0=(vr-vl)/(2*d);
end
function v1=speed(vk)
    vr=vk(1);
    vl=vk(2);
    v1=(vr+vl)/2;
end

[Tsubasa Mano]

Thank you very very much!

If you don't mind,May I ask you to tell me why doing so would solve the problem?

[Alan Stevens]

You were calling the function with a single initial value of zero. Ode45 needed to call it with the same size vector as is returned (one with three elements here).

[Tsubasa Mano]

I understand, thank you.Let me ask you one more thing.

[t,y]=ode45(@TwoWheel2,tspan,xi,[],vk);

→[t,y]=ode45(@TwoWheel2,tspan,xi,vk,[]);Is this okay?I think [] is maybe option

dxi = TwoWheel2(~,xi,vk)

what does mean '~'?　Sorry for all the questions.

[Alan Stevens]

1. Yes, [] is a placeholder for options.
2. You would often have t, the time value there (more generally, the name of the independent variable); but, in your case, t is not used explicitly within TwoWheel2, so MATLAB suggests replacing it by ~. If it did make explicit use of the value of t, then ~ would need to be replaced by t. The ~ isn't essential; the routine would still work if you did replace it with t.

[Tsubasa Mano]

Thank you for everything.