Fossen's dynamic AUV model implementation

Hi,

I'm looking for an implementation of Fossen's dynamic model of an AUV in Matlab. It would be nicer if it was written in code as a function, so I can implement the control inputs based on any control method but it would be okay if it was in simulink aswell.

The model is shown in the picture,

Answer 1

[Sam Chak]

Hi @John Terry

You can follow a few examples on this link and apply the [V, S] = odeToVectorField(eqns) command.

https://www.mathworks.com/help/symbolic/odetovectorfield.html#bvlo61d-4

help odeToVectorField

 odeToVectorField Converting scalar differential equations to coupled 
                  first order systems (vector fields).
    odeToVectorField will not accept equations as strings in a future release. 
    Use symbolic expressions or sym objects instead.
 
    V = odeToVectorField('eqn1','eqn2', ...) accepts symbolic equations 
    representing ordinary differential equations given in terms of  
    expressions.
 
    The differential equations must be linear in the highest  
    derivatives of the unknown functions involved.
 
    The output 'V' is a SYM object containing the components of the  
    coupled first order system associated with 'eqn1','eqn2', ... 
    The output 'V' can be used as input for matlabFunction to generate  
    a MATLAB function. Such a function then can be used to define input  
    for a numerical ODE solver in MATLAB. 
  
    V = odeToVectorField('eqn1','eqn2', ...) returns a SYM object   
    containing the components of the coupled first order system 
    associated with 'eqn1','eqn2', ...
 
    [V,Y] = odeToVectorField('eqn1','eqn2', ...) additionally returns 
    the SYM object 'Y' listing the substitutions that have been made 
    for converting the input equations 'eqn1','eqn2', ... into the 
    components of 'V'.  In 'Y', derivatives are written as variables
    whose names are formed as detailed above.
 
    Note that the result for 'V' can directly be used as input for 
    matlabFunction in order to create a MATLAB function that can passed
    to one of MATLAB's numerical ODE solvers. See the examples below. 
  
    Example 1:
 
       syms x(t)
       V = odeToVectorField(diff(x, 2) == -3*t) returns
 
         V =
    
          Y[2]
          -3*t
 
       [V,Y] = odeToVectorField(diff(x, 2) + t*diff(x) + x == -3*t)
 
         V =
 
                           Y[2]
          - 3*t - t*Y[2] - Y[1]
  
  
         Y = 
  
           x
          Dx
 
       The result contained in 'V' can be used as input for 
       MATLABFUNCTION:
 
       M = matlabFunction(V,'vars', {'t', 'Y'})
 
         M = @(t,Y)[Y(2),t.*-3.0-t.*Y(2)-Y(1)]
 
    Example 2:
       You can also apply odeToVectorField on systems of scalar  
       differential equations: 
 
       syms f(t) g(t)
       [V,Y] = odeToVectorField(diff(f, 2) == f + g, diff(g) == -f + g)
  
         V =
   
          Y[1] - Y[2]
                 Y[3]
          Y[1] + Y[2]
    
         Y =
   
           g
           f 
          Df
 
       We compute the state space representation for y''=(1-y^2)*y'-y       
 
       syms y(t)
       [V,Y] = odeToVectorField(diff(y, 2) == (1-y^2)*diff(y) - y)
  
         V =
 
                                Y[2]
          - (Y[1]^2 - 1)*Y[2] - Y[1]
   
         Y =
  
           y
          Dy
 
       use it as input for MATLABFUNCTION 
 
       M = matlabFunction(V,'vars', {'t', 'Y'})
 
         M = @(t,Y)[Y(2);-(Y(1).^2-1.0).*Y(2)-Y(1)]
 
       and then use MATLAB's numerical ODE solver ODE45 to create a 
       plot of the solution: 
 
       sol = ode45(M,[0 20],[2 0]);
       x = linspace(0,20,100);
       y = deval(sol,x,1);
       plot(x,y);
 
 
    See also DSOLVE, matlabFunction.

    Documentation for odeToVectorField
       doc odeToVectorField