How to add dof(s) for the basis of 'Shape' object

[Beta-y]

Hi, Dr. Caasenbrood. I have been working hard on study this kit for several days via investigating the codes and your corresponding papers and thesis. It is really an excellent tool for simulating soft stuffs.

Actually, I am wondering if there is a way to add degree of freedom(s) for the basis of Shape object so that it can be directly drived according to some controller or being under-actuated while no control input provided, of course. I did notice that there is a function named setBase which can change the basis location by setting an exact pose. But it seems like it can not be drived by using a hdle function like addControl. The following is an example using PCC model with only one segment, in which I increase the $x$-angle of basis according to time $t$ using setBase function:

Could you please give me some advices? Thank your pretty much! 😃

[BJCaasenbrood]

I've had the idea of free floating Cosserat beams for a while but never gotten the time to implement it. I do think most of the ingredients are there, except some minor computations here and there. I recently stumbled upon the paper from Caradonna et al. (2024) (see Section 3B), maybe this can help?

The paper can be found here Model_and_Control_of_R-Soft_Inverted_Pendulum.pdf

I'll have to look into it to make a working implementation...

[BJCaasenbrood]

@Beta-y I am thinking about posting an issue/future enhancement.

[Beta-y]

Ohhh! Thanks Dr.! That is exactly what I am looking for! It is really fresh out of the oven. I will take a deep look into this paper, as well as looking forward to the on-coming enhancement! ❤

[BJCaasenbrood]

@Beta-y I currently have a working implementation. I'll be submitting the code tomorrow. You can construct a free-floating Cosserat beam using Shapes(pod, dof, dof_base). An example is for instance:

M   = 8 % number of modes
pod = chebyspace(50,M);
dof_beam = [0,M,0,0,0,0];
dof_base = [0,1,0,0,0,0]; % only leave rotation free

shp = Shapes(pod, dof_beam, dof_base)

Here is the result with the system under gravity.

[BJCaasenbrood]

The plotting and simulation is done with this code:

while shp.solver.Time < shp.solver.TimeHorizon
    shp = shp.update();
    plotcurve(shp);
end

function shp = plotcurve(shp)
    cla;
    p = backbone(shp.system.Backbone);
    plot(p(:,1), p(:,3),'k-','LineW',3);
    axis equal;
    axis([-100, 100, -100, 100]*1.2);
    drawnow;
end

[BJCaasenbrood]

@Beta-y There are still some things that I need to polish out, and I also need to make sure it is compatible with the other examples of the toolkit. I noticed there is still a bug for when base_dof(4:6) != 0 (i.e., the beam can move freely in 3D space) -- the free-floating origin of the beam does not to seem evolve naturally in $\mathbb{R}^3$, but considering only rotation (i.e., its evolution on the $SO(3)$ manifold) seems to work fine! I also noticed that twist base_dof(1) != 0 destabilizes the system quickly -- I will fix this at some point.

Nevertheless, here is an pre-release version. Make sure to compile the new mex files sorotokimodel/mex/freebodyforwardkin/buildMexFFKFG.m and sorotokimodel/mex/freebodylagrangian/buildMexCFLGF.m

The model now has joint coordinates $[q_1, ..., q_M, \theta_1]$ when dof_beam = [0,M,0,0,0,0] and dof_base = [0,1,0,0,0,0]. The DOFs of the base are always added at the end.

prereleaseFreeShapes.zip

Please let me know if it works for you.

[BJCaasenbrood]

@Beta-y Below you'll find the code and result for making an unactuated soft pendulum, you may change @Control to a desired stabilizing controller. Let me know if the code below works for you 😉

M = 12;
mat = NeoHookean(0.1,0.4);
mat.params.Zeta = 0.2;

shp = Shapes(chebyspace(50,M), [0,M,0,0,0,0], [0,1,0,0,0,0]);
shp = shp.setRadius([8,8,0.85]);
shp = shp.setMaterial(mat);
shp = shp.setBase('-z');
shp = shp.rebuild();

shp.solver.TimeStep = 1/160;
shp.solver.TimeHorizon = 5;

shp.options.Display = @plotcurve;
shp = shp.addGravity([0;0;-9800]);

shp = shp.addControl(@Control);

ii = 1;
while shp.solver.Time < shp.solver.TimeHorizon
    shp = shp.update();
    plotcurve(shp);
    if ii == 1
        gif('soft_pendulum_active.gif','nodither',...
            'DelayTime', 1/60,...
            'frame',gca);
    else
        gif;
    end
    ii =  ii + 1;
end

function tau = Control(shp)
    t = shp.solver.Time;
    tau = zeros(shp.NJoint,1);
    tau(end) = .75 * sin(6*pi*t);
end

function shp = plotcurve(shp)
    cla;
    p = backbone(shp.system.Backbone);
    plot(p(:,1), p(:,3),'k-','LineW',3);
    axis equal;
    axis([-100, 100, -100, 100]*1.2);
    drawnow;
end

[Beta-y]

Hi, Dr.! I have tested the attached zip file. It seems like some properties of shapesoptions and beamoptions classes are lost, such as NBase; BaseTable; NBaseDof; and BaseDofMap, which are defined in dir named >sorotokimodel and not provided in zip file yet. I have added them by myself. And now it works perfectly. I will try to add some closed-loop controller and reply as soon as possible. Thank you a lot for your kind help! ❤

[BJCaasenbrood]

@Beta-y here are the missing files: beam_shapeoptions.zip

Edit: Nevermind, saw u added them yourself.