Dynamics Identification Identification Model

[ahundt]

I'm interested in trying out the IDIM module on my robot arm. I looked at your papers and the comments and it seems an important aspect is dealing with the rubber feet on your bot. Can these algorithms be used for the dynamics of an arm without such a rubber component?

I'd normally just jump in and try things, but I also assume this will require physically moving the robot to make the estimates so I want to ensure I proceed safely. Any advice would be appreciated!

[haudren]

I never personally used the IDIM module but it's generally used for identifying more than only the elastic components at the feet, but rather to obtain all the inertial and dynamic properties of the robot. The IDIM module provided in Tasks actually does not compute the viscoelasticity regressors. To use it:

• Have your robot perform some trajectory with high speed/accelerations to stimulate all components and save all the relevant data (joint angles, velocity, acceleration, torque)
• At each step, compute the linearized dynamics using the IDIM. The point is to obtain:

Y \Phi = \tau

Where Y depends on the trajectory parameters (joint angles, velocity and acceleration), Phi represents all parameters. You can then inverse however you'd like Y to obtain the parameters back. I recommend generating joint-level trajectories and playing them directly on the robot to excite at most the joints.

In code:

IDIM idim(mb);
Eigen::MatrixXd regressors(samples.size()*mb.nrDof(), mb.nrBodies()*10);
Eigen::VectorXd torques(samples.size()*mb.nrDof());
for(int i = 0; i < samples.size(); ++i)
{
    updateFromSample(sample, mbc);
    regressors.block(i*mb.nrDof(), 0, mb.nrDof(), mb.nrBodies()*10) = idim.computeY(mb, mbc);
    torque.segment(i*mb.nrDof(), mb.nrDof()) = sample.torque;
}
params = regressors.jacobiSvd(ComputeThinU | ComputeThinV).solve(torque)

See: https://www.researchgate.net/publication/303840688_Humanoids_and_Humans_Inertia_Parameters_Identification_using_Hierarchical_Optimization
For more advanced discussions on this topic.

[ahundt]

awesome! I'll give it a look.

So I can create an appropriate trajectory in joint space using position commands, then as it follows that path record the position, velocity, acceleration, and torque on each joint at each time step. I then feed it into the solver as you mentioned in code, and that should extract my parameters.

My arm is attached to a base on wheels which I want to consider "fixed" I can attach the base solidly to a beam if that will help, but do I correctly assume that will affect the ability to get the parameters for the first few joints?

[haudren]

Having an fixed base is an asset and a drawback:

• It allows you to generate much more aggressive trajectories, that will stimulate all modes of the dynamics without having to worry about the stability and without having to observe the free-flyer dynamics.
• It prevents you from observing the free-flyer dynamics that contain all the necessary information (summed) to perform the identification, and thus contribute to having good identification.

If your trajectories are well-designed, you should be able to reconstruct every parameter of every body regardless of the base being fixed or not.

e/ Here is a video showing the kind of movement you should be aiming for: https://www.youtube.com/watch?v=qoUSdh3aW7I