Damping matrix for bending and twisting

[aliseleem-ui]

Hello,

I have two question:

(1) I just trying to change the material properties from steeel as in your example TendonRobotPDE.m to soft material with the following properties
E=2Mpa, Poisson ration = 0.49, Density= 1200 kg/m^3. I got a singularity at vs_and_us = K\rhs; due to K. how to overcome the singularity due to change of material properties?

(2) How did you estimate the Damping matrix for bending and twisting (Dbt) and Square law drag coefficient matrix (C).

Thanks.

[JohnDTill]

Hi @aliseleem-ui,

Unfortunately I do not have access to a MATLAB license with fsolve, so I can no longer run the simulation. From playing around with the C++ version, I think the backbone geometry needs adjustment as well to be physically realistic given the reduced stiffness. When I change the radius from 0.00135/2m for spring steel to 0.05m for the new soft material, the solver does work again. That matches the intuition that a thin 1.35mm diameter soft backbone would quickly buckle, and soft robots are typically thicker.

In general solver failures are annoying to debug, since they could mean:

• Attempting to solve a physically unrealistic model
• A scenario like buckling which is physically realistic, but singular within the modeling framework
• A scenario which is merely difficult and badly conditioned, but fundamentally solveable
• Improper choice of discretisation N or Δt
• Numerical issues with the solver Jacobian

In this case it seems to be updated geometry though.

I believe the damping values were manually tuned to have similar decay to the experimental behaviour here: https://youtu.be/YHFm_TigsbA?si=hG_WWGjaZysJJ70b&t=171. Granted, the tuning isn't perfect and the oscillations take longer to settle in the simulation. It was a qualitative tuning.