Hello r0m1!
If I understand well your problem, you want to control some control points on the deformable object to reach a certain deformation, in 3D or 2D (in the image) if you think of a visual servoing control law as you suggest.
– Computing the jacobian for such a problem is possible but very challenging since you need some “inverse simulation” tools to compute a compliance matrix which is somehow the equivalent to your jacobian, but which however has to be projected to 2D in the case of an image based visual servoing, through the interaction matrix of a point.
Anyway you can refer to the works by the DEFROST team (https://team.inria.fr/defrost/) in Lille which focuses on these problems, and especially to this paper: https://hal.archives-ouvertes.fr/hal-01618330/document
The control inputs are here forces exerted by the some specified actuators.
best regards,
Antoine
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