Compute the kinematics chain for MultibodyPlant

[hongkai-dai]

It would be great if we have a function in MBP, to return all the joints on the kinematics chains from one link to another link. This function is useful for imposing the sparsity structure in Jacobian matrix computation.

[hongkai-dai]

Is it OK if we can support this functionality? We found that the solver performance can benefit greatly from constraint sparsity (see https://github.com/RobotLocomotion/drake/pull/21492#pullrequestreview-2086168608 with a factor of 6 improvement). Very often in inverse kinematics, the constraint only depend on a partial set of the joints.

[sherm1]

FYI this is easily supported in the new MbP topology code. Let me see if I understand the request:

• we have arbitrary links R and S in a system with branches
• moving down towards World, there is a "highest" ancestor link A common to the paths from R->World and S->World
• you would like all the links (or dofs) in the R->A path and the S->A path, since only those dofs can affect a constraint acting between R and S

Is that correct? The MbP topology code already has an API for finding A but doesn't currently return the paths.