How do I take gradients of MultibodyPlant computations w.r.t. mass, center-of-mass, inertia, etc.?

Question

I see the current chapter of Underactuated: System Identification and the corresponding notebook, and it currently does it through symbolics.

I'd like to try out stuff like system identification using forward-mode automatic differentiation ("autodiff" via AutoDiffXd, etc.), just to check things like scalability, get a better feel for symbolics and autodiff options in Drake, etc.

As a first steps towards system identification with autodiff, how do I take gradients of MultibodyPlant quantities (e.g. generalized forces, forward dynamics, etc.) with respect to inertial parameters (say mass)?

---

• Note: Permalinks of Underactuated chapter + notebook at time of writing: sysid.html, sysid.ipynb

Answer 1

Drake's formulation of MultibodyPlant, in conjunction with the Drake Systems framework, can allow you to take derivatives (via autodiff) with respect to inertial parameters by using the parameter accessors of RigidBody<T> on the given plant's Context<AutoDiffXd>.

Please see the following tutorial:
https://nbviewer.jupyter.org/github/RobotLocomotion/drake/blob/nightly-release/tutorials/multibody_plant_autodiff_mass.ipynb