Paper ID: 2203.00679

Details of Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics

Shubham Singh, Ryan P. Russell, Patrick M. Wensing

The details of second-order partial derivatives of rigid-body Inverse/Forward dynamics are provided. Several properties and identities using Spatial Vector Algebra are listed, along with their detailed derivations. The expressions build upon previous work by the author on first-order partial derivatives of inverse dynamics. The first/second-order derivatives are also extended for systems with external forces. Finally, the KKT Forward dynamics and Impact dynamics derivatives are derived.

Submitted: Mar 1, 2022