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

2022/03/01 by Singh, Shubham, Russell, Ryan P., Wensing, Patrick M.
#FOS: Computer and information sciences #Robotics (cs.RO)

paper · doi:10.48550/arxiv.2203.00679

Abstract

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.

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