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Details of Second-Order Partial Derivatives of Rigid-Body Inverse Dynamics (2203.00679v5)
Published 1 Mar 2022 in cs.RO
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.