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Derivatives of equations of motion describing the rigid body dynamics arebecoming increasingly relevant for the robotics community and find manyapplications in design and control of robotic systems. Controlling robots, andmultibody systems comprising elastic components in particular, not onlyrequires smooth trajectories but also the time derivatives of the controlforces/torques, hence of the equations of motion (EOM). This paper presentsnovel nth order time derivatives of the EOM in both closed and recursive forms.While the former provides a direct insight into the structure of thesederivatives,the latter leads to their highly efficient implementation for largedegree of freedom robotic system.

Nth Order Analytical Time Derivatives of Inverse Dynamics in Recursive and Closed Forms