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

Shivesh Kumar, Andreas Mueller

In: 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE International Conference on Robotics and Automation (ICRA-2021) May 30-June 5 Xi'an China IEEE 6/2021.


Derivatives of equations of motion describing the rigid body dynamics are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the equations of motion (EOM). This paper presents novel nth order time derivatives of the EOM in both closed and recursive forms. While the former provides a direct insight into the structure of these derivatives, the latter leads to their highly efficient implementation for large degree of freedom robotic system.


20210614_Nth_Order_Analytical_Time_Derivatives_of_Inverse_Dynamics_in.pdf (pdf, 2 MB )

German Research Center for Artificial Intelligence
Deutsches Forschungszentrum für Künstliche Intelligenz