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), (ICRA-2021), 30.5.-05.6.2021, Xi'an, IEEE, Jun/2021. IEEE.
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.