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

TL;DR

This paper introduces novel methods for computing the nth order time derivatives of the equations of motion in robotic systems, enabling smoother control and better dynamic analysis for complex multibody robots.

Contribution

It presents new recursive and closed-form expressions for nth order derivatives of EOM, improving computational efficiency and structural understanding for robotic control.

Findings

Closed-form derivatives reveal structural properties of EOM.

Recursive derivatives enable efficient computation for high-DOF robots.

Enhances control and trajectory planning in robotics.

Abstract

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.