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

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 n th 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.

A recursive inverse dynamics algorithm for robotic manipulators with elastic joints and its application to control

“…17 Recently, Mu¨ller and Kumar has extended the highorder inverse dynamics and kinematics based on the spatial representation of twists, and given the closed forms time derivatives of the equations of motion. [18][19][20] Another application of high-order differential dynamics is the inverse optimal control in human motion analysis which has a cost function that depends on the second order time-derivative of torque. 21 Apart from the above control methods based on the high-order inverse dynamics, there are so many trajectory tracking control methods were presented since the well-known comparative study of three kinds of global tracking control methods, including the decoupling-based schemes, the backsteppingbased scheme, and the passivity-based schemes.…”