An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists

TL;DR

This paper introduces an efficient $O(n)$-algorithm for higher-order kinematics and inverse dynamics of serial manipulators using spatial twist representation, improving computational efficiency for robotic control.

Contribution

It presents a novel spatial representation formulation for recursive $O(n)$ algorithms in higher-order kinematics and inverse dynamics, enhancing computational efficiency and simplicity.

Findings

Demonstrated on a 7 DOF Franka Emika Panda robot.

Achieved compact and efficient recursive algorithms.

Validated the effectiveness of the spatial representation approach.

Abstract

Optimal control in general, and flatness-based control in particular, of robotic arms necessitate to compute the first and second time derivatives of the joint torques/forces required to achieve a desired motion. In view of the required computational efficiency, recursive $O(n)$-algorithms were proposed to this end. Aiming at compact yet efficient formulations, a Lie group formulation was recently proposed, making use of body-fixed and hybrid representation of twists and wrenches. In this paper a formulation is introduced using the spatial representation. The second-order inverse dynamics algorithm is accompanied by a fourth-order forward and inverse kinematics algorithm. An advantage of all Lie group formulations is that they can be parameterized in terms of vectorial quantities that are readily available. The method is demonstrated for the 7 DOF Franka Emika Panda robot.