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

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.

References in corpus (3)

• Screw and Lie Group Theory in Multibody Dynamics -- Recursive Algorithms and Equations of Motion of Tree-Topology Systems
• Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation
• An Overview of Formulae for the Higher-Order Kinematics of Lower-Pair Chains with Applications in Robotics and Mechanism Theory

Cited by in corpus (4)

• Dynamics of Parallel Manipulators with Hybrid Complex Limbs -- Modular Modeling and Parallel Computing
• A Constraint Embedding Approach for Dynamics Modeling of Parallel Kinematic Manipulators with Hybrid Limbs
• Closed Form Time Derivatives of the Equations of Motion of Rigid Body Systems
• A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of parallel Kinematic Manipulators