Closed Form Time Derivatives of the Equations of Motion of Rigid Body Systems

Abstract

Derivatives of equations of motion(EOM) describing the dynamics of rigid body systems 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 EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

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• Screw and Lie Group Theory in Multibody Dynamics -- Recursive Algorithms and Equations of Motion of Tree-Topology Systems
• An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists

Cited by in corpus (3)

• A Constraint Embedding Approach for Dynamics Modeling of Parallel Kinematic Manipulators with Hybrid Limbs
• A Recursive Lie-Group Formulation for the Second-Order Time Derivatives of the Inverse Dynamics of parallel Kinematic Manipulators
• Robust Co-Design of Canonical Underactuated Systems for Increased Certifiable Stability