#6816. Closed-form time derivatives of the equations of motion of rigid body systems

December 2026publication date
Proposal available till 26-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Control and Optimization;
Modeling and Simulation;
Aerospace Engineering;
Mechanical Engineering;
Computer Science Applications;
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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.
Keywords:
Closed form; Derivatives of equations of motion; Higher-order inverse dynamics; Inverse dynamics; Lie group; Rigid body dynamics; Screws

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