Closed-form time derivatives of the equations of motion of rigid body systems. (English) Zbl 1483.70026
Summary: 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.
MSC:
| 70E55 | Dynamics of multibody systems |
| 70E60 | Robot dynamics and control of rigid bodies |
| 70G65 | Symmetries, Lie group and Lie algebra methods for problems in mechanics |
Keywords:
rigid body dynamics; derivatives of equations of motion; inverse dynamics; closed form; screws; Lie group; higher-order inverse dynamicsReferences:
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