推导刚体系统运动方程的二阶时间导数闭式解，助力机器人控制设计。
Closed Form Time Derivatives of the Equations of Motion of Rigid Body Systems
- 基于李群方法构建紧凑可参数化的运动方程导数表达式
- 首次给出刚体系统运动方程二阶时间导数的闭式解
- 适用于需要高阶控制力矩导数的机器人与多体系统设计
描述刚体系统动力学的运动方程（EOM）的时间导数在机器人领域日益重要，广泛应用于机器人设计与控制。控制机器人，特别是包含弹性部件的多体系统，不仅需要平滑轨迹，还需控制力/力矩的时间导数，即运动方程的导数。本文提出一种闭式方法，计算刚体系统运动方程至二阶时间导数，作为现有递归算法的替代方案，可直接揭示导数结构。采用李群（Lie group）形式化框架，使方程表达极为紧凑且易于参数化。
原文摘要 · Abstract (English)
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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