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

Abstract Derivatives of equations motion (EOM) describing the dynamics rigid body systems are becoming increasingly relevant for robotics community and find many applications in design control robotic systems. Controlling robots, multibody comprising elastic components particular, not only requires smooth trajectories but also time derivatives forces/torques, hence EOM. This paper presents EOM closed form up to second-order as an alternative formulation existing recursive algorithms this purpose, which provides a direct insight into structure derivatives. The Lie group is used giving rise very compact easily parameterized equations.