The kinematic simulation of a free-floating multibody system, with joint motion commands as inputs and inertial description of the motion as outputs, can be performed by the following methods: (1) joint commands are treated as rheonomic inputs to a multibody dynamics code and the motion of the free-floating base is computed by integrating the resulting dynamic differential equations of motion; (2) the kinematics is coupled with momentum integrals of equations of motion of the system to result in a map between the inertial velocities and joint velocities, which on integration results in inertial description of the system. The first method requires the full simulation tools of multibody dynamics, while the second method constructs the same information starting at the velocity level. The second viewpoint results in a compact mapping between the joint velocities and inertial velocities of the system, which is useful for motion planning.
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