A Unified View of the Equations of Motion used for Control Design of Humanoid Robots The Role of the Base Frame in Free-Floating Mechanical Systems and its Connection to Centroidal Dynamics

This paper contributes towards the development of a unified standpoint on the equations of motion used for the control of free-floating mechanical systems. In particular, the contribution of the manuscript is twofold. First, we show how to write the system equations of motion for any choice of the base frame, without the need of re-applying algorithms for evaluating the mass, coriolis, and gravity matrix. A particular attention is paid to the properties associated with the mechanical systems, which are shown to be invariant with respect to the base frame choice. Secondly, we show that the so-called centroidal dynamics can be obtained from any expression of the equations of motion via an appropriate system state transformation. In this case, we show that the mass matrix associated with the new base frame is block diagonal, and the new base velocity corresponds to the so-called average 6D velocity.

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