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A Comparison Study on Coupling Effects in Balance Control Methods of Humanoid Robots through an Extended Task Space Formulation

Even though several control methods on the task space dynamics of humanoids have been proposed, they cannot cover the entire dynamics of the system since there are hidden null space dynamics due to kinematic redundancy. Besides, there are few studies on the coupling effects between task space and null space dynamics. Through an extended task space formulation, the coupling effects between each space are manifested because this form allows representing the entire system dynamics. Moreover, by using an adequate selection of weighting matrices, the coupling effects can be inertially decoupled. Regarding the effectiveness of the decoupling process, two whole-body control approaches and provide their mathematical comparisons is proposed. A kinematically decomposed control approach without the decoupling process is first introduced, and its extension to an inertially decoupled control approach is then developed. Furthermore, conventional operational space-based control is discussed to compare the above control approaches. This paper constructs a mathematical analysis of their relationships. Finally, simulation results are given in this paper to demonstrate the validity of the mathematical analysis.