An O(N) Algorithm for the Computation of the Centroidal Dynamics with Application in the Postural Balance of a Humanoid Robot Using Whole Body Control

In this paper, we introduce an [Formula: see text] algorithm for the computation of the centroidal momentum matrix (CMM) and its time derivative using spatial algebra and expressed with Lie algebra operators. The proposed algorithm is applied to the postural balance of a humanoid robot using whole body control with quadratic programming. The employed tasks only require the CMM and its time derivative without the need of the joint space inertia matrix and the Coriolis terms reducing this way the computational cost of the controller. Finally, four simulation scenarios programmed in Julia are considered where several perturbations for the balance of the robot have been taken into account and according to the tracking graphs of the center of mass, centroidal momentum and the trajectories of the center of pressure it is concluded that the performance of the proposed algorithm is satisfactory.