In this paper, we introduce an O(N) 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.

中文翻译：

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一种用于计算质心动力学的 O(N) 算法及其在使用全身控制的仿人机器人姿势平衡中的应用

在本文中，我们介绍了一个○(ñ)使用空间代数计算质心动量矩阵 (CMM) 及其时间导数的算法，并用李代数算子表示。将所提出的算法应用于使用二次规划的全身控制的仿人机器人的姿势平衡。所采用的任务只需要 CMM 及其时间导数，而不需要联合空间惯性矩阵和科里奥利项，从而减少了控制器的计算成本。最后，考虑了用 Julia 编程的四种模拟场景，其中考虑了机器人平衡的几个扰动，并根据质心、质心动量和压力中心轨迹的跟踪图得出结论：所提算法的性能令人满意。