This work links optimization approaches from hierarchical least-squares programming to instantaneous prioritized whole-body robot control. Concretely, we formulate the hierarchical Newton's method which solves prioritized non-linear least-squares problems in a numerically stable fashion even in the presence of kinematic and algorithmic singularities of the approximated kinematic constraints. These results are then transferred to control problems which exhibit the additional variability of time. This is necessary in order to formulate acceleration based controllers and to incorporate the second order dynamics. However, we show that the Newton's method without complicated adaptations is not appropriate in the acceleration domain. We therefore formulate a velocity based controller which exhibits second order proportional derivative convergence characteristics. Our developments are verified in toy robot control scenarios as well as in complex robot experiments which stress the importance of prioritized control and its singularity resolution.

翻译：本研究将层次化最小二乘规划中的优化方法与瞬态优先级全身机器人控制相结合。具体而言，我们提出了层次化牛顿法，该方法即使在近似运动学约束存在运动学奇异性与算法奇异性时，仍能以数值稳定方式求解优先级的非线性最小二乘问题。这些成果随后被推广至具有时间可变性的控制问题中——这是构建加速度控制器并融入二阶动力学所必需的。然而，我们证明未经复杂改进的牛顿法并不适用于加速度域。因此我们构建了具有二阶比例微分收敛特性的速度控制器。我们的研究在玩具机器人控制场景及复杂机器人实验中均得到验证，凸显了优先级控制及其奇异性处理的重要性。