数值稳定优先动态控制的递阶牛顿法
The hierarchical Newton's method for numerically stable prioritized dynamic control
摘要：
这项工作链接的优化方法，从分层最小二乘编程瞬时优先全身机器人控制。具体地说，我们制定的层次牛顿的方法，解决优先的非线性最小二乘问题，在数值上稳定的方式，即使在存在的运动学和算法奇异的近似运动学约束。这些结果，然后转移到控制问题，表现出额外的可变性的时间。这是必要的，以制定基于加速度的控制器，并纳入二阶动态。然而，我们表明，牛顿的方法没有复杂的适应是不合适的加速度域。因此，我们制定了一个基于速度的控制器，具有二阶比例导数收敛特性。我们的发展验证了玩具机器人控制方案，以及在复杂的机器人实验，强调优先控制和奇异性分辨率的重要性。
英文摘要：
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.
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