Mathematical optimization is the workhorse behind several aspects of modern robotics and control. In these applications, the focus is on constrained optimization, and the ability to work on manifolds (such as the classical matrix Lie groups), along with a specific requirement for robustness and speed. In recent years, augmented Lagrangian methods have seen a resurgence due to their robustness and flexibility, their connections to (inexact) proximal-point methods, and their interoperability with Newton or semismooth Newton methods. In the sequel, we present primal-dual augmented Lagrangian method for inequality-constrained problems on manifolds, which we introduced in our recent work, as well as an efficient C++ implementation suitable for use in robotics applications and beyond.
翻译:数学优化是现代机器人和控制的若干方面背后的工作马匹。 在这些应用中,重点是限制优化和对多个元件(如古典矩阵 Lie Group ) 的操作能力(如古典矩阵 Lie Group ), 以及坚固和速度的具体要求。 近年来,拉格朗格方法的增强再次出现,原因是其坚固和灵活性、与(不精确的)准点方法的关联以及它们与牛顿或半摩特牛顿方法的互操作性。 在续集中,我们介绍了用于多元件上受不平等制约的原始拉格朗格方法(我们在最近的工作中引入了这一方法 ), 以及适用于机器人应用和之外的高效的C++实施。