论文标题
跟踪均匀空间的控制控制：e夫式调节器（EQR）
Tracking control on homogeneous spaces: the Equivariant Regulator (EqR)
论文作者
论文摘要
在扰动存在下，准确跟踪计划的轨迹是控制和机器人技术的重要问题。对称性是许多动态系统的基本数学特征，并且利用此属性为改进的跟踪性能提供了潜力。在本文中，我们调查了同质空间上系统的跟踪问题，这些歧管允许与及其群体动作对称。我们表明，有自然的方式可以将这种系统的任何所需轨迹提升到对称组上的提升轨迹。这种构造使我们能够定义全局跟踪误差并应用LQR设计以在单个坐标图中获得大约最佳的控制。然后将所得控制应用于原始工厂，并显示出出色的跟踪性能。我们将产生的设计方法称为e夫式调节器（EQR）。我们提供了一个在均匀空间上构成的示例系统，在误差坐标中得出轨迹线性化，并证明了与模拟中标准方法相比，EQR的有效性。
Accurate tracking of planned trajectories in the presence of perturbations is an important problem in control and robotics. Symmetry is a fundamental mathematical feature of many dynamical systems and exploiting this property offers the potential of improved tracking performance. In this paper, we investigate the tracking problem for systems on homogeneous spaces, manifolds which admit symmetries with transitive group actions. We show that there is natural manner to lift any desired trajectory of such a system to a lifted trajectory on the symmetry group. This construction allows us to define a global tracking error and apply LQR design to obtain an approximately optimal control in a single coordinate chart. The resulting control is then applied to the original plant and shown to yield excellent tracking performance. We term the resulting design methodology the Equivariant Regulator (EqR). We provide an example system posed on a homogeneous space, derive the trajectory linearisation in error coordinates and demonstrate the effectiveness of EqR compared to standard approaches in simulation.
