High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance control algorithms. We propose a design methodology that takes any given symmetry, linearises the associated error in a single set of coordinates, and uses LQR design to obtain a high performance control; an approach we term Equivariant Regulator design. We show that quadrotor vehicles admit several different symmetries: the direct product symmetry, the extended pose symmetry and the pose and velocity symmetry, and show that each symmetry can be used to define a global error. We compare the linearised systems via simulation and find that the extended pose and pose and velocity symmetries outperform the direct product symmetry in the presence of large disturbances. This suggests that choices of equivariant and group affine symmetries have improved linearisation error.

翻译：测量是物理系统的基本属性,并有可能为设计高性能控制算法提供一个工具。我们建议采用一个设计方法,在单一的坐标组中进行任何特定的对称,将相关错误线性化,并使用LQR设计来获得高性能控制;一种方法,我们称“等式调节器”设计。我们表明, quadrtor 车辆承认了几种不同的对称:直接产品对称、扩展的对称以及形状和速度对称,并表明每一种对称都可用于界定全球错误。我们通过模拟比较线性系统,发现在出现大扰动时,扩展的形状和形状及速度对称在直接产品对称上不同于直接产品对称。这表明,对等性和群体对称的选择改进了线性误差。