耦合机械系统轨迹跟踪的反馈正则化和几何PID控制：斜面上的环箍机器人
Feedback Regularization and Geometric PID Control for Trajectory Tracking of Coupled Mechanical Systems: Hoop Robots on an Inclined Plane
摘要：
本文应用几何PID控制的期望轨迹的渐近跟踪环机器人存在的干扰和不确定性。环式机器人是球形机器人的一种平面模拟物，它由一个沿一维表面无滑动滚动的圆形物体组成。可以使用各种耦合的机械系统来致动环式机器人。本文具体考虑两种不同的致动器，一个单摆和其他内部车。几何PID控制器要求被控对象是机械系统，而环箍机器人不满足这一条件。因此，提出了一种几何内环，使箍机器人所需的结构。这个过程在这里被称为反馈正则化。反馈正则化-与反馈线性化相反-是坐标独立的，因此反映了基本的系统结构。还要注意，所得到的机械系统是非线性的和欠驱动的。随后，几何PID外环保证了具有局部指数收敛的几乎半隐式跟踪，并且PID的积分动作保证了对恒定干扰和参数不确定性（包括滚动表面的恒定倾斜）的鲁棒性。完整的跟踪控制器是两个坐标无关回路的组成，因此也是坐标无关的。
英文摘要：
This paper applies geometric PID control for asymptotic tracking of a desired trajectory by a hoop robot in the presence of disturbances and uncertainties. The hoop robot, consisting of a circular body rolling without slip along a one-dimensional surface, is a planar analog of a spherical robot. A variety of coupled mechanical system may be used to actuate the hoop robot. This paper specifically considers two different actuators, one a simple pendulum and the other an internal cart. The geometric PID controller requires the plant to be a mechanical system, and the hoop robot does not satisfy this condition. Therefore a geometric inner loop is presented that gives the hoop robot the required structure. This procedure is here referred to as feedback regularization. Feedback regularization--in contrast to feedback linearization--is coordinate independent, and hence reflects the fundamental system structure. Note also that the resulting mechanical system is nonlinear and underactuated. Subsequently, the geometric PID outer loop guarantees almost-semiglobal tracking with locally exponential convergence, and the integral action of the PID guarantees robustness to constant disturbances and parameter uncertainties, including constant inclination of the rolling surface. The complete tracking controller is the composition of the two coordinate-independent loops, and therefore is also coordinate independent.
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