论文标题
最大坐标中的线性季度最佳控制
Linear-Quadratic Optimal Control in Maximal Coordinates
论文作者
论文摘要
线性季度调节器（LQR）是线性和线性化系统的有效控制方法。通常，LQR在最小坐标（也称为广义或“关节”坐标）中实现。但是，其他坐标是可能的，最近的研究表明，在动态系统使用较高尺寸的非微小状态参数化时，可能存在数值和控制理论的优势。一个这样的参数化是最大坐标，其中多体系统中的每个链接都由其整个六个自由度进行参数化，并且链接之间的关节用代数约束对其进行建模。这样的约束也可以代表封闭的运动循环或与环境接触。本文研究了最小和最大坐标LQR控制定律之间的差异。将LQR应用于简单的摆和模拟的案例研究比较了最小和最大坐标LQR控制器的吸引力和跟踪性能的盆地，这表明与非线性系统应用于最小的LQR相比，最大坐标LQR可实现更大的鲁棒性，并改善了跟踪性能。
The linear-quadratic regulator (LQR) is an efficient control method for linear and linearized systems. Typically, LQR is implemented in minimal coordinates (also called generalized or "joint" coordinates). However, other coordinates are possible and recent research suggests that there may be numerical and control-theoretic advantages when using higher-dimensional non-minimal state parameterizations for dynamical systems. One such parameterization is maximal coordinates, in which each link in a multi-body system is parameterized by its full six degrees of freedom and joints between links are modeled with algebraic constraints. Such constraints can also represent closed kinematic loops or contact with the environment. This paper investigates the difference between minimal- and maximal-coordinate LQR control laws. A case study of applying LQR to a simple pendulum and simulations comparing the basins of attraction and tracking performance of minimal- and maximal-coordinate LQR controllers suggest that maximal-coordinate LQR achieves greater robustness and improved tracking performance compared to minimal-coordinate LQR when applied to nonlinear systems.
