论文标题
通过控制合成的基于里程碑的计划的最佳线性多重估计的技术报告
Technical Report on Optimal Linear Multiple Estimation for Landmark-Based Planning via Control Synthesis
论文作者
论文摘要
在移动机器人中实施导航的一种常见方法是使用地标。在这种情况下，控制器的主要目标是在避免环境边界（安全）的同时，朝着目标位置（稳定性）取得进步。在我们以前的工作中，我们提出了一种方法，以合成具有多面体分解的环境的全局控制器。我们的解决方案使用二次限制的二次程序，并具有机会限制，以考虑地标测量的不确定性。在这项工作的基础上，我们介绍了虚拟地标的概念，这些概念被定义为实际地标测量的线性组合，可最大程度地减少所得控制动作中的不确定性。有趣的是，我们的结果表明，第一个最小值的地标与反馈控制矩阵无关，从而将地标的设计与控制器之一解耦。但是，试图得出其他统计独立的地标，需要解决涉及控制器的非凸问题。数值实验表明，通过最大程度地减少输入的方差，最终的控制器将不那么保守，并且机器人能够更有效地完成导航任务（更快，轨迹中的抖动更少）。
A common way to implement navigation in mobile robots is through the use of landmarks. In this case, the main goal of the controller is to make progress toward a goal location (stability), while avoiding the boundary of the environment (safety). In our previous work, we proposed a method to synthesize global controllers for environments with a polyhedral decomposition; our solution uses a Quadratically Constrained Quadratic Program with Chance Constraints to take into account the uncertainty in landmark measurements. Building upon this work, we introduce the concept of virtual landmarks, which are defined as linear combinations of actual landmark measurements that minimize the uncertainty in the resulting control actions. Interestingly, our results show that the first minimum-variance landmark is independent of the feedback control matrix, thus decoupling the design of the landmark from the one of the controller; attempting to derive additional, statistically independent landmarks, however, requires solving non-convex problems that involve also the controller. Numerical experiments demonstrate that, by minimizing the variance of the inputs, the resulting controller will be less conservative, and the robot is able to complete navigation tasks more effectively (faster and with less jitter in the trajectory).
