T-LQG: Closed-loop belief space planning via trajectory-optimized LQG
T-LQG: Closed-loop belief space planning via trajectory-optimized LQG
复制标题
T-LQG：通过轨迹优化的 LQG 进行闭环置信空间规划
DOI：
10.1109/icra.2017.7989080
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
P. Kumar
中科院分区：
文献类型：
--
作者：
Mohammadhussein Rafieisakhaei;S. Chakravorty;P. Kumar
运动和观测不确定性下的规划需要在反馈策略空间中解决随机控制问题。本文通过将策略类限定为线性反馈策略，将一般的（n ~ 2 + n）维信念空间规划问题转化为（n）维问题。与之前在开环最优控制策略空间中搜索的文献相反，我们通过获得具有最佳名义性能的线性二次高斯（LQG）设计来获得闭环策略空间中的这种减少。然后，通过将LQG控制器的整个基本轨迹作为决策变量，我们将轨迹和估计器的耦合设计（同时保持控制器的设计分离）作为一个非线性规划（NLP），可以通过一般的NLP求解器来解决。我们证明，根据一阶近似和分离原理的谨慎使用，我们的近似是有效的。我们提供了现有的主要信念空间规划方法的分析，并表明，我们的算法保持最低的计算负担，而在政策空间中搜索。最后，我们扩展我们的解决方案，包含一般的状态和控制约束。我们的模拟结果支持我们的设计。
Planning under motion and observation uncertainties requires the solution of a stochastic control problem in the space of feedback policies. In this paper, by restricting the policy class to the linear feedback polices, we reduce the general (n2 + n)-dimensional belief space planning problem to an (n)-dimensional problem. As opposed to the previous literature that search in the space of open-loop optimal control policies, we obtain this reduction in the space of closed-loop policies by obtaining a Linear Quadratic Gaussian (LQG) design with the best nominal performance. Then, by taking the entire underlying trajectory of the LQG controller as the decision variable, we pose a coupled design of the trajectory and estimator (while keeping the design of the controller separate) as a NonLinear Program (NLP) that can be solved by a general NLP solver. We prove that under a first-order approximation and a careful usage of the separation principle, our approximations are valid. We provide an analysis on the existing major belief space planning methods and show that our algorithm keeps the lowest computational burden while searching in the policy space. Finally, we extend our solution to contain general state and control constraints. Our simulation results support our design.