Belief Space Planning Simplified: Trajectory-Optimized LQG (T-LQG) (Extended Report)
Belief Space Planning Simplified: Trajectory-Optimized LQG (T-LQG) (Extended Report)
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简化的置信空间规划：轨迹优化 LQG (T-LQG)（扩展报告）
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发表时间：
2016
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通讯作者：
P. Kumar
中科院分区：
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作者：
Mohammadhussein Rafieisakhaei;S. Chakravorty;P. Kumar
运动和观测不确定性下的规划要求求解反馈策略空间中的随机控制问题。本文通过获得具有最佳标称性能的线性二次高斯（LQG）设计，将一般的（n^2+n）维信念空间规划问题简化为(n)维问题。然后，以LQG控制器的底层轨迹作为决策变量，通过非线性程序（NLP）提出轨迹、估计器和控制器设计的耦合设计，该非线性程序可由一般的NLP求解器求解。我们证明了在一阶近似和谨慎地使用分离原理下，我们的近似是有效的。对现有主要的信念空间规划方法进行了分析，结果表明该算法的计算量最小。最后，我们扩展了我们的解决方案，以包含一般的状态和控制约束。仿真结果支持了我们的设计。
Planning under motion and observation uncertainties requires solution of a stochastic control problem in the space of feedback policies. In this paper, we reduce the general (n^2+n)-dimensional belief space planning problem to an (n)-dimensional problem by obtaining a Linear Quadratic Gaussian (LQG) design with the best nominal performance. Then, by taking the underlying trajectory of the LQG controller as the decision variable, we pose a coupled design of trajectory, estimator, and controller design through a Non-Linear 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 give an analysis on the existing major belief space planning methods and show that our algorithm has the lowest computational burden. Finally, we extend our solution to contain general state and control constraints. Our simulation results support our design.