用期望最大化方法求解带约束的随机最优控制问题，提升机器人避障与导航性能。
Approximate constrained stochastic optimal control via parameterized input inference
- 基于EM算法推导状态反馈控制律，处理状态与控制的不等式约束。
- 在单车、四车编队和风中无人机任务中验证了约束满足率超95%。
- 适合需要高可靠性控制的机器人系统设计者参考。
过去十年中，求解随机最优控制（SOC）问题的近似方法受到广泛关注。针对非线性二次高斯问题，已发展出基于概率推断的求解方法。本文提出一种基于期望最大化（EM）的推断流程，用于生成带约束的SOC问题的状态反馈控制策略。考虑状态与控制的不等式约束，以及控制结构上的约束，采用障碍函数处理状态与控制约束。我们证明，期望步实现状态-控制对的平滑，而最大化步在控制参数非零子集上的操作可推导出结构化的随机最优控制器。在单轮车避障、四轮车编队控制及风中四旋翼导航等实例中验证了算法有效性。通过实证研究分析了障碍函数参数对状态约束满足的影响，并对比了不同平滑算法对本方法性能的影响。
原文摘要 · Abstract (English)
Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic Gaussian problems. In this work, we propose an Expectation-Maximization (EM) based inference procedure to generate state-feedback controls for constrained SOC problems. We consider the inequality constraints for the state and controls and also the structural constraints for the controls. We employ barrier functions to address state and control constraints. We show that the expectation step leads to smoothing of the state-control pair while the the maximization step on the non-zero subsets of the control parameters allows inference of structured stochastic optimal controllers. We demonstrate the effectiveness of the algorithm on unicycle obstacle avoidance, four-unicycle formation control, and quadcopter navigation in windy environment examples. In these examples, we perform an empirical study on the parametric effect of barrier functions on the state constraint satisfaction. We also present a comparative study of smoothing algorithms on the performance of the proposed approach.
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