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 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 and four-unicycle formation control 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.

中文翻译：

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通过参数化输入推断近似约束随机最优控制


在过去十年中，解决随机最优控制 （SOC） 问题的近似方法引起了研究人员的极大兴趣。SOC 的概率推理方法已被开发用于解决非线性二次高斯问题。在这项工作中，我们提出了一种基于期望最大化 （EM） 的推理程序，为受限的 SOC 问题生成状态反馈控制。我们考虑了 state 和 controls 的不等式约束，也考虑了 controls 的结构约束。我们使用 barrier 函数来解决状态和控制约束。我们表明，期望步骤导致状态控制对的平滑，而控制参数的非零子集的最大化步骤允许推断结构化随机最优控制器。我们证明了该算法在独轮车避障和四轮独轮车编队控制实例上的有效性。在这些例子中，我们对屏障函数对状态约束满足的参数效应进行了实证研究。我们还对平滑算法对所提出的方法的性能进行了比较研究。