论文标题
与因子图的平等约束线性最佳控制
Equality Constrained Linear Optimal Control With Factor Graphs
论文作者
论文摘要
本文提出了一种基于图形的新型方法，可以解决离散时间有限的线性二次调节器问题，这些问题受到辅助线性相等性约束，内部和跨时间步骤的辅助线性相等约束。我们使用约束因子图表示这种最佳控制问题，并优化了因子图，以使用修改后的GRAM-SCHMIDT进程使用变量消除算法获得最佳轨迹和反馈控制策略。我们证明我们的方法具有与最先进的动态编程方法相同的计算复杂性顺序。此外，当前的动态编程方法只能在同一时间步骤中处理变量之间的平等约束，但是我们可以在任何时间步长的任何变量组合之间处理平等约束，同时保持对轨迹长度的线性复杂性。我们的方法可用于有效生成轨迹和反馈控制政策，以实现定期运动或重复操作。
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal control problems using constrained factor graphs and optimize the factor graphs to obtain the optimal trajectory and the feedback control policies using the variable elimination algorithm with a modified Gram-Schmidt process. We prove that our approach has the same order of computational complexity as the state-of-the-art dynamic programming approach. Furthermore, current dynamic programming approaches can only handle equality constraints between variables at the same time step, but ours can handle equality constraints among any combination of variables at any time step while maintaining linear complexity with respect to trajectory length. Our approach can be used to efficiently generate trajectories and feedback control policies to achieve periodic motion or repetitive manipulation.
