微分平坦系统的最优控制出人意料地简单
Optimal Control of Differentially Flat Systems is Surprisingly Easy
AI总结：
针对非线性信息物理系统实时最优控制复杂度高、数值不稳定的问题，该研究利用微分平坦特性简化Euler-Lagrange方程，给出最优轨迹显式微分方程并拓展至约束场景，在双关节平面机械臂仿真中实现4.5毫秒的约束轨迹生成。
摘要：
随着我们朝着愈发复杂的信息物理系统（CPS）发展，亟需新的方法来实时规划高效的状态轨迹。本文提出一种方法，可大幅降低求解一类具非线性动力学的CPS最优控制问题的复杂度。我们利用微分平坦特性简化优化过程中产生的Euler-Lagrange方程，这一简化消除了普遍困扰最优控制的数值不稳定性问题。我们还给出了描述最优状态轨迹演化的显式微分方程，并将结果拓展至无约束和有约束两种情形。此外，我们通过为一台带两个转动关节的平面机械臂生成最优轨迹，验证了所提方法的性能。仿真结果表明，我们的方法能在4.5毫秒内生成有约束的最优轨迹，同时满足工作空间约束，且可在肘关节的“左”弯和“右”弯之间切换。
英文摘要：
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler-Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in $4.5$ ms while respecting workspace constraints and switching between a `left' and `right' bend in the elbow joint.
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