论文标题
通过差分动态编程诱导稀疏性诱导最佳控制
Sparsity-Inducing Optimal Control via Differential Dynamic Programming
论文作者
论文摘要
最佳控制是一种综合高度动态运动的流行方法。通常，在控制输入上使用$ L_2 $正则化，以最大程度地减少所使用的能量并确保控件输入的平稳性。但是，对于某些系统（例如卫星），由于推进系统的运行方式，需要在稀疏的爆发中应用控制。在本文中，我们研究了在最佳控制解决方案中诱导稀疏性的方法 - 即通过平滑的$ L_1 $和HUBER正则罚款。我们将这些损失条款应用于最新的基于DDP的求解器，以创建稀疏性诱导最佳控制方法的家族。我们分析和比较不同损失对诱导稀疏性，其数值调节，对收敛的影响以及讨论超参数设置的影响。我们演示了我们在规范动力学系统，卫星控制和NASA女武器类人形机器人的模拟和硬件实验方面的方法。我们提供了我们的方法的实现，以及所有示例，以在GitHub上可重复。
Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such as satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions -- namely via smooth $L_1$ and Huber regularization penalties. We apply these loss terms to state-of-the-art DDP-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.
