利用预热的广义邦德斯分解加速混合模型预测控制
Accelerating Hybrid Model Predictive Control using Warm-Started Generalized Benders Decomposition
AI总结：
本文提出一种基于广义邦德斯分解的混合MPC算法，通过预热切割平面提升求解速度，适用于机器人控制任务。
摘要：
混合模型预测控制在连续和离散变量方面被广泛应用于机器人控制任务，尤其是涉及与环境接触的任务。由于组合复杂性，混合MPC的求解速度可能不足以满足实时应用的需求。在本文中，我们提出了一种基于广义邦德斯分解的混合MPC算法。该算法在线枚举并存储切割平面，将其转移到MPC迭代中，为新的问题实例提供预热，显著提高了求解速度。我们通过时间位移和伸缩建模模式序列的偏差，理论分析了这种预热性能，推导了转移的最优切割与真实最优成本之间的对偶间隙界限，并利用这些界限来量化Benders主问题第一次求解中保证的次优程度。我们的算法通过控制带有软接触墙壁的cart-pole系统、绕障碍物飞行的自由飞行机器人以及单腿站立并用手推墙以保持平衡的人形机器人进行仿真验证。对于我们的基准问题，该算法枚举的切割数量仅为几十到几百，而求解速度比现成的Gurobi求解器快2-3倍，有时超过1000 Hz。代码可在https://github.com/XuanLin/Benders-MPC上获得。
英文摘要：
Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contacts with the environment. Due to combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we propose a hybrid MPC algorithm based on Generalized Benders Decomposition. The algorithm enumerates and stores cutting planes online inside a finite buffer and transfers them across MPC iterations to provide warm-starts for new problem instances, significantly enhancing solving speed. We theoretically analyze this warm-starting performance by modeling the deviation of mode sequences through temporal shifting and stretching, deriving bounds on the dual gap between transferred optimality cuts and the true optimal costs, and utilizing these bounds to quantify the level of suboptimality guaranteed in the first solve of the Benders Master Problem. Our algorithm is validated in simulation through controlling a cart-pole system with soft contact walls, a free-flying robot navigating around obstacles, and a humanoid robot standing on one leg while pushing against walls with its hands for balance. For our benchmark problems, the algorithm enumerates cuts on the order of only tens to hundreds while reaching speeds 2-3 times faster than the off-the-shelf solver Gurobi, oftentimes exceeding 1000 Hz. The code is available at https://github.com/XuanLin/Benders-MPC.
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