Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotics tasks. Due to the combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we propose to accelerate hybrid MPC using Generalized Benders Decomposition (GBD). GBD enumerates cuts online and stores inside a finite buffer to provide warm-starts for the new problem instances. Leveraging on the sparsity of feasibility cuts, a fast algorithm is designed for Benders master problems. We also propose to construct initial optimality cuts from heuristic solutions allowing GBD to plan for longer time horizons. The proposed algorithm successfully controls a cart-pole system with randomly moving soft-contact walls reaching speeds 2-3 times faster than Gurobi, oftentimes exceeding 1000Hz. It also guides a free-flying robot through a maze with a time horizon of 50 re-planning at 20Hz. The code is available at https://github.com/XuanLin/Benders-MPC.

翻译：混合模型预测控制因其同时包含连续与离散变量，在机器人任务中具有广泛适用性。然而受组合复杂性制约，混合MPC的求解速度往往难以满足实时应用需求。本文提出采用广义Benders分解（GBD）加速混合MPC求解。该方法在线枚举切割并存储于有限缓冲区，为新问题实例提供热启动。通过利用可行性切割的稀疏特性，我们为Benders主问题设计了快速求解算法。同时提出基于启发式解构建初始最优性切割，使GBD能够规划更长时域。所提算法成功实现了对带有随机移动软接触壁的倒立摆系统的控制，其求解速度达到Gurobi求解器的2-3倍，通常超过1000Hz。该算法还能以20Hz频率、50步时域为自由飞行机器人完成迷宫路径重规划。代码开源地址：https://github.com/XuanLin/Benders-MPC。