Hybrid model predictive control (MPC) with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contact with the environment. Due to the combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we proposed a hybrid MPC solver based on Generalized Benders Decomposition (GBD) with continual learning. The algorithm accumulates cutting planes from the invariant dual space of the subproblems. After a short cold-start phase, the accumulated cuts provide warm-starts for the new problem instances to increase the solving speed. Despite the randomly changing environment that the control is unprepared for, the solving speed maintains. We verified our solver on controlling a cart-pole system with randomly moving soft contact walls and show that the solving speed is 2-3 times faster than the off-the-shelf solver Gurobi.

翻译：混合模型预测控制（MPC）同时包含连续变量与离散变量，广泛应用于机器人控制任务，尤其是涉及与环境接触的场景。由于组合复杂度问题，混合MPC的求解速度难以满足实时应用需求。本文提出一种基于广义本德斯分解（GBD）与持续学习的混合MPC求解器。该算法通过累加子问题对偶空间中的切割平面，在短暂的冷启动阶段后，利用累积的切割平面为新问题实例提供热启动，从而提升求解速度。即使面对控制器未预处理的随机变化环境，求解速度仍能保持稳定。我们在随机移动软接触壁的小车-倒立摆系统控制中验证了该求解器，实验表明其求解速度比商业求解器Gurobi快2-3倍。