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）同时包含连续变量和离散变量，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。由于组合复杂性，混合MPC的求解速度可能难以满足实时应用需求。本文提出了一种基于持续学习的广义Benders分解（GBD）混合MPC求解器。该算法从子问题的对偶不变空间中累积割平面，在短暂的冷启动阶段后，累积的割平面可为新的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料的随机环境变化，求解速度仍能保持稳定。我们在具有随机移动软接触墙壁的推车-摆杆系统中验证了该求解器，实验表明其求解速度比商用求解器Gurobi快2-3倍。