  Hybrid model predictive control 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). The algorithm enumerates and stores cutting planes online
inside a finite buffer. After a short cold-start phase, the stored cuts provide
warm-starts for the new problem instances to enhance the solving speed. Despite
the disturbance and randomly changing environment, the solving speed maintains.
Leveraging on the sparsity of feasibility cuts, we also propose a fast
algorithm for Benders master problems. Our solver is validated through
controlling a cart-pole system with randomly moving soft contact walls, and a
free-flying robot navigating around obstacles. The results show that with
significantly less data than previous works, the solver reaches competitive
speeds to the off-the-shelf solver Gurobi despite the Python overhead.
