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Hybrid model predictive control with both continuous and discrete variablesis widely applicable to robotic control tasks, especially those involvingcontact with the environment. Due to the combinatorial complexity, the solvingspeed of hybrid MPC can be insufficient for real-time applications. In thispaper, we proposed a hybrid MPC solver based on Generalized BendersDecomposition (GBD). The algorithm enumerates and stores cutting planes onlineinside a finite buffer. After a short cold-start phase, the stored cuts providewarm-starts for the new problem instances to enhance the solving speed. Despitethe disturbance and randomly changing environment, the solving speed maintains.Leveraging on the sparsity of feasibility cuts, we also propose a fastalgorithm for Benders master problems. Our solver is validated throughcontrolling a cart-pole system with randomly moving soft contact walls, and afree-flying robot navigating around obstacles. The results show that withsignificantly less data than previous works, the solver reaches competitivespeeds to the off-the-shelf solver Gurobi despite the Python overhead.

Fast and Continual Learning for Hybrid Control Policies using Generalized Benders Decomposition