<p>This paper proposes a robust model predictive control (MPC) framework that integrates an adaptive robust term with an accelerated Hildreth-type quadratic programming solver and validates the framework on the head stabilization problem of a two-degree-of-freedom snake robot. The adaptive robust term is designed from an error-based compensation law with gains estimated by a radial-basis-function neural network and is incorporated into the MPC formulation through an explicit disturbance model, enabling constraint-aware optimal control while preserving Lyapunov stability. To improve computational efficiency, the conventional Hildreth algorithm is enhanced with a Nesterov-momentum-inspired update. Simulation results show that the proposed controller provides stronger robustness and better constraint-handling performance than nominal MPC and tube MPC under external disturbances and tight constraints. In particular, the maximum and average output violations of the second joint are reduced to 0.007 and 0.002, respectively, whereas tube MPC exhibits violations of 0.60 and 0.016. In addition, the accelerated Hildreth solver reduces the number of dual iterations from 8531 to 4947 compared with the classical Hildreth method. These results indicate that the proposed framework improves robustness and computational efficiency while maintaining a simple structure, promising for embedded implementation.</p>