Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with acados

Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties separately from the nominal dynamics. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.