Multi‐Phase Optimal Control Problems for Efficient Nonlinear Model Predictive Control With acados

ABSTRACT Computationally efficient nonlinear model predictive control (NMPC) relies on elaborate discrete‐time optimal control problem (OCP) formulations trading off accuracy with respect to the continuous‐time problem and online computational burden. Such formulations, however, are in general not easy to implement within specialized software frameworks tailored to numerical optimal control. This article introduces a new multi‐phase optimal control problem (MOCP) interface for the open‐source software acados allowing to conveniently formulate such problems and generate fast solvers that can be used for NMPC. While multi‐phase OCP formulations occur naturally in many applications, such as, for example, walking robots, this work focuses on MOCP formulations that can be used to efficiently approximate standard continuous‐time OCPs in the context of NMPC. To this end, the article discusses advanced control parametrizations, such as closed‐loop costing and piecewise polynomials with varying degree, as well as partial tightening and formulations that leverage models of different fidelity. An introductory example is presented to showcase the usability of the new interface. Finally, three numerical experiments demonstrate that NMPC controllers based on multi‐phase formulations can efficiently trade off computation time and control performance.