FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs

Abstract

Real-time implementation of optimisation-based control and trajectory planning can be very challenging for nonlinear systems. As a result, if an implementation based on a fixed linearisation is not suitable, the nonlinear problems are typically locally approximated online, in order to leverage the speed and robustness of embedded solvers for convex quadratic programs (QP) developed during the last decade. The purpose of this paper is to demonstrate that, using simple standard building blocks from nonlinear programming, combined with a structure-exploiting linear system solver, it is possible to achieve computation times in the range typical of solvers for QPs, while retaining nonlinearities and solving the nonlinear programs (NLP) to local optimality. The implemented algorithm is an interior-point method with approximate Hessians and adaptive barrier rules, and is provided as an extension to the C code generator FORCES. Three detailed examples are provided that illustrate a significant improvement in control performance when solving NLPs, with computation times that are comparable with those achieved by fast approximate schemes and up to an order of magnitude faster than the state-of-the-art interior-point solver IPOPT.