Interior-Point Approach to Trajectory Optimization

This paper presents an interior-point approach for solving optimal control problems. We combine the idea of logarithmic penalization (used to solve large-scale problems with relatively few iterations) with dedicated linear algebra solvers (QR factorization for band matrices). The method also takes advantage of recent progress in the analysis of discretization errors. At each major iteration of the interior-point algorithm (i.e., at a solution of the penalized problem for a given value of the penalty parameter), we determine whether discretization points should be added (and how to do so at low cost), because the number of operations is proportional to one of discretization points. Numerical results are displayed for various problems, including seven variants of atmospheric reentry of a space shuttle. We can find feasible points for all of them and compute a seemingly accurate solution for five of them. It can be seen from physical considerations that the two other problems are more difficult.