SPARTAN: A Novel Pseudospectral Algorithm for Entry, Descent, and Landing Analysis

Abstract

In the last decades the theoretical development of more and more refined direct methods, together with a new generation of CPUs, led to a significant improvement of numerical approaches for solving optimal-control problems. One of the most promising class of methods is based on Pseudospectral Optimal Control. These methods not only provide an efficient algorithm to solve optimal-control problems, but also define a theoretical framework for linking the discrete numerical solution to the analytical one in virtue of the covector-mapping theorem. However, sveral aspects in their implementation can be refined. In this framework SPARTAN, the first European tool based on flipped Radau pseudospectral methods, has been developed. The tool, and the method behind it include two novel aspects. First, the discretized problem is automatically scaled with a novel technique, called Projected Rows Jacobian Normalization. This avoids ill-conditioned problems, which could lead to non-reliable solutions. Second, the structure of the Jacobian matrix is exploited, and the dual-number theory is used for its computation. This yields faster and more accurate solutions, since the associated Jacobian matrix computed in this way is exact. Two concrete examples show the validity of the proposed approach, and the quality of the results obtained with SPARTAN.