Making things optimal, not just better

WORHP: a European nonlinear optimization solution for the aerospace industry

The aim of modern modeling and simulation calculations used in aerospace is not just to gain an understanding of existing (i.e., real) systems, but also to make actual improvements in any given situation. But making improvements isn’t the same as achieving the optimum. Enter nonlinear optimization (NLP), an approach being used in aerospace that has developed into a key technology capable of delivering competitive advantage. One particularly important solution in this area is WORHP (pronounced “warp”), the European NLP solver which was developed to provide a tool for solving real optimization problems in everyday practice. Optimization, Control and Adjustment Control, the Steinbeis Enterprise based at the University of Bremen, is coordinating adaptations to WORHP as part of a project looking at reducing pollution in aviation.

Since time immemorial, mathematics has been a tool for and the language of science and engineering. Without mathematics, it would not be possible to carry out modeling and simulation and thus improve technical and commercial processes. In essence, modern hi-tech is mathematical engineering. This was the finding of a report issued by a study commission of the American Academy of Sciences, which looked at the role played by mathematics in industry and science. This age-old science, driven by the imagination of intellect, is as enduring as ever, even if it often only sits in the wings and frequently goes unnoticed by society. Mathematics is not just the language of science, it is also a lynchpin between vastly different disciplines, fulfilling a function that transcends scientific endeavor. This lynchpin role is not just essential between different disciplines within science but also, in a direct sense, as a derivation of mathematics – forming connections, as is the case with knowledge and technology transfer and connections forged to the hi-tech field of aerospace.

Nonlinear optimization makes use of highly efficient mathematical processes. This involves drawing on the latest developments in computer technology to solve problems relating to the best-possible trajectories of aircraft during take-off and landing, of space shuttles during ascent, or of satellite constellations. It can also involve working out the optimal engine strategy for a landing on the moon or Mars. The potential this offers to the aerospace industry has also been picked up on by both the German Aerospace Center (DLR) and the European Space Agency (ESA), who started backing the development of the NLP solver (WORHP) as early as 2007. WORHP stands for We Optimize Really Huge Problems. Initially this involved software development, but later it spread out to address numerous development and service ques-tions relating to aerospace, plus specific application scenarios.

Unlike most NLP processes, WORHP was not developed purely as a test environment for mathematical processes. Instead, its aim was to solve actual optimization problems relating to real applications. The result was a modern software package that not only meets the stringent standards out-lined by the European Cooperation for Space Standardization (ECSS), but the European Space Research and Technology Centre (ESTEC) and the European Space Operations Centre (ESOC) have also given it technology readiness level 6-7 (TRL 6-7). TRLs are a method for estimating the maturity of software. For comparison, the scientific software used at most universities typically achieves a score of TRL 1-2. 

High-dimensional models with millions of degrees of freedom, variables, and additional conditions are a particular specialty of WORHP, which it solves just as reliably and efficiently as little problems. WORHP is currently considered the most robust NLP process in existence. Since it was launched around five years ago, WORHP has taken the world by storm and it is now supported by other processes based on WORHP, among them: TransWORHP, which is used to calculate the optimum controls and trajectories, and WORHP Zen, which is used for the parametric sensitivity and stability analysis of optimum solutions.

A particular highlight within science is the supporting role played by WORHP at ESOC in the planning of optimal trajectories for BepiColombo, Europe’s first mission to Mercury, which is scheduled to start in 2017 and is a collaborative venture between the ESA and the Japanese Aerospace eXploration Authority (JAXA).

Another area in which the WORHP NLP solver is being used is in optimizing the trajectories of aeronautical applications for Clean Sky, an EU project looking at “green operations” systems as part of Man-agement of Aircraft Trajectory and Mission (MTM). The aim of the initiative is to make European aviation and the aero-space industry more competitive and – as the name implies – reduce pollution caused by emissions and aircraft noise, and thus develop cleaner and quieter aircraft. The Grasberg-based Steinbeis Innovation Center for Optimization, Control and Adjustment Control is also coordinating a sub-project looking at adapting WORHP to avionic constraints.

Another challenge for WORHP lies in a research project called KaNaRiA (a German acronym for “cognition-based, autonomous navigation based on resource depletion in space”). The underlying idea of this project, which is backed by the DLR and involves five partners, is to equip a space vehicle with an autonomous decision-making system capable of suggesting cognitively motivated strategies for the investigation and exploitation of resources on distant asteroids. The role played by WORHP in KaNaRiA is to calculate the optimum routes, subject to limitations, and to optimize landing trajectories and make optimal re-adjustments at different stages of navigation during missions.

For the Cognitive Autonomous Subsur-face Exploration (CAUSE) project, WORHP has to automatically identify dynamic systems based on merged measurement data from a melting probe on Enceladus, one of Saturn’s moons. It should also plan optimum trajectories and automatically interpret model-based and adaptive control concepts. The concepts that have to be developed to do this should not be restricted to exploration projects, however, but also feed into other application scenarios, such as autonomous robotic systems on Earth or diesel engine controls in cars.

The aim of another WORHP project in the aerospace field is to de-termine the optimum flight manoeuver for a landing module orbiting the moon such that different limitations are taken into consideration and the vehicle can land safely on the surface. This involves compensating for the high starting speed of the landing module, primarily with nonmodular engines, which should be switched off one at a time at the optimum moment. WORHP Zen is also playing a successful role in understanding the quality and susceptibility of trajectories.

Aside from the scenarios outlined above, WORHP is also being used on a multitude of practical issues involving automatic optimization. For example, scientists thinking about future missions to Mars are interested in understanding safe landing trajectories, taking the Martian atmosphere and reduced energy consumption into consideration. Similarly, WORHP can optimize the positioning of satellites orbiting the Earth to save energy and resources.

The application scenarios covered by WORHP are not just restricted to the aerospace industry, however. Many of the current research projects involve energy systems important to the German transition to alternative energy or the automotive sector. As part of the portfo-lio of the Steinbeis Research Center for Optimization, Control and Adjustment Control, the WORHP NLP solver is an im-portant building block in transferring technology into industrial applications, after all, many practical applications are essentially based on optimization processes.


Prof. Dr. Christof Büskens is director of the Steinbeis Research and Innovation Center for Optimization, Control and Adjustment Control at the University of Bremen. The experts at the Steinbeis Enterprise work in the fields of modeling, the simulation and identification of static and dynamic systems, optimal control and adjustment, real-time optimization, online optimization, and numerical methods and processes. In 2008, the Steinbeis experts and OHB System AG won the Steinbeis Foundation’s transfer award (the Löhn Award) for the mathematical optimization of satellite resource management systems.

Prof. Dr. Christof Büskens
Optimization, Control and Adjustment Control (Grasberg)

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