Constrained Trajectory Optimization

The importance of optimization methods for control applications has steadily increased over the last decades. This is mainly motivated by the advancement of computational power which makes the online solution of optimization problems a realistic goal. On the other hand, the competitive international markets require an increasingly efficient operation of industrial processes within specific constraints. Typical tasks are, for instance, load changes in process control or point-to-point motion control of industrial manufacturing robots in a time-optimal or energy-optimal way while accounting for constraints due to a limited actuator performance or security constraints. The goal of the proposed research project is the development of a new systematic concept for constrained trajectory optimization. In previous works of the applicant, a methodology has been developed in order to systematically account for a class of constraints. By incorporating the constraints in the underlying system dynamics, the original constrained optimal control problem is transformed into an unconstrained one ("analytic preprocessing"), which can be numerically solved with standard unconstrained methods from optimization or optimal control. The so far achieved theoretical, numerical, and experimental results show the effectiveness of this systematic approach for incorporating constraints and indicate its potential in the field of real-time trajectory optimization. In the proposed research project, the preparatory work of the applicant shall be systematically extended to a larger class of trajectory optimization problems. Based on these results, a toolbox shall be developed for the efficient numerical computation of constrained optimal trajectories. A strong emphasis of the research project will be put on real-time feasibility in order to allow the application of the methodology to fast dynamical systems, e.g. mechatronic systems. In addition, the developed methodology and numerical methods shall be experimentally implemented and compared with established optimization tools in terms of performance and effectiveness.

Innovative control design is an essential step stone for addressing the complexity of modern technical systems and the steadily increasing demand on efficiency and productivity. An important aspect in the field of control is path planning and trajectory optimization. Typical examples are the realization of minimum time or energy optimal transitions in robotics, the minimization of the energy consumption in process control or the computation of highly accurate flight paths in aerospace applications. However, a significant problem in trajectory optimization is the computational effort, in particular if constraints, e.g. on actuators or security margins, have to be taken into account. The main focus of the research project was to develop new methods that allow for an efficient computation of optimal trajectories for technical systems subject to constraints. To this end, a two-stage approach was pursued in the project. On the analytical side, a new method was developed for systematically incorporating process constraints within a new mathematical description of the system. This approach can be seen as an analytic preprocessing step that facilitates the subsequent numerical solution step. From a numerical viewpoint, research during the project focused on developing numerical optimization methods that are tailored to the mentioned analytical preprocessing step in order to enable a highly efficient computation of constrained trajectories for technical systems. Besides the methodological development, a further focus of the research project was on the applicability and actual realization of the methods, in particular in the context of nonlinear model predictive control. Owing to the developed methods and as one of the first results in this field, this advanced control concept was successfully implemented on a programmable logical controller (PLC), which is one of the most common and standard components of automation systems. Moreover, the research results were applied and evaluated for several control applications, in particular from mechatronics. For instance, the mentioned PLC implementation and its application for the highly dynamical control of a laboratory-scale overhead crane were presented at the worlds leading industrial exhibition, the Hannover Fair 2013.