As global energy demand will continue to rise and man's negative impact on global warming is known to be a fact, there is a strong desire to minimise the energy usage of industrial machinery. A significant opportunity lies in optimisations which do not require any adaptations or investments in installed hardware such as trajectory optimisation. Machine builders and users often only define the time to move from one point to another and the position of start- and endpoint. The exact position as a function of the time, or position function, in between these two points is very often not an issue for machine users. This flexibility opens the opportunity to optimise the position function. The literature mentions cases where ad-hoc optimisations reduce the energy usage of machinery used for repetitive tasks up to 50% by choosing optimised trajectories over the usual standard movement profiles. However, there is no scientific consensus on a computationally efficient technique which can guarantee to find the global optimum for systems with position varying mechanical load properties. Therefore, this project will assess the use and implementation of direct calculus optimisation. Applying this pure mathematical technique based on symbolic methods of trajectory optimisation would be a genuinely fundamental novelty, especially for machines with position varying dynamics. For one thing, this would eliminate the necessity of time-consuming iterative optimisations. On the contrary, direct calculus methods would lead to closed mathematical functions for the position function.
To enable the use of this direct calculus methods, closed mathematical equations, describing the position-varying mechanical load properties, will be necessary. Obtaining such functions can be done theoretically based on Lagrange formulations. However, such an approach is not feasible in practice where the complexity of the machinery hampers analytical analysis. On the other hand, machine builders increasingly rely on CAD multibody software to design their machines. The promotor has expertise in extracting data by applying specific simulations on these virtual CAD models. The sampled data, obtained in this way, can be translated to explicit formulas, based on the expertise of the co-promotor. Developing such a technique to transform the sampled data to closed mathematical equations will be a core challenge of the project and the major enabler to apply direct calculus optimisation.
Furthermore, to guarantee the machine still operates at its optimum if machine behaviour changes during operation, an online tracking method is necessary. For this purpose, the knowledge of the promotor on tracking the position dependency of machine parameters online in the frequency domain is essential. The data samples obtained in this way will again be translated to a mathematical description to allow a re-optimisation of the trajectory. For this purpose, the direct calculus optimisation method will be advantageous as it defines the optimised path as a function of position varying parameters. This definition enables direct re-optimisation. Moreover, where the current state of the art focusses on offline a priori or online optimisation, facilitating online re-optimisation based on a priori offline determined information will be another fundamental novelty of this project.