While many engineering problems are nowadays translated into a numerical optimization problem, the associated numerical data are often inaccurate or uncertain. As this uncertainty of data may turn the numerical optimum into a poor or even unacceptable solution for the true problem, there is a great push for robust optimization techniques suited for engineering applications. Robust optimization seeks a solution that is feasible and most optimal for all possible values of the numerical data. As the data is generally considered to vary in infinite sets (e.g. a real interval), robust optimization problems are numerically intractable in general. Therefore most problems are currently relaxed to a tractable problem by relying on either Pólya’s theorem or sum-of-squares certificates of positivity. As these approaches suffer from limited applicability or high computational load, we recently initiated novel relaxation schemes based on B-splines, i.e. particular piecewise polynomial basis functions, and their properties. Within this research project you will develop the initial results into a general methodology for constructing B-spline based relaxations of robust optimization problems. In addition to the theoretical research this involves, you will develop a software toolbox for efficient spline manipulations and optimization, and validate the methodology on robust optimization applications such as robust control and motion planning in obstructed environments. The research will be carried out in the MECO research group at the division PMA of the department of Mechanical Engineering, KU Leuven, Leuven, Belgium.