Spline-Based Motion Planning in an Obstructed 3D Environment * *This work benefits from KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC), from the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office (DYSCO), from the project G0C4515N of the Research Foundation-Flanders (FWO-Flanders) and the KU Leuven Research project C14/15/067: B-spline based certificates of positivity with applications in engineering. Ruben Van Parys is a PhD fellow of FWO-Flanders. The MECO Research Group is an associated research lab of Flanders MakeThis work benefits from KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC), from the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office (DYSCO), from the project G0C4515N of the Research Foundation-Flanders (FWO-Flanders) and the KU Leuven Research project C14/15/067: B-spline based certificates of positivity with applications in engineering. Ruben Van Parys is a PhD fellow of FWO-Flanders. The MECO Research Group is an associated research lab of Flanders MakeThis work benefits from KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC), from the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office (DYSCO), from the project G0C4515N of the Research Foundation-Flanders (FWO-Flanders) and the KU Leuven Research project C14/15/067: B-spline based certificates of positivity with applications in engineering. Ruben Van Parys is a PhD fellow of FWO-Flanders. The MECO Research Group is an associated research lab of Flanders Make.