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

Abstract

This paper presents a motion planning approach that steers systems in an optimal way through an obstructed 3D environment. The motion trajectories are parameterized as polynomial splines and by exploiting the properties of B-spline basis functions, constraints on the trajectories are efficiently enforced. The approach is applied on two relevant cases. The first one elaborates a pick and place task for a Cartesian robot which is validated experimentally on an industrial plate transportation system. Depending on the task, the proposed method can reduce the motion time with 10 - 30% with respect to the currently applied trajectories. In a second case the approach is applied on the navigation of Unmanned Aerial Vehicles (UAVs) flying in an uncertain dynamic environment. This problem is formulated in a receding-horizon fashion which can update trajectories with a rate of 2.5 Hz. A supporting software toolbox is provided that implements the proposed approach and facilitates its use.