Minimising computational complexity of the RRT algorithm a practical approach

Sampling based techniques for robot motion planning have become more widespread during the last decade. The algorithms however, still struggle with for example narrow passages in the configuration space and suffer from high number of necessary samples, especially in higher dimensions. A widely used method is Rapidly-exploring Random Trees (RRT's). One problem with this method is the nearest neighbour search time, which grows significantly when adding a large number of vertices. We propose an algorithm which decreases the computation time, such that more vertices can be added in the same amount of time to generate better trajectories. The algorithm is based on subdividing the configuration space into boxes, where only specific boxes needs to be searched to find the nearest neighbour. It is shown that the computational complexity is lowered from a theoretical point of view. The result is an algorithm that can provide better trajectories within a given time period, or alternatively compute trajectories faster. In simulation the algorithm is verified for a simple RRT implementation and in a more specific case where a robot has to plan a path through a human inhabited environment.