Ghosh, Mukulika (2019-04). Geometric Approximations and their Application to Motion Planning. Doctoral Dissertation. Thesis uri icon

abstract

  • Geometric approximation methods are a preferred solution to handle complexities (such as a large volume or complex features such as concavities) in geometric objects or environments containing them. Complexities often pose a computational bottleneck for applications such as motion planning. Exact resolution of these complexities might introduce other complexities such as unmanageable number of components. Hence, approximation methods provide a way to handle these complexities in a manageable state by trading off some accuracy. In this dissertation, two novel geometric approximation methods are studied: aggregation hierarchy and shape primitive skeleton. The aggregation hierarchy is a hierarchical clustering of polygonal or polyhedral objects. The shape primitive skeleton provides an approximation of bounded space as a skeleton of shape primitives. These methods are further applied to improve the performance of motion planning applications. We evaluate the methods in environments with 2D and 3D objects. The aggregation hierarchy groups nearby objects into individual objects. The hierarchy is created by varying the distance threshold that determines which objects are nearby. This creates levels of detail of the environment. The hierarchy of the obstacle space is then used to create a decom-position of the complementary space (i.e, free space) into a set of sampling regions to improve the efficiency and accuracy of the sampling operation of the sampling based motion planners. Our results show that the method can improve the efficiency (10 - 70% of planning time) of sampling based motion planning algorithms. The shape primitive skeleton inscribes a set of shape primitives (e.g., sphere, boxes) inside a bounded space such that they represent the skeleton or the connectivity of the space. We apply the shape primitive skeletons of the free space and obstacle space in motion planning problems to improve the collision detection operation. Our results also show the use of shape primitive skeleton in both spaces improves the performance of collision detectors (by 20 - 70% of collision detection time) used in motion planning algorithms. In summary, this dissertation evaluates how geometric approximation methods can be applied to improve the performance of motion planning methods, especially, sampling based motion planning methods

publication date

  • May 2019
  • May 2019