Geometric Eccentricity and the Complexity of Manipulation Plans

Complexity bounds for algorithms for robotic motion and manipulation can be misleading when they are constructed with pathological `worst-case' scenarios that rarely appear in practice. Complexity can in some cases be reduced by characterizing nonpathological objects in terms of intuitive geometric properties. In this paper we consider the number of push and push-squeeze actions needed to orient a part without sensors and improve on the upper bound of O(n) for polygonal parts given by Chen and Ierardi in 9]. We de ne the geometric eccentricity of a planar part based on the aspect ratio of a distinguished bounding box. We show that only O(1) actions are required for parts with non-zero eccentricity. The analysis also applies to curved parts, providing the rst complexity bound for non-polygonal parts. Our results also yield new bounds on part feeders that use fences and conveyor belts.

• Type: Journal
• Year: 2000
• Where: ALGORITHMICA
• Authors: A. Frank van der Stappen, Kenneth Y. Goldberg
• Keywords: ALGORITHMICA 2000, Distinguished Bounding Box, Intuitive Geometric Properties, Robotic Motion