Solution to the gripper envelope problem using a planar sweep

摘要

The determination of sweep shadows is important when analyzing the potential interference effects of obstacles in a robotic environment and is well suited for application to the gripper envelope problem. This report presents techniques for generating the planar sweep shadow of polyhedral objects. Algorithmic details for computing the sweep shadow for both straight-line and simple-rotation trajectories are described. Methods for analyzing the resultant sweep shadow are also presented and the time complexity of the algorithms is discussed. Various test cases are provided in an appendix showing the actual results generated by software solving the problem.