Computing configuration space obstacles using polynomial transforms

In this paper, we propose an algorithm to compute configuration space obstacles based on the polynomial transform (PT) which requires only real arithmetic. The PT-based algorithm is not restricted by the geometrical characteristics of the robot and obstacles in the world and also it can be expanded to the three-dimensional work space without any difficulties. We prove the minimum possible number of multiplications of constructing the configuration space bitmap and present a quantificational standard to select the size of the resolution N. By comparing our algorithm with works prior, the experimental results show that our PT-based algorithm is efficient.