The problem of moving an elliptic object A, surrounded by a set of elliptic obstacles B//j , is considered. The initial and final positions of the object are known and the intention is to move A solely by performing translations in the plane. The motion must be performed in such a way that A does not collide with any of the obstacles. The following algorithms are presented: (i) An algorithm, of complexity O(N log N), where N is the number of obstacles, which yields the set of all directions along which the object is separable from the obstacles by a single translation: (ii) An algorithm, quadratic in the number of obstacles, which yields a path for A to be moved from its starting configuration to its final configuration. The proposed technique first transforms the ellipse A into a circle A prime . This same transformation changes each ellipse B//j into another figure B//j prime , which is also elliptic. The algorithms then compute the path of translation by processing the configuration obstacles of space of B//j prime with respect to the circle A prime .

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Conference Proceedings - 1986 IEEE International Conference on Robotics and Automation.
Citation
Oommen, J, & Reichstein, Irwin (Irwin). (1986). ON TRANSLATING ELLIPSES AMIDST ELLIPTIC OBSTACLES. In Proceedings - 1986 IEEE International Conference on Robotics and Automation. (pp. 1755–1760).