Two algorithms are presented which deal with translating an elliptic object, A, without collision amidst elliptic obstacles. These are: (i) An exact algorithm, of complexity O(N log N), where N is the number of obstacles, yielding all directions along which the object is separable from the obstacles by a single translation. (ii) An algorithm quadratic in N, which yields, with a degree of approximation determined by the user, a path of the object from its initial to its final position.

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Journal Robotica
Oommen, J, & Reichstein, I. (Irwin). (1987). On the problem of translating an elliptic object through a workspace of elliptic obstacles. Robotica, 5(3), 187–196. doi:10.1017/S0263574700015824