A fast procedure for computing the distance between complex objects in three-dimensional space

@article{Gilbert1988AFP,
  title={A fast procedure for computing the distance between complex objects in three-dimensional space},
  author={Elmer G. Gilbert and Daniel W. Johnson and S. Sathiya Keerthi},
  journal={IEEE J. Robotics and Automation},
  year={1988},
  volume={4},
  pages={193-203}
}
An efficient and reliable algorithm for computing the Euclidean distance between a pair of convex sets in Rm is described. Extensive numerical experience with a broad family of polytopes in R 3 shows that the computational cost is approximately linear in the total number of vertices specifying the two polytopes. The algorithm has special features which makes its application in a variety of robotics problems attractive. These are discussed and an example of collision 
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