Autonomous Robots

, Volume 32, Issue 3, pp 243–266

Generalization of the collision cone approach for motion safety in 3-D environments


DOI: 10.1007/s10514-011-9270-z

Cite this article as:
Chakravarthy, A. & Ghose, D. Auton Robot (2012) 32: 243. doi:10.1007/s10514-011-9270-z


Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.


Collision coneDynamic environmentsObstacle avoidancePath planningQuadric surfaces

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and the Department of Electrical EngineeringWichita State UniversityWichitaUSA
  2. 2.Guidance, Control and Decision Systems Laboratory (GCDSL) in the Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia