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Collision Cones for Quadric Surfaces in n-Dimensions

Chakravarthy, A and Ghose, D (2018) Collision Cones for Quadric Surfaces in n-Dimensions. In: IEEE Robotics and Automation Letters, 3 (1). pp. 604-611.

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Official URL: https://doi.org/10.1109/LRA.2017.2776347


In this letter, we present analytical expressions for collision cones associated with a class of hyperquadric surfaces moving in n-dimensional configuration space. Using a relative velocity paradigm, a geometric analysis of the distance, time, and point of closest approach between moving objects in n -dimensional space, is carried out to obtain a characterization of the collision cone between a point and a hyperspheroid as well as a constrained hyperboloid, which represent an interesting and useful class of objects in configuration space. It is shown that these n -dimensional collision cones can be integrated with sampling-based motion planners, avoiding the need to evaluate waypoints that lie inside the collision cone. The cones can also consist of the heading angles toward desirable regions in the configuration space, in which case planners may evaluate more waypoints inside the cone. Finally, analytical expressions of the collision cones are used, in conjunction with the concept of level sets, and incorporated into a Lyapunov-based design approach, to determine analytical expressions of nonlinear guidance laws that can manipulate the velocity vector of an object in n -dimensional space. © 2016 IEEE.

Item Type: Journal Article
Publication: IEEE Robotics and Automation Letters
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Air navigation; Collision avoidance; Electronic guidance systems; Motion planning; Planning; Wave functions, Analytical expressions; Configuration space; Geometric analysis; Lyapunov based design; Motion and path planning; N-dimensional space; Nonlinear guidance laws; Point of closest approaches, Vector spaces
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 02 Sep 2022 03:55
Last Modified: 02 Sep 2022 03:55
URI: https://eprints.iisc.ac.in/id/eprint/76341

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