Departmental Papers (ESE)



We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no collisions along the way. We use power diagrams, generalized Voronoi diagrams with additive weights, to identify the robot’s collision free convex neighborhood, and to generate the value of our proposed candidate solution vector field at any free configuration via evaluation of an associated convex optimization problem. We prove that this scheme generates a continuous flow with the specified properties. We also propose its practical extension to the nonholonomically constrained kinematics of the standard differential drive vehicle.

For more information: Kod*lab

Sponsor Acknowledgements

This work was supported in part by AFOSR under the CHASE MURI FA9550–10–1−0567.

Document Type

Conference Paper

Subject Area

GRASP, Kodlab

Date of this Version


Publication Source

2016 IEEE International Conference on Robotics and Automation (ICRA)

Start Page


Last Page





Collision-free robot navigation, Navigation functions, Collision avoidance, Sphere worlds, Differential-drive robots, Local free space, Generalized Voronoi diagrams, Power diagrams

Bib Tex

@InProceedings{arslan_kod_ICRA2016B, Title = {Exact Robot Navigation Using Power Diagrams}, Author = {Omur Arslan and Daniel E. Koditschek}, Booktitle = {Robotics and Automation, 2016 IEEE International Conference on}, Year = {2016}, Pages = {1-8}, DOI = {10.1109/ICRA.2016.7487090} }



Date Posted: 04 November 2016

This document has been peer reviewed.