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Algorithmic Foundations of Robotics XII pp 912–927Cite as

Assignment Algorithms for Variable Robot Formations

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Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 13))

Abstract

This paper describes algorithms to perform optimal assignment of teams of robots translating in the plane from an initial formation to a variable goal formation. We consider the case when each robot is to be assigned a goal position, the individual robots are interchangeable, and the goal formation can be scaled or translated.We compute the costs for all candidate pairs of initial, goal robot assignments as functions of the parameters of the goal formation, and partition the parameter space into equivalence classes invariant to the cost order using computational geometry techniques. We compute a minimum completion time assignment for an equivalence class by formulating it as a linear bottleneck assignment problem (LBAP). To improve efficiency, we solve the LBAP problem for each equivalence class by incrementally updating the solution as the formation parameters are varied. This work is motivated by applications that include the motion of droplet formations in digital microfluidic lab-on-a-chip devices, and of robot and drone formations in the plane.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA

    Srinivas Akella

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  1. Srinivas Akella
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Correspondence to Srinivas Akella .

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Editors and Affiliations

  1. Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA

    Ken Goldberg

  2. Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA

    Pieter Abbeel

  3. Rutgers University, Piscataway, NJ, USA

    Kostas Bekris

  4. University of California, Berkeley, CA, USA

    Lauren Miller

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Akella, S. (2020). Assignment Algorithms for Variable Robot Formations. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_58

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