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Quaternions and Dual Quaternions: Singularity-Free Multirobot Formation Control

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Abstract

Cluster space control is a method of multirobot formation keeping that considers a group of robots to be a single entity, defining state variables to represent characteristics of the group, such as position, orientation, and shape. This technique, however, suffers from singularities when a minimal state representation is used. This paper presents three alternative implementations of this control approach that eliminate singularities through changes in the control architecture or through redundant formation definitions. These proposed solutions rely on quaternions, dual quaternions, and control implementations that produce singularity-free trajectories while maintaining a cluster level abstraction that allows for simple specification and monitoring. A key component of this work is a novel concept of representing formation shape parameters with dual quaternions. Simulation results show the feasibility of the proposed solutions and illustrate their differences and limitations.

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Authors and Affiliations

  1. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and Instituto Tecnologico de Buenos Aires (ITBA), Buenos Aires, Argentina

    Ignacio Mas

  2. Robotic Systems Laboratory, Santa Clara University, Santa Clara, CA, USA

    Christopher Kitts

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  1. Ignacio Mas
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  2. Christopher Kitts
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Correspondence to Ignacio Mas.

Additional information

This work has been sponsored through USAIT Grant W911NF-14-1-0008, ITBACyT 2013-17, and Agencia Nacional de Promoción Científica y Tecnológica, FONCYT PICT 2014-2055.

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Mas, I., Kitts, C. Quaternions and Dual Quaternions: Singularity-Free Multirobot Formation Control. J Intell Robot Syst 87, 643–660 (2017). https://doi.org/10.1007/s10846-016-0445-x

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