Congruence, similarity and symmetries of geometric objects
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
The theory and applications of algebraic metric spaces
The theory and applications of algebraic metric spaces
The self-reconfiguring robotic molecule: design and control algorithms
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Distributed reconfiguration of metamorphic robot chains
Distributed Computing
The design of a representation and analysis method for modular self-reconfigurable robots
Robotics and Computer-Integrated Manufacturing
Designing Modular Lattice Systems with Chiral Space Groups
International Journal of Robotics Research
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
An amoeboid modular robot that exhibits real-time adaptive reconfiguration
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
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In order for a modular self-reconfigurable robotic system to autonomously change from its current state to a desired one, it is critical to have a cost function (or metric) that reflects the effort required to reconfigure. A reconfiguration sequence can consist of single module motions, or the motion of a “branch” of modules. For single module motions, the minimization of metrics on the set of sets of module center locations serves as the driving force for reconfiguration. For branch motions, the question becomes which branches should be moved so as to minimize overall effort. Another way to view this is as a pattern matching problem in which the desired configuration is viewed as a void, and we seek branch motions that best fill the void. A precise definition of goodness of fit is therefore required. In this paper, we address the fundamental question of how closely geometric figures can be made to match under a given group of transformations (e.g., rigid-body motions), and what it means to bisect two shapes. We illustrate these ideas in the context of applications in modular robot motion planning.