SIAM Journal on Control and Optimization
Reduction and control of nonlinear symmetric distributed robotic systems
Reduction and control of nonlinear symmetric distributed robotic systems
Motion Planning for Nonlinear Symmetric Distributed Robotic Formations
International Journal of Robotics Research
Brief paper: Structured semidefinite programs for the control of symmetric systems
Automatica (Journal of IFAC)
Bifurcations and symmetries of optimal solutions for distributed robotic systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
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This paper considers nonlinear symmetric control systems. By exploiting the symmetric structure of the system, stability results are derived that are independent of the number of components in the system. This work contributes to the fields of research directed toward compositionality and composability of large-scale system in that a system can be ''built-up'' by adding components while maintaining system stability. The modeling framework developed in this paper is a generalization of many existing results which focus on interconnected systems with specific dynamics. The main utility of the stability result is one of scalability or compositionality. If the system is stable for a given number of components, under appropriate conditions stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system. The results are general and applicable to a wide class of problems. The examples in this paper focus on the formation control problems for multi-agent robotic systems.