University of Groningen
Constructing tensegrity frameworks and related applications in multi-agent formation control
Yang, Qingkai
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Publication date: 2018
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Yang, Q. (2018). Constructing tensegrity frameworks and related applications in multi-agent formation control. University of Groningen.
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Summary
Tensegrity frameworks have drawn substantial attention from a range of disciplines, including civil engineering, biology, and mechanics, due to their identified features, such as strong stability, flexible scalability, and robustness. Motivated by these advantages, we study how to grow tensegrity framework from the graphic and algebraic point of view such that the superior features can be inherited. Another central topic of this thesis is the distributed controller design for coordination of multi-agent systems using virtual tensegrity frameworks.
We first investigate the problem of merging two separate rigid and infinitesimally rigid tensegrity frameworks in the plane, respectively. For infinitesimally rigid tenserity frameworks, the existence of the proper self-stress of the linked framework has been proven, which implies that the infinitesimal rigidity can be preserved. In addition, the type of the linked members can also be indicated by checking the sign of the corresponding stress. When merging rigid frameworks, we have proposed a disturbance perturbation-based method to justify the rigidity of the combined framework by properly inserting new members, whose type can be determined using rigidity matrix. Moreover, the Henneberg construction has been extended to grow super stable tensegrity frameworks. It has been proven that the super stability can also been preserved under the operation of vertex addition, edge splitting, and merging.
Inspired by the “ turning back” method to generate sparse matrix, we propose a numerical algorithm to construct universally rigid tensegrity frameworks given a generic configuration. Then by projecting multi-agent system into the virtual tensegrity framework, we study how to reach desired formations with the constraint that inter-agent distances are upper or lower bounded. We design a control strategy based on the idea that each edge is assigned to be a virtual cable or strut, with which the physical distance constraints can be obtained.
We also propose a control strategy using the stress matrix associated with a universally rigid tensegrity framework to scale the formation. We show that the size
142 Summary
of the formation can be controlled by d pairs of agents whose configuration spans
Rd. By employing the orthogonal projection operator, the number of the agents
controlling formation size can be reduced to two. We further design estimator-based control laws in combination with the stresses, in which the prescribed formation can be realized even only one agent knows the desired size of the entire formation. Finally, we address the issue of formation tracking for multi-agent systems using only local measurements in local coordinate systems. Finite-time continuous estimators are designed to dynamically estimate the centroid of the whole group. We then make use of the estimations to propose a class of control algorithms such that the desired formation shape can be achieved and at the same time the external reference signal is tracked by the real centroid.
