University of Groningen
Angle Rigidity Graph Theory and Multi-agent Formations Chen, Liangming
DOI:
10.33612/diss.169592252
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Publication date: 2021
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Chen, L. (2021). Angle Rigidity Graph Theory and Multi-agent Formations. University of Groningen. https://doi.org/10.33612/diss.169592252
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1. Angle rigid structures can enable more motion freedom than distance or bearing rigid frameworks, but the tradeoff is the increase of nonlinearity and complexity of constraints in terms of the orders of polynomials. (Chapters 1 and 2)
2. The Henneberg construction is efficient in both generating and disassembling a minimal distance rigid graph. Type-I and Type-II operations for angle rigidity are efficient in generating a minimal angle rigid structure, but might be inefficient to disassemble. (Chapters 2 and 5)
3. Graphs have been used mainly in rigidity theory for multi-point frameworks under distance constraints. However, to describe angle constraints where each of them is associated with three vertices, the multi-point structure, called angularity in this thesis, is more
effective.
(Chapters 1 and 2)
4. The designed angle-only formation control laws have the advantage of requiring fewer sensing measurements, but have difficulty in achieving the desired formation globally.
(Chapters 3 and 6)
5. Under the proposed angle-based feedback control law, the closed-loop dynamics of the formation when each agent is governed by double-integrator dynamics, can be studied comparatively with the closed-loop dynamics of the same formation but with
single-integrator agent dynamics. The comparison can reveal the separate roles of formation topologies and agent dynamics, as has been done for other nonlinear control systems.
(Chapter 4)
6. Before starting to solve a problem, one needs to understand the essence of the problem; the time spent on understanding a problem can in fact make it more efficient to find a correct solution. (Chapter 1)
7. To achieve something one must lose something. This principle might exist everywhere, particularly in a control system. (Chapter 1) 8. To build a wall usually needs many days, but to destroy it might only need one day. A control system may have many advantages, but one disadvantage may be enough to prevent its practical applications. (Chapter 3)
