Studies On Motion Planning Strategies For Modular Self-reconfiguring Systems

Multi-agent systems have wide applications in aerospace, military, service, etc. due to their advantages such as robustness, low cost, and scalability. A special branch iso-lated from multi-agent systems, named modular self-reconfiguring systems even becomes a hotspot for its versatility, i.e., the ability to change among different morphologies. How-ever, due to the fact that the geometric characters as well as the rigid or compressible properties should be taken into consideration, motion planning for such a kind of system faces with more difficulties compared with those traditional multi-agent systems focusing on point mass models or unicycle models. Theoretical research on motion planning for modular self-reconfiguring systems is still in its initial stage. Thus, the work is of great challenges.This study begins with a point-mass agents based distributed control problem for achieving a geometric pattern formation. It then follows the reconfiguration problems, i.e., the motion planning for planar hexagonal modules by formulating the problem from three different perspectives. In summary, we mainly focus on the following pieces of work.An existing switching control strategy for achieving an approximate circle formation based on multiple point-mass agents is improved. The modified strategy is more reason-able and approaches the practical scenarios. Rigorous analysis is provided to support the stability of the system under the proposed revised control law and the convergence of the eventual formation. Results validate that the eventual formation is a curve with constant width (not limited to circles). The method to choose appropriate parameters makes the obtaining of curves with any desired width guaranteed.Study a regular hexagonal modules based self-reconfiguring problem from the per-spective of control. Consider a self-reconfiguring system consisting of two kinds of mod-ules, which are of the same geometric shape but with different detecting abilities, saying heterogeneous modules. A distributed motion strategy is developed for each module (actu- ally two kinds of strategies, one for each category), based on which the self-reconfiguring system converges to a continuous straight chain from an arbitrary initial configuration that satisfies certain conditions. The global-to-local idea is introduced to decompose the desired goal configuration into local control objectives that depend only on modules’local informa-tion. As a result, the representation of the desired goal configuration generally depending on global information is evaded. The applying of the so-called curve shortening method guarantees the monotonicity of the system configuration during reconfiguration. Hence the convergence of the goal configuration is guaranteed. The analysis method adopted in this study offers positive suggestions for the reconfiguration problems, that are, taking into ac-count the geometric properties of the goal configuration rather than focusing on the goal configuration itself, sometimes may make the problem simplified. Besides, the usage of heterogeneous modules is not only reasonable but also economical.Study a regular hexagonal modules based self-reconfiguring problem from the per-spective of task-driven. Consider a self-reconfiguring system consisting of a set of homo-geneous modules. A distributed motion strategy is developed for each module, such that the overall behavior of the system results in the reconfiguration from an initial configuration to any unprespecified goal configuration that fulfills the given tracking and enveloping task. By guaranteeing the connectivity of the information flow of the system, and the monotonic motion of a part of modules with respect to the target object, the goal configuration is proved to be stable in the absence of global coordinate frame. The relationship between the converging time and the sensing radius is discussed, which acts as a reference for choosing appropriate parameters when such kinds of applications are done. Besides, it is pointed out that for those goal configurations allowing minor errors (in most applications are reason-able), it is always able to reformulate them as a tracking and enveloping problem. Thus the proposed strategy in this study can solve a wide range of reconfiguration problems.Study a regular hexagonal modules based self-reconfiguring problem from the per-spective of search. Different from existing works, in which module configurations are usu-ally described by a set of charts, a matrix representation method is developed to mathemat- ically describe not only a static module configuration, but also the dynamic transformation of configurations between two contiguous discrete iterations. Therefore the problem can be reformulated as to find a feasible sequence of transformation matrices under matrices with respect to the initial configuration and the goal configuration. A programming for the convergence order with respect to the lattice cells the goal configuration living in is devel-oped combining with the introduced matrix representation method, by which the system configuration achieves reconfiguration from any initial configuration to the goal configu-ration that satisfies certain conditions without deadlocks. The mathematical descriptions of both a static configuration and its dynamic transformation make it possible to precisely define a module configuration. It also lays a foundation for bringing analysis tools such as graph theory and matrix theory maturely used in traditional multi-agent systems to modular self-reconfiguring systems.Besides theoretical analysis and proofs, the main conclusions and contributions ap-peared in this study are also validated based on Matlab.