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Distributed formation maneuver control by manipulating the complex Laplacian
arXiv - CS - Robotics Pub Date : 2020-09-16 , DOI: arxiv-2009.07625 Hector Garcia de Marina
arXiv - CS - Robotics Pub Date : 2020-09-16 , DOI: arxiv-2009.07625 Hector Garcia de Marina
This paper proposes a novel maneuvering technique for the
complex-Laplacian-based formation control. We show how to modify the original
weights that build the Laplacian such that a designed steady-state motion of
the desired shape emerges from the local interactions among the agents. These
collective motions can be exploited to solve problems such as the shaped
consensus (the rendezvous with a particular shape), the enclosing of a target,
or translations with controlled speed and heading to assist mobile robots in
area coverage, escorting, and traveling missions, respectively. The designed
steady-state collective motions correspond to rotations around the centroid,
translations, and scalings of a reference shape. The proposed modification of
the weights relocates one of the Laplacian's zero eigenvalues while preserving
its associated eigenvector that constructs the desired shape. For example, such
relocation on the imaginary or real axis induces rotational and scaling
motions, respectively. We will show how to satisfy a sufficient condition to
guarantee the global convergence to the desired shape and motions. Finally, we
provide simulations and comparisons with other maneuvering techniques.
中文翻译:
基于复杂拉普拉斯算子的分布式编队机动控制
本文提出了一种新的机动技术,用于基于复杂拉普拉斯算子的编队控制。我们展示了如何修改构建拉普拉斯算子的原始权重,以便从代理之间的局部交互中产生所需形状的设计稳态运动。这些集体运动可用于解决诸如形状共识(与特定形状的会合)、目标的包围或以受控速度和航向进行平移等问题,以协助移动机器人完成区域覆盖、护送和旅行任务,分别。设计的稳态集体运动对应于围绕质心的旋转、平移和参考形状的缩放。建议的权重修改重新定位了拉普拉斯算子之一 s 零特征值,同时保留其构建所需形状的关联特征向量。例如,在虚轴或实轴上的这种重新定位分别引起旋转和缩放运动。我们将展示如何满足充分条件以保证全局收敛到所需的形状和运动。最后,我们提供了与其他机动技术的模拟和比较。
更新日期:2020-09-17
中文翻译:
基于复杂拉普拉斯算子的分布式编队机动控制
本文提出了一种新的机动技术,用于基于复杂拉普拉斯算子的编队控制。我们展示了如何修改构建拉普拉斯算子的原始权重,以便从代理之间的局部交互中产生所需形状的设计稳态运动。这些集体运动可用于解决诸如形状共识(与特定形状的会合)、目标的包围或以受控速度和航向进行平移等问题,以协助移动机器人完成区域覆盖、护送和旅行任务,分别。设计的稳态集体运动对应于围绕质心的旋转、平移和参考形状的缩放。建议的权重修改重新定位了拉普拉斯算子之一 s 零特征值,同时保留其构建所需形状的关联特征向量。例如,在虚轴或实轴上的这种重新定位分别引起旋转和缩放运动。我们将展示如何满足充分条件以保证全局收敛到所需的形状和运动。最后,我们提供了与其他机动技术的模拟和比较。