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.

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。可以利用这些集体运动来解决诸如形状共识（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，以协助移动机器人执行区域覆盖、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、参考形状的平移和缩放。建议的权重修改重新定位拉普拉斯算子的零特征值之一，同时保留其构建所需形状的相关特征向量。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。