This paper studies the problem of safe and optimal continuum deformation of a large-scale multi-agent system (MAS). We present a novel approach for MAS continuum deformation coordination that aims to achieve safe and efficient agent movement using a leader-follower multi-layer hierarchical optimization framework with a single input layer, multiple hidden layers, and a single output layer. The input layer receives the reference (material) positions of the primary leaders, the hidden layers compute the desired positions of the interior leader agents and followers, and the output layer computes the nominal position of the MAS configuration. By introducing a lower bound on the major principles of the strain field of the MAS deformation, we obtain linear inequality safety constraints and ensure inter-agent collision avoidance. The continuum deformation optimization is formulated as a quadratic programming problem. It consists of the following components: (i) decision variables that represent the weights in the first hidden layer; (ii) a quadratic cost function that penalizes deviation of the nominal MAS trajectory from the desired MAS trajectory; and (iii) inequality safety constraints that ensure inter-agent collision avoidance. To validate the proposed approach, we simulate and present the results of continuum deformation on a large-scale quadcopter team tracking a desired helix trajectory, demonstrating improvements in safety and efficiency.

翻译：本文研究大规模多智能体系统（MAS）的安全与最优连续变形问题。我们提出了一种新颖的MAS连续变形协调方法，旨在通过一个包含单输入层、多个隐藏层和单输出层的领导者-跟随者多层分层优化框架，实现安全高效的智能体运动。输入层接收主要领导者的参考（材料）位置，隐藏层计算内部领导者智能体和跟随者的期望位置，输出层计算MAS构型的标称位置。通过引入MAS变形应变场主原则的下界，我们获得线性不等式安全约束并确保智能体间避碰。连续变形优化被形式化为一个二次规划问题，包含以下组成部分：（i）表示第一隐藏层权重的决策变量；（ii）惩罚标称MAS轨迹偏离期望MAS轨迹的二次代价函数；（iii）确保智能体间避碰的不等式安全约束。为验证所提方法，我们模拟并展示了大规模四旋翼机队在跟踪期望螺旋轨迹时的连续变形结果，证明了安全性和效率的提升。