In cooperative multi-agent robotic systems, coordination is necessary in order to complete a given task. Important examples include search and rescue, operations in hazardous environments, and environmental monitoring. Coordination, in turn, requires simultaneous satisfaction of safety critical constraints, in the form of state and input constraints, and a connectivity constraint, in order to ensure that at every time instant there exists a communication path between every pair of agents in the network. In this work, we present a model predictive controller that tackles the problem of performing multi-agent coordination while simultaneously satisfying safety critical and connectivity constraints. The former is formulated in the form of state and input constraints and the latter as a constraint on the second smallest eigenvalue of the associated communication graph Laplacian matrix, also known as Fiedler eigenvalue, which enforces the connectivity of the communication network. We propose a sequential quadratic programming formulation to solve the associated optimization problem that is amenable to distributed optimization, making the proposed solution suitable for control of multi-agent robotics systems relying on local computation. Finally, the effectiveness of the algorithm is highlighted with a numerical simulation.

翻译：在协作式多智能体机器人系统中，协调对于完成给定任务至关重要。重要实例包括搜救行动、危险环境作业以及环境监测。协调过程需要同时满足安全关键约束（以状态约束和输入约束的形式）和连通性约束，从而确保在每一时刻网络中任意一对智能体之间都存在通信路径。本文提出一种模型预测控制器，该控制器在满足安全关键约束和连通性约束的同时解决多智能体协调问题。前者以状态和输入约束的形式表述，后者则表述为与通信图拉普拉斯矩阵相关的第二小特征值约束（即Fiedler特征值），该约束强制执行通信网络的连通性。我们提出一种适用于分布式优化的序列二次规划形式来解决关联优化问题，使得所提方案适用于依赖局部计算的多智能体机器人系统控制。最后通过数值仿真验证了算法的有效性。