A Gradient-Free Three-Dimensional Source Seeking Strategy With Robustness Analysis

Distributed source seeking in a three-dimensional (3-D) environment without explicit estimation of the gradient of the field is challenging. Nevertheless, for a swarm of an arbitrary number of agents, we develop a strategy to perform a source seeking behavior by requiring agents to synchronize their direction of motion using only local interactions while modulating their speed based only on the field value measured by each agent. The agents collectively move toward the source without estimating gradient and without sharing measurements of the field. We formulate a cascaded input-to-state stability problem from which we obtain Lyapunov-based convergence and robustness results. We validate the convergence of the swarm to the minimum of the field through simulated source seeking behavior in a 3-D scalar field.

在三维（3 - D）环境中，在不明确估计场梯度的情况下寻找分布式源是具有挑战性的。然而，对于任意数量的智能体群体，我们开发了一种策略来执行源寻找行为，该策略要求智能体仅通过局部交互来同步它们的运动方向，同时仅根据每个智能体所测量的场值来调节它们的速度。这些智能体在不估计梯度且不共享场测量值的情况下集体朝着源移动。我们构建了一个级联的输入到状态稳定性问题，由此我们获得了基于李雅普诺夫的收敛性和鲁棒性结果。我们通过在三维标量场中模拟源寻找行为验证了群体收敛到场的最小值。