From prehistoric encirclement for hunting to GPS orbiting the earth for positioning, target encirclement has numerous real world applications. However, encircling multiple non-cooperative targets in GPS-denied environments remains challenging. In this work, multiple targets encirclement by using a minimum of two tasking agents, is considered where the relative distance measurements between the agents and the targets can be obtained by using onboard sensors. Based on the measurements, the center of all the targets is estimated directly by a fuzzy wavelet neural network (FWNN) and the least squares fit method. Then, a new distributed anti-synchronization controller (DASC) is designed so that the two tasking agents are able to encircle all targets while staying opposite to each other. In particular, the radius of the desired encirclement trajectory can be dynamically determined to avoid potential collisions between the two agents and all targets. Based on the Lyapunov stability analysis method, the convergence proofs of the neural network prediction error, the target-center position estimation error, and the controller error are addressed respectively. Finally, both numerical simulations and UAV flight experiments are conducted to demonstrate the validity of the encirclement algorithms. The flight tests recorded video and other simulation results can be found in https://youtu.be/B8uTorBNrl4.

翻译：从史前狩猎包围到GPS环绕地球定位，目标包围在现实世界中具有广泛的应用价值。然而，在无GPS环境中包围多个非合作目标仍具挑战性。本研究考虑使用至少两个任务智能体实现多目标包围，其中智能体与目标间的相对距离测量可通过机载传感器获取。基于这些测量数据，所有目标的中心位置通过模糊小波神经网络(FWNN)与最小二乘拟合法直接估计。随后，设计了一种新型分布式反同步控制器(DASC)，使得两个任务智能体能够在保持相对位置的同时包围所有目标。特别地，期望包围轨迹的半径可动态确定，以避免两个智能体与所有目标间潜在的碰撞风险。基于李雅普诺夫稳定性分析方法，分别给出了神经网络预测误差、目标中心位置估计误差及控制器误差的收敛性证明。最后，通过数值仿真与无人机飞行实验验证了所提包围算法的有效性。飞行测试录像及其他仿真结果可在https://youtu.be/B8uTorBNrl4查看。