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Synchronization and balancing around simple closed polar curves with bounded trajectories
Automatica ( IF 6.4 ) Pub Date : 2023-01-03 , DOI: 10.1016/j.automatica.2022.110810
Aditya Hegde, Anoop Jain

The problem of synchronization and balancing around simple closed polar curves is addressed for unicycle-type multi-agent systems. Leveraging the concept of barrier Lyapunov function in conjunction with bounded Lyapunov-like curve-phase potential functions, we propose distributed feedback control laws and show that the agents asymptotically stabilize to the desired closed curve in synchronized and balanced curve-phase patterns, and their trajectories remain bounded within a compact set. Our control design methodology is based on the proposition of two models, namely the parametric-phase control model and the curve-phase control model. We also characterize the trajectory-constraining set based on the magnitude of the safe distance of the exterior boundary from the desired curve. We further establish a connection between the perimeters and areas of the trajectory-constraining set with the perimeter and area of the desired curve. We obtain bounds on different quantities of interest in the post-design analysis and provide simulation results to illustrate the theoretical findings.



中文翻译:

围绕具有有界轨迹的简单闭合极坐标曲线的同步和平衡

针对单轮型多智能体系统解决了围绕简单闭合极坐标曲线的同步和平衡问题。利用障碍 Lyapunov 函数的概念结合有界 Lyapunov 类曲线相位势函数,我们提出了分布式反馈控制法则,并表明代理在同步和平衡曲线相位模式及其轨迹中渐近稳定到所需的闭合曲线保持在紧集内。我们的控制设计方法基于两种模型的提出,即参数相位控制模型和曲线相位控制模型。我们还描述了轨迹约束根据外部边界与所需曲线的安全距离的大小进行设置。我们进一步在轨迹约束集的周长和面积与所需曲线的周长和面积之间建立联系。我们在后期设计分析中获得了不同兴趣量的界限,并提供了仿真结果来说明理论发现。

更新日期:2023-01-03
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