自主机器人编队问题的几何分析
Geometric Analysis of the Formation Problem for Autonomous Robots
摘要：
在自主机器人的编队控制问题中，分布式控制律将机器人引导到期望的目标编队。目标编队的局部稳定性结果可以通过线性化和中心流形理论的方法或通过基于Lyapunov的方法导出。众所周知，机器人的闭环动力学存在各种其他不期望的不变集。利用微分几何方法研究了不变流形的全局稳定性及其局部稳定性。然后将理论结果应用于著名的循环三角形形成的例子，并导致不稳定的所有不变集以外的目标形成。
英文摘要：
In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. It is well known that there are various other undesired invariant sets of the robots' closed-loop dynamics. This paper addresses a global stability analysis by a differential geometric approach considering invariant manifolds and their local stability properties. The theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation.
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