In this paper, the problems of specified finite-time distributed attitude estimation and velocity-free attitude synchronization are studied for rigid bodies on special orthogonal group SO(3). Using the geometric convexity on SO(3), the exponential distributed observers are proposed for each rigid body to estimate the common time-varying reference states which are only available to a part of followers. Then, the specified finite-time distributed observers are proposed by using the time-rescaling approach, where the finite terminal time can be specified in advance according to the task requirements. The advantage of time-rescaling method is that the asymptotic, exponential, or finite-time distributed observers can be converted to the specified finite-time distributed observers via choosing an appropriate continuously differentiable scaling function that satisfies some required properties to rescale time. Based on the distributed observers, the velocity-free attitude synchronization control torques are designed by virtue of observer-like systems. The performances of the specified finite-time distributed observers and the velocity-free attitude synchronization with distributed observers are illustrated through numerical/SimMechanics simulations.

中文翻译：

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SO(3)上基于指定有限时间分布式观测器的刚体无速度姿态同步

本文研究了特殊正交群SO(3)上刚体的指定有限时间分布式姿态估计和无速度姿态同步问题。利用SO(3)上的几何凸性，为每个刚体提出了指数分布的观测器来估计公共时变参考状态，这些状态只对部分跟随者可用。然后，利用时间重标法提出指定的有限时间分布式观测器，其中可以根据任务要求提前指定有限终端时间。时间重标方法的优点是渐近、指数、或有限时间分布式观测器可以通过选择合适的连续可微缩放函数来转换为指定的有限时间分布式观测器，该函数满足重新缩放时间所需的一些属性。基于分布式观测器，利用类观测器系统设计无速度姿态同步控制转矩。指定的有限时间分布式观测器的性能和与分布式观测器的无速度姿态同步通过数值/SimMechanics 模拟来说明。