One Way to Obtain the Smoothed Estimate of Phase Vector in the Task of Motion Control of Convoy Robots

In this paper, we formulated and solved the problem of fixed-lag smoothing estimation for continuous linear dynamical systems. The problems of other fixed-lag smoothing algorithm for continuous linear dynamical systems are indicated. Firstly, sometimes the fixed-lag smoothing algorithm is not stable. Secondly, the knowledge of state transition matrix is needed to implement algorithm. It is different to get it, especially for time-vary system. An algorithm is developed for generating the optimal smoothed estimate x(t - T|t) of the state x(t) of a continuous linear system, where t is the most recent measurement and T is a positive real constant. The recurrent algorithm is obtained using the properties of state transition matrix Ф(t₁, t₂) of a linear dynamical system. The developed method makes it possible to bypass the time-consuming procedure of finding state-transition matrix. The process of computing the fixed-lag smoothed estimate is discussed in terms of the algorithm's dependence on the solutions of the filtering and fixed-point smoothing problems. Therefore, the calculation of the estimation of fixed-lag smoothing depends on the value obtained during the filtering process. We give the simulation result of fixed-lag smoothing algorithms for a nonstationary linear system and compared it with the simulation result of filtering algorithms. It is showed that the estimation errors of fixed-lag smoothing are less than the estimation errors of filtering. We also used the fixed-lag smoothing algorithms to improve the localization accuracy of robots in the task of motion control of convoy robots. A node named fix_lag_smoothing is written using C++ in ROS

оценки сглаживания, постоянное запаздывание, непрерывная линейная система, управление движением строя типа "конвой", smoothed estimate, fixed-lag smoothing, continuous linear system, motion control of convoy robots

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6. URL: https://www.dropbox.com/sh/irekgv6ch2fhj0s/ AADkiUXSpvoBv6sJJ4Zk3C-Ha?dl=0