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Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 7, pp. 458—463
DOI: 10.17587/mau.19.458-463
**One Way to Obtain the Smoothed Estimate of Phase Vector in the Task of Motion Control of Convoy Robots**
**S. L. Zenkevich**, zenkev@bmstu.ru, **Hua Zhu**, zhuhua1302@gmail.com, **Meixin Zhai, **982696853@163.com, Robotics Training-Research Center, Bauman Moscow State Technical University, Moscow, 105005, Russian Federation
Corresponding author: **Zhu Hua, **Ph. D., Robotics Training-Research Center, Bauman Moscow State Technical University, Moscow, 105005, Russian Federation, e-mail: zhuhua1302@gmail.com
Accepted on February 05, 2018
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 Ô(t_{1}, t_{2}) 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.
**Keywords**: smoothed estimate, fixed-lag smoothing, continuous linear system, motion control of convoy robots
For citation:
**Zenkevich S. L., Zhu Hua, Zhai Meixin**. One way to obtain the smoothed estimate of phase vector in the task of motion control of convoy robots,* Mekhatronika, Avtomatizatsia, Upravlenie*, 2018, vol. 19, no. 7, pp. 458—463.
DOI: 10.17587/mau.19.458-463
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