Abstract
In this paper, the propagation of uncertainty in a cooperative navigation algorithm (CNA) for a group of flying robots (FRs) is investigated. Each FR is equipped with an inertial measurement unit (IMU) and range-bearing sensors to measure the relative distance and bearing angles between the agents. In this regard, an extended Kalman filter (EKF) is implemented to estimate the position and rotation angles of all the agents. For further studies, a relaxed analytical performance index through a closed-form solution is derived. Moreover, the effects of the sensors noise covariance and the number of FRs on the growth rate of the position error covariance is investigated. Analytically, it is shown that the covariance of position error in the vehicles equipped with the IMU is proportional to the cube of time. However, the growth rate of the navigation error is, considerably more rapid compared to a mobile robot group. Furthermore, the covariance of position error is independent of the path and noise resulting from the relative position measurements. Further, it merely depends on both the size of the group and noise characteristics of the accelerometers. Lastly, the analytical results are validated through comprehensive Guidance, Navigation, and Control (GNC) in-the-loop simulations.
Highlights
In recent years, autonomous robots have achieved significant impacts on business, industry and people’s social and private affairs as well
The percentage of error covariance difference in both accelerated and non-accelerated trajectory is defined as a criterion, which can be calculated through the following relation:
Based on the presented results, it is concluded that the growth of the covariance ellipse of position error in the vehicles equipped with the inertial measurement unit (IMU) does not depend on the path
Summary
Autonomous robots have achieved significant impacts on business, industry and people’s social and private affairs as well. Later, Roumeliotis and Bekey (2000) presented a new method called “Collective Localization” based on which the localization problem in a group of mobile robots (MR) is solved in a distributed configuration and without any external source like GNSS or map data. At the same time, Chakraborty et al (2016) presented a centralized cooperative localization for a group of fixedwing UAVs, based on relative measurements between the agents and some landmarks with a known position, in a GNSS denied condition. One of the contributions of this work is that in this research a closed-form solution is derived as a function of time to predict the covariance of the position error due to the CN which is applied in a group of FRs. the validation process is conducted via numerical GNC in-the-loop simulations. The conclusions and future work are presented in the last section
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