Enhancement of Quadrotor Positioning Using EKF-SLAM

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1 , pp Enhancement of Quadrotor Positioning Using EKF-SLAM Jae-young Hwang 1,1 and Young-wan Cho 1 1 Dept. of Computer Engineering, Seokyeong University 124, Seo-kyeong-Ro, Seong-buk-Gu, Seoul, , Korea canss2@naver.com, ywcho@skuniv.ac.kr Abstract. In this paper, a method for estimating the location of a quadcopter is proposed by applying EKF-SLAM algorithm to its flight control, to autonomously control the flight of an unmanned quadcopter. The usefulness of this method is validated through simulations. For autonomously flying the unmanned quadcopter, an algorithm is required to estimate its accurate location, and various approaches exist for this. Among them, SLAM, which has seldom been applied to the quadcopter flight control, was applied in this study to simulate a system that estimates flight trajectories of the quadcopter. Keywords: Kalman Filter, Extended Kalman Filter, SLAM, EKF-SLAM, Quadcopter dynamics. 1 Introduction Recently, markets relating to service robots, extremely dangerous environment robots for safety, and medical robots have maintained their growth rate. Especially studies on unmanned aerial vehicles have got to be carried out actively and the necessity of application has been strongly on the rise. Under these circumstances, in the work requiring autonomous motion, quadcopters lifted and propelled by 4 rotors are attracting much attention and many studies on them are being carried out due to flight stability and relative ease of control. [1] A method of estimating a position by merging GPS and inertial navigation sensor information [2][3] is mainly used for the self-localization of unmanned aerial vehicles including quadcopters. However, this approach cannot avoid GPS noise and the cumulative error of inertial sensor information. This paper suggests a method using SLAM (Simultaneous Localization And Mapp) as technology for estimating the position of quadcopter. SLAM is an algorithm by which, in order that a robot carries out location-based work in the specific environment, the robot simultaneously constructs a map and estimates the position of robot within the constructed map.[4] In this paper, for the self-localization and autonomous flight of quadcopter, a motion and observation model for applying 1 Young-wan Cho: Department of Computer Engineering, SEOKYEONG UNIVERSITY ISSN: ASTL Copyright 2015 SERSC

2 SLAM to a quadcopter on the basis of a dynamic model of a quadcopter was suggested and its performance was identified through simulation. 2 Quadcopter Model 2.1 Equations of Motion The equation of motion in the body frame is as follows. [ ] (1) [ ] 3 EKF-SLAM 3.1 Quadcopter EKF-SLAM EKF-SLAM is carried out by repeating prediction process and estimation process shown in Fig. 1. Taking a look at the upper part, it is a part for predicting the position of landmark and the present state of a quadcopter by using the input of a quadcopter and previous state information. After that, Euler angles get to be calculated by using all body acceleration information in the state information. In the estimation process, first of all, a branch occurs according to whether information about relative position of landmark is obtained through the observation model. In case there is no observation information, it returns to the observation process again. In case there is observation information, a Jacobian matrix is first calculated, and then Kalman gain is calculated. And, present observation information and state vector calculated in the prediction process are merged by using the Kalman gain, and then, finally, present state information, that is to say, information about the position of landmark and the position of a quadcopter gets to be estimated. 4 Simulation In order to evaluate the performance of SLAM, it is necessary to compare information about the flight trajectory of dynamic model of a quadcopter with the quadcopter flight Copyright 2015 SERSC 57

3 Fig. 1. Block diagram of EKF-SLAM trajectory estimated through SLAM. Simply, there cannot be difference between the flight trajectory of dynamic model of a quadcopter and the flight trajectory estimated through SLAM. Accordingly, Gaussian noise is added to the observation information and the location information of a quadcopter respectively. And, simulation is evaluated by comparing the flight trajectory of a quadcopter with the flight trajectory of SLAM. 4.1 Straight Flight Simulation In the straight flight simulation, landmarks are arranged as follows. 4 landmarks are arranged in the 3D space as shown in Fig. 2, and then a quadcopter is caused to make a straight flight. The quadcopter flies straight, observes 4 landmarks in sequence, and obtains information about distance from a near landmark and information about direction relative to the attitude of the quadcopter. The quadcopter flies along an elliptical path of which the size depends on the magnitude of error covariance around the observed landmark. Fig. 2. Straight flight Simulation 58 Copyright 2015 SERSC

4 Fig. 3 shows the sum of error covariance matrixes of landmark position and the sum of error covariance matrixes of quadcopter position. As a whole, a decreasing pattern is shown and it is possible to identify that the performance of Kalman filter doesn t diverge. The error covariance matrix of a quadcopter also has a pattern where the error covariance decreases on the whole, as the number of observed landmarks increases. Fig. 3. Straight Flight landmark position error covariance (left) Quadcopter position error covariance(right) 5 Conclusion This paper introduced EKF-SLAM for estimating the position of a quadcopter and designed simulation for that. Accurate localization within the sphere of action of robot is required for the autonomous flight of mobile robot, and a field of study that best suits the purpose is SLAM. SLAM is being applied to various fields in various types. In addition, it is a field that is being still actively studied. However, in Korea, there were rare cases of being applied to quadcopters yet. Thus, in order to apply this, a simplified dynamic model of qaudcopter was used. Finally, the motion model of EKF-SLAM was determined by using an equation of state of modeled quadcopter, and a virtual sensor enabling direction information and distance information to be obtained was modeled, and then SLAM technology was applied to a quadcopter, and its simulation was carried out. References 1. M. G. Kim and Y. D. Kim, Multiple UAVs nonlinear guidance laws for stationary target observation with waypoint incidence angle constraint, Int l J. of Aeronautical & Space Sci, vol. 14, no. 1, pp , Z. Yan, S. Peng, J. Zhou, and H. Jia, Research on an improved dead reckoning for AUV navigation, Proc. of Control and Decision Conference (CCDC), pp , H. Zhang, J. Rong, X. Zhong, H. Yang, L. Xiao, and L. Zhang, The application and design of EKF smoother based on GPS/DR integration for land vehicle navigation, Computational Intelligence and Industrial Applicaion, vol. 1, pp , Copyright 2015 SERSC 59

5 4. Song, Jae-Bok, and Seo-Yeon Hwang. "Past and State-of-the-Art SLAM Technologies." (2014). Journal of Institute of Control, Robotics and Systems (in Korean) 20(3), , (8 pages). 5. GIBIANSKY, Andrew. Quadcopter Dynamics, Simulation, and Control Copyright 2015 SERSC