회전익 무인기의 비선형 공간 모델을 사용한 항법 알고리즘

Abstract

This paper presents a Lie group theory based navigation method. The method is applied for dynamic-model-aided navigation of a multiple-rotor aerial vehicle. The method can be used for dead-reckoning of the vehicle when sensors providing absolute location and attitude are missing temporarily. The dynamic model describes the relationship between the rotor speed and the motion of the rotors to the thrust force by the rotors. The combination of thrust force produces linear and rotational motion of the vehicle. Finally, the revolution speed of the rotors are related to the linear velocity and rotational velocity of rhe vehicle by the dynamic model. Especially, the model uses unit quaternions to represent the attitude of the vehicle. The unit quaternions constitute the Lie group called the three-sphere group(). Lie group theory provides sound structure to deal with attitude in the estimation process. The estimation process uses Kalman filter which is derived in the linear spaces on which derivative and integration is valid. Because attitude constructs nonlinear space, the derivative and integration produce the results which violate the constraint on the nonlinear space. By using Lie group theory, it becomes possible to use derivatives and integrals in the nonlinear space. Also, errors and disturbances in attitude or rotation can be described in a consistent manner. These are made possible by the introduction of Lie algebra and the related operations. The operations of exponential map and logarithmic map facilitate differentiation and integration of the variables in . The Lie group theory is used to implement the Kalman filter in . Difference between attitudes are calculated in Lie algebra using the function of logarithm. Increment in attitude is incorporated the attitude using the exponential function. In the Kalman filter, the function of logarithms is used to calculate the measurement residuals. The exponential function is used to predict attitude and to incorporate adjustment value to the predicted attitude at the measurement update stage. The EKF and UKF are implemented using the Lie theory. The performance of the proposed method in verified by experiments. The experiments used a quadrotor unmanned aerial vehicle. The vehicle is equipped with inertial measurement unit. GNSS is also equipped on the vehicle to provide position reference for evaluation of the navigation performance. The result of the experiments show that the navigation performance of the proposed method is better than or comparable to the existing methods. Also the convergence property of the proposed method is better than the previous method. Further research on compatible integration of the Lie theory based approach with the previous method is expected.