It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry theory, rather than directly decomposing the motion in the Cartesian coordinates. The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper, based on the classical differential geometry curve theory. Firstly, the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS, the kinematic equations of LOS are established, and the concepts of curvature and torsion of LOS are proposed. Simultaneously, the new relative dynamic equations between interceptor and target are constructed. Secondly, it is found that there is an instantaneous rotation plane of LOS (IRPL) in the space, in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems. The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN. In addition, the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL. After that, the differential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced, and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC. Moreover, the performance of the original guidance laws will be reduced after the differential geometric transformation. At last, an exoatmospheric interception is taken for simulation to demonstrate the differential geometric modeling proposed in this paper. kinematic equations of LOS, instantaneous rotation plane of LOS, proportional navigation, augmented true proportional navigation, LOS angular acceleration guidance law, differential geometric guidance commands Citation:
Abstract:Measuring the success of sustainable urban development has been difficult in the past. However, as this has become more important in the past few years, this paper develops an innovative sustainable urban development capacity measurement model based on principal component analysis (PCA) and Grey TOPSIS methodology, which has a significantly more comprehensive measurement, and reduces processing time and calculation difficulty. First, PCA is used to extract the main components that affect a city's sustainable development capacity. Then, the actual sustainable development capacity level is measured using Grey TOPSIS, from which the sustainable development capacity measurement value is then calculated. To prove the model's effectiveness and operability, it is then applied to measure the sustainable development capacity in 13 cities in Jiangsu province, China.
This paper describes a novel trajectory planning algorithm for an unmanned aerial vehicle (UAV) under the constraints of system positioning accuracy. Due to the limitation of the system structure, a UAV cannot accurately locate itself. Once the positioning error accumulates to a certain degree, the mission may fail. This method focuses on correcting the error during the flight process of a UAV. The improved genetic algorithm (GA) and A* algorithm are used in trajectory planning to ensure the UAV has the shortest trajectory length from the starting point to the ending point under multiple constraints and the least number of error corrections.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.