Continuous Low-thrust Trajectory Design Method Based On Bezier Curve

With the development of deep space detection technology,people hope that the detection range of spacecraft will be farther and the detection task will be more complicated.The continuous small thrust propulsion of spacecraft with small thrust and high specific impulse has become a popular research topic.The initial orbit design based on the shape method is used as the basis for orbit optimization.The quality of the initial orbit estimation has a great influence on the subsequent orbit optimization.Using reasonable and accurate methods and strategies to initially estimate the orbit of the spacecraft transfer is One of the hot spots of continuous thrust spacecraft orbit research.The Bezier curve has the characteristics of simple shape control and infinite continuous curve.In this paper,the Bezier curve is applied to the initial design of the continuous thrust spacecraft orbit.A continuous thrust maneuver orbit design method based on the Bezier curve is proposed.The main work of the paper is as follows:First,this paper introduces the time system and reference coordinate system required in orbit research,and based on the ideal two-body model ignoring the perturbation effect,the orbit of the continuous thrust spacecraft in the two-dimensional polar coordinate system and the three-dimensional cylindrical coordinate system is derived in detail The kinetic equation is the theoretical basis of the subsequent research in this article.Then,in this paper,Bezier curve is applied to the two-dimensional plane maneuver orbit,the polar axis and polar angle describing the spacecraft motion are developed under the Bezier curve,and the solution of the orbit parameter problem is converted to the solution of the Bezier curve function position parameter problem.For the optimal time and fuel optimization indexes,the track design process based on Bezier curves is given.And compared with the optimized orbit obtained by using Gaussian pseudo-spectral method for optimization,the ability of Bezier curve in the design of two-dimensional plane maneuvering orbit is evaluated.Afterwards,for the current research and application of solar sail spacecraft and electric propulsion spacecraft,the two maneuver orbit design problems based on Bezier curves were studied respectively.The initial design results obtained by the Bezier curve method are compared with the optimization results to evaluate the track design performance of the Bezier curve under the complex thrust model.Finally,this paper applies the Bezier curve to the design of the 3D maneuvering orbit.Taking the transfer orbit of the "Earth-Asteroid 3671" with a large orbit inclination as an example,the performance of the Bezier curve in the 3D orbit design is studied.Based on the initial track design results based on Bezier curves,Gaussian pseudospectral method was used to obtain the optimized track,and the initial design results were evaluated.The results show that the continuous thrust maneuvering orbit design method based on Bezier curve can realize the maneuvering orbit design in two-dimensional plane and three-dimensional space,and can also achieve reasonable orbit design for the electric propulsion of complex thrust models and solar sails.By comparing with the optimized track,it can be considered that the Bezier curve method can obtain accurate and effective results in a short time.