Research On Trajectory Optimization And Control For Asteroid Landing

Small bodies are the bodies orbiting the sun,whose mass and volume are much less that planets.Exploring small bodies are of great scientific value and practical significance on understanding the origin and evolution of space and life,avoiding the impact of foreign celestial bodies,exploiting space resources,and verifying new space technologies.The way of small body exploration has developed from flyby,rendezvous to landing and sampling return,to obtain high resolution images and precious soil samples.Therefore,landing technologies on small bodies are paid more and more attention.Guidance of small body landing usually includes trajectory optimization and trajectory tracking control,to realize a landing maneuver with high precision,several factors need to be carefully considered,such as irregular and weak gravitational potential of a small body,gravitational orbit-attitude coupling effect,external perturbation,etc.Based on the demands of project named Research on Dynamics and Control of Sample Collection on the Surface of Weak Gravitational Small Bodies,trajectory optimization and control technologies for asteroid landing are studied in this paper.Specifically,this paper includes the modeling and improvement of gravitational potential of an asteroid,trajectory optimization for asteroid landing considering gravitational orbit-attitude coupling,trajectory tracking for asteroid landing with six degree of freedom,and development of asteroid landing software.Firstly,light mass and irregular shape of an asteroid generates an irregular gravitational potential field,based on the consideration of which,the modeling and improvement of gravitational potential of an asteroid is studied.To describe the relative position between the spacecraft and the asteroid,reference frames are defined.The gravitational potential field are modeled by spherical harmonic and polyhedron method,respectively.Simplify the polyhedral model based on point decimation algorithm,expediting its calculation speed while maintaining its calculation accuracy.Simulation of a specific asteroid is carried out to compare analyze characteristics of the two modeling methods,and the simplifying algorithm of the polyhedral model is verified.Secondly,the existing studies usually model the spacecraft as a point mass,neglecting the influence on spacecraft’s motion cause by gravitational orbit-attitude coupling,which may lead to the declination of landing accuracy.To solve this problem,a trajectory optimization method considering the coupling effect is considered.The spacecraft is modeled as a distributed point-mass model rather than a point mass,the six-degree-of-freedom dynamic model of the spacecraft is established based on the gravitational potential field of the asteroid.The trajectory optimization problem is transformed into a fuel optimal control problem based on the consideration of constraints of the landing mission.To reduce the solving difficulty,the traditional homotopic approach is improved to solve the optimal control problem in two phases.Simulations are carried out to prove the feasibility and advantage of the proposed method.Thirdly,to improve the robustness to the uncertainty of system parameters and external perturbations,a six-degree-of-freedom trajectory tracking algorithm is studied.The six-degree-of-freedom error model is established based on the dynamic model.The control law is design by combining nonsingular terminal sliding mode control and partial-derivative control.The rapid and stable tracking of the landing trajectory can be guaranteed.Finally,a simulation software for asteroid landing trajectory optimization and tracking is developed.The software functionalizes the theoretical achievements,which is capable of design an optimal trajectory and tracking it for different asteroid and under different mission constraints.Thus the methods proposed in this paper and the value of the software are proved.