On Optimal Fuel Trajectory Of Asteroid Probe For Soft Landing Based On Homotopic Method

Since the U.S.-Soviet space race in the 20th century,deep-space exploration has always been a representative of the powerful aerospace power of all countries in the world.At the same time,the exploration field has been more and more extensive and the detection methods are more and more.Among them,asteroid exploration is a new research hotspot in the world.The exploration of asteroids will not only help to study the mechanism of asteroid orbital evolution,prevent asteroids from hitting the earth,but also help to reveal the formation of the solar system and the origin of life on earth.Therefore,this thesis focuses on the soft landing problem,using fuel consumption as the performance index to optimize the probe’s soft landing trajectory.First,due to the irregular shape of the asteroid,the distribution of its gravitational field is uneven.Concerning the characteristics of the asteroid Bacchus2063,a combined model is constructed to simulate the gravitational field of the asteroid Bacchus2063 based on the advantages of the ellipsoidal harmonic function model and the polyhedral model.Second,for the optimization of the asteroid probe trajectory,the traditional indirect method need to treat a non-smooth optimization problem when solving the optimization performance index with fuel consumption.This paper introduces the homotopy method to construct a decreasing homotopy parameter sequence.When the homotopy parameter is gradually approaching zero,the solution of the energy optimal control problem is close to the solution of the fuel optimal control problem,which is effectively solving the problem of non-smooth optimization,thereby weakening the sensitivity of the initial value guessing for some unknown variables.Finally,according to the gravitational field model of the asteroid Bacchus2063 and the trajectory optimization method established in the thesis,a simulation example is carried out for the asteroid Bacchus2063.The soft landing of the probe is divided into two stages: the "dynamic descent phase" and the "final landing phase".The gravitational field in the dynamic descent phase adopts the ellipsoidal harmonic function model,and the gravitational field in the final landing phase adopts the polyhedral model.The landing trajectory optimization in these two phases is solved based on the homotopy method.The simulation results show that the probe can satisfy the respective predetermined landing conditions well,so that the probe will finally land smoothly to the designed landing site on the surface of the asteroid Bacchus2063.Therefore,the homotopy method has certain feasibility and effectiveness in solving the optimal fuel control problem.In addition,the time optimal control problem is designed as a comparative example,and the simulation results are compared and analyzed.The time optimal control problem pursues "efficiency",the probe engine thrust has always been at full thrust,and the fuel optimal control problem pursues "saving",the probe engine switches back and forth between firing and turning off to save fuel.The best fuel consumption is at the cost of time,and the best time consumption is at the cost of fuel.