Research On Aircraft Formation Control Technology Using Legendre Pseudospectral Method

Aimed at the actual situation of limited fuel which the satellite carried,an effective method was proposed to formulate and solve a fuel-optimal satellites maneuver control problem using a continuous low-thrust system.How to design a passive and periodic formations under the dominant perturbation is the primary problem of long-term satellite formation flying.In this view,the design of the desired final satellite formation is a passive and periodic circular-like formation at critical inclination under J2 perturbation,which ensures practically possible long-term flying formation.The final orbit condition constraints are formulated as six implicit equations and the final injection time is unknown,so final time of the formulated fuel-optimal control problem is free.In order to avoid complexities and difficulties in calculate,on the nonlinear optimal control problem is converted into a nonlinear programming problem by using the Legendre pseudospectral method.The design includes the precise final condition constraint and uses a continuous low-thrust,thereby the optimal control law will achieve the minimum fuel consumption.In this paper,specific work is as follows:At first,dynamic equations of satellite relative motion are derived based on some assumptions.Then this paper analyzes and gives the initial conditions,the path constraint and terminal constraints.At last,an optimal control problem is formulated based on scaling dynamic equations.Second,this paper introduces several satellite trajectory optimization theory and methods.By analyzing and comparing,we select Legendre pseudospectral method to solve the problem of fuel optimal maneuver.The principles of Legendre pseudospectral method and how to solve an optimal control problem are described in detail.Finally,using Legendre pseudospectral method transforms the continuous-time optimal control problem to an algebraic nonlinear programming problem.Then the problem is solved sparse nonlinear optimization software named TOMLAB.Simulation results demonstrate the effectiveness of proposed method.