Reentry trajectory optimization using direct collocation method and nonlinear programming

Paper number

IAC-06-C1.4.06

Author

Dr. Lianghui Tu, Northwestern Polytechnical University, China

Coauthor

Prof. Jianping Yuan, Northwestern Polytechnical University, China

Year

2006

Abstract

Direct collocation method has been widely used for trajectory optimization. In this paper, the application of direct optimization method (direct collocation method \& nonlinear programming (NLP)) to reusable launch vehicle (RLV) three-dimension trajectory optimization is introduced. 
  Firstly, the model of trajectory optimization control problem to RLV reentry trajectory is established and appropriate environmental models were chosen and implemented, where the motion equation is a three degree-of-freedom model. Mass, density and reentry angle are also considered. Performance is selected to minimize the sum of heat, overload and dynamic pressure. The control variables are attack angle and bank angle. During the flight, reentry vehicle is subjected to the heating rate, overload and dynamic pressure constraints. Terminal state variables constraints are path angle, altitude and latitude constraints. Then, the optimal control problem is discredited into nonlinear programming problem using direct collocation method. The state variables and control variables are selected as optimal parameters at all nodes and collocation nodes. Parameter optimization problem is solved using the SNOPT software package. The major advantage of SNOPT software package is an integration method with step-size control, which makes the algorithm almost independent from the discretization grids. Once converged, the solution is always optimal due to the control discretization. The SNOPT software package was tested using data for RLV. 
  A numerical example is presented to demonstrate the effectiveness of this method. The results of optimal trajectory shows that all the state variables meet state constraints very well and the control variables satisfy the control inequality constraints. The simulation result demonstrates that the direct collocation method using as few as twenty nodes in flight could meet the trajectory optimization requirements. The direct collocation method is not sensitivity on reentry initial conditions. And it also shows that the optimal solutions of trajectory optimization problem are in real-time. Using the direct collocation method can improve the radius of convergence of traditional methods. Therefore, the direct collocation method is a viable approach to RLV reentry trajectory optimization problem.

Abstract document

IAC-06-C1.4.06.pdf

Manuscript document

IAC-06-C1.4.06.pdf (🔒 authorized access only).

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