Document Type : Original Article


Mechanical Engineering; Ghilan University


In this paper, a new method for optimal guidance in the atmospheric return phase is proposed. This guidance method is based on instantaneous and online trajectory optimization in which optimal guidance commands are obtained from sequential solving of optimal control problems. In order to solve optimal control problems quickly and online, a combined approach including the concepts of differential flatness, B-spline curves, direct collocation, and non-linear programming is used. By performing the trajectory optimization process in the form of closed-loop control and implementing the receding horizon control, the open-loop responses of optimal control can be dependent on the instantaneous conditions of the object and the target. In this case, guidance commands can be generated based on various objective functions and constraints, and model uncertainties can be considered by entering the vehicle conditions into the trajectory optimizer. In order to show the capabilities of the proposed guidance method, a numerical example of the guidance of a reentry vehicle in the presence of model uncertainties is presented.


[1]    Shneydor N. A., Missile Guidance and Pursuit: Kinematics, Dynamics, and Control, Horwood Publishing, Chichester, England, 1998.
[2]    Palumbo N. F., Blauwkamp R. A., and Lloyd J., “Modern Homing Missile Guidance Theory and Techniques”, Johns Hopkins APL Technical Digest, vol. 29, no. 1, pp. 42-59, 2010.
[3]    Contensou P., “Contribution á l’Etude Schematique des Trajectories Semi-Balistique á Grand Portée”, Communication to Association Technique Maritime et Aeronautique, 1965.
[4]    Eisler G. R. and Hull D. G.,0 “Guidance law for hypersonic descent to a point”, Journal of Guidance, Control, and Dynamics, AIAA, vol. 17, no. 4, pp. 649-654, 1994.
[5] R. Esmaelzadeh, “Atmospheric entry near optimal guidance with the use of inverse approach”,  Pd.D. thesis, Amirkabir University of Technology, Tehran, 1386.
[6]    Naghash A., Esmaelzadeh R., Mortazavi M., and Jamilnia R., “Near Optimal Guidance Law for Descent to a Point Using Inverse Problem Approach”, Journal of Aerospace Science and Technology, Elsevier, vol. 12, pp. 241-247, 2008.
[7]    VonStryk O., “Numerical Solution of Optimal Control Problems by Direct Collocation”, International Series of Numerical Mathematics, Birkhauser Verlag, 1993.
[8]    Betts J. T., “Survey of Numerical Methods for Trajectory Optimization”, Journal of Guidance, Control, and Dynamics, AIAA, vol. 21, no. 2, pp. 193-207, 1998.
[9] R. Jamilnia, “Combined online method expansion for trajectory optimization”, Ph.D. thesis, Faculty of aerospace engineering, Amirkabir University of Technology, Tehran, 1390
[10]  Seywald H., “Trajectory Optimization based on Differential Inclusion”, Journal of Guidance, Control, and Dynamics, AIAA, vol. 17, pp. 480-487, 1994.
[11]  Fliess M., Levine J., Martin P., and Rouchon P., “Flatness and Defect of Nonlinear Systems”, International Journal of Control, vol. 61, pp. 1327-1361, 1995.
[12]  De Boor C., A Practical Guide to Splines, Springer, 1978.
[13]  Betts J. T., Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd ed., Society for Industrial and Applied Mathematics, 2010.
[14]  Wächter A., “An Interior Point Algorithm for Large Scale Nonlinear Optimization with Applications in Process Engineering”, Ph.D. dissertation, Carnegie Mellon University, Pennsylvania, 2002.
[15]  Jadbabaie A., “Nonlinear Receding Horizon Control: A Control Lyapunov Function Approach”, Ph.D. dissertation, California Institute of Technology, Pasadena, 2001.
[16] Milam M. B., “Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems”, Ph.D. dissertation, California Institute of Technology, Pasadena, 2003.