Constrained Trajectory Optimization for Planetary Entry via Sequential Convex Programming

In this paper, the highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution. The nonconvex control constraint is avoided by introducing a new state variable to the original three-dimensional equations of motion. The nonconve...

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Bibliographic Details
Published in:Journal of guidance, control, and dynamics control, and dynamics, 2017-10, Vol.40 (10), p.2603-2615
Main Authors: Wang, Zhenbo, Grant, Michael J
Format: Article
Language:English
Subjects:
Aeronautics
Algorithms
Approximation
Atmospheric flight
Computational geometry
Constraints
Convergence
Convex analysis
Convexity
Equations of motion
Flight mechanics
Iterative methods
Linear programming
Mathematical programming
Microprocessors
Nonlinear control
Nonlinear dynamics
Nonlinear programming
Optimal control
Optimization
Personal computers
Real time
Series expansion
Solvers
State variable
Three dimensional motion
Trajectory optimization
Velocity
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Summary:In this paper, the highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution. The nonconvex control constraint is avoided by introducing a new state variable to the original three-dimensional equations of motion. The nonconvex objective function and path constraints are convexified by first-order Taylor-series expansions, and the nonconvex terms in the dynamics are approximated by successive linearizations. A successive solution procedure is developed to find an approximated solution to the original problem, and its convergence is discussed. In each iteration, a convex optimization problem is solved by the state-of-the-art interior-point method with deterministic convergence properties. Finally, the proposed method is verified and compared to a general-purpose optimal control solver by numerical solutions of minimum terminal-velocity and minimum heat-load entry problems. The sequential method converges to accurate solutions with faster speed than the general-purpose solver using MATLAB on a desktop computer with a 64-bit operating system and an Intel Xeon E3-1225 V2 3.2 GHz processor, which demonstrates its potential real-time application for computational guidance. Presented as Paper 2016-3241 at the AIAA Atmospheric Flight Mechanics Conference, Washington, D.C., 13-17 June 2016.
ISSN:0731-5090
1533-3884
DOI:10.2514/1.G002150