Journal of Astronautics ›› 2014, Vol. 35 ›› Issue (11): 1254-1261.doi: 10.3873/j.issn.1000-1328.2014.11.005

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3D Trajectory Rational Bezier Curve Based Shaping and Optimization Technique

ZHANG Song , HOU Ming shan,DU Ting   

  1. School of Automation, Northwestern Polytechnical University, Xi’an 710072,China
  • Received:2013-08-05 Revised:2013-10-16 Online:2014-11-15 Published:2014-11-25


The convergence and optimality of ordinary trajectory optimization method is influenced by many factors such as initial guess and search algorithm, and so on. In view of this, a novel spatial trajectory shaping and optimization strategy based on the rational Bezier curves is proposed. According to boundary conditions, the unknown spatial trajectory is shaped by using the rational Bezier curves with few shaping variables. And the flight-path angle, the heading angle as well as their rate, the normal acceleration and the performance index are determined by the inverse dynamics technique and dynamics equations of the missile. Consequently, the optimal spatial trajectory can be obtained through optimizing the shaping variables. Finally, the original continuous optimization problem is translated into a simple parameter optimization one in the proposed method, and the resulting optimal trajectory is perfectly smooth and flyable. Compared with the indirect method, the solving for two-point boundary value problem is avoided in this method, thus the accessibility and robustness are guaranteed. In contrast with the direct method, no discretization on the states and controls is involved and few optimizing variables are introduced in this method, thus the solution can be easy to converge to the perfectly smooth and global optimal one. Both validity and practicality of the proposed method are demonstrated by comparison simulation.

Key words: Trajectory optimization, Trajectory shaping, Rational Bezier trajectory, Minimum-time trajectory

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