Journal of Astronautics ›› 2018, Vol. 39 ›› Issue (8): 847-855.doi: 10.3873/j.issn.1000-1328.2018.08.003

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Mesh Refinement Method for Trajectory Optimization by Analyzing Interpolation Error and Slope Analysis

ZHAO Ji song, SHANG Teng   

  1. 1. College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    2. Beijing Aerospace Automatic Control Institute, Beiiing 100854, China
  • Received:2017-10-11 Revised:2018-04-13 Online:2018-08-15 Published:2018-08-25


An adaptive mesh refinement method for solving the trajectory optimization problem is presented, which consists of the grid point insertion algorithm and the grid point elimination algorithm. The grid point insertion algorithm analyzes the interpolation errors of control variables at each of the grid point, and adds some neighboring grid points if the interpolation errors are large. The grid point elimination algorithm calculates the left and the right slopes of control variables at each of the grid point, and deletes the grid point where both the left and the right slopes are equal to zero. The proposed method is verified by using three typical optimal control problems and compared with several other mesh refinement methods. The numerical results indicate that the proposed method generates significantly smaller mesh size and requires even fewer mesh iterations for a given accuracy when compared with other mesh refinement methods. As a result, the proposed method can solve non-smooth trajectory optimization problems rapidly and accurately.

Key words: Trajectory optimization, Mesh refinement, Adaptive, Interpolation error, Slope

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