Nonlinear homotopy interior-point algorithm for 6-DoF powered landing guidance

Abstract

The six-degree-of-freedom (6-DoF) powered landing guidance problem usually is difficult to solve for several reasons. First, this problem coupled with low-frequency translational and high-frequency rotational equations of motion is naturally large-scale. Second, the constraints enforced into the problem are highly coupled, nonlinear and non-convex, which makes the problem quite sensitive to the initial value guesses. Third, the initial position, velocity and attitude of the landing vehicle is quite difficult to forecast due to the complex endo-atmospheric environment, thus the traditional guidance methods are difficult to obtain a predetermined trajectory. In this paper, for the first time we proposed a nonlinear homotopy interior-point optimization algorithm (NHOPT) for solving the 6-DoF powered landing guidance problem. Different from general external homotopy strategies, we embed the concept of homotopy methods into the barrier line-search interior-point method. Using vertical landing without position and velocity offset, it is easy to provide initial guesses, which we define as the initial homotopy subproblem. Then a class of related homotopy subproblems is solved along a homotopy path using the algorithm until the original problem is converged. Numerical results demonstrate that the algorithm has high performance in terms of convergence and computational efficiency.