Indirect Trajectory Optimization for Mars Entry with Maximum Terminal Altitude

Abstract

In this paper, a novel computational optimization framework is presented for the design of Mars entry trajectories with maximum terminal altitude. The second-order path constraints included in the framework are the constraints on the dynamic pressure, aerodynamic acceleration, and heat rate. The framework is built on the so-called Pontryagin’s maximum principle, exact penalty method, and simplicial homotopy method. In this framework, the exact penalty method is used to transform the original path-constrained maximum terminal altitude problem into an equivalent path-unconstrained maximum terminal altitude problem. A novel one-parameter penalty function, which is continuous and differentiable at any point, is introduced to penalize the performance index. Then, the resulting path-unconstrained maximum terminal altitude problem is converted to a two-point boundary value problem based on Pontryagin’s maximum principle. Several auxiliary problems are properly constructed such that the simplicial homotopy method can be applied to address the problem of initial guess. By doing so, a ballistic entry trajectory can be taken as an initial guess for the solution of the path-unconstrained maximum terminal altitude problem. Finally, numerical results are presented to demonstrate the effectiveness of the proposed computational optimization framework.