Abstract:
This research presents a novel guidance method for a lunar landing problem. The method facilitates efficiency and autonomy in a landing. The lunar landing problem is posed as a finite-time, fixed-terminal, optimal control problem. As a key finding of this work, the method of solution that is applied to construct the guidance mechanism employs a new extension of the State-Dependent Riccati Equation (SDRE) technique for constrained nonlinear dynamical systems in finite time. In general, the solution procedure yields a closed-loop control law for a dynamical system with point terminal constraints. Being a closed-loop solution, this SDRE technique calculates corrections for unpredicted external inputs, hardware errors, and other anomalies. In addition, this technique allows all calculations to be performed in real time, without requiring that gains be calculated a priori. This increases the flexibility to make changes to a landing in real time, if required. The new SDRE-based feedback control technique is thoroughly investigated for accuracy, reliability, and computational efficiency. The pointwise linearization of the underlying SDRE methodology causes the new technique to be considered a suboptimal solution. To investigate the efficiency of the solution method, various numerical experiments are performed, and the results are presented. In addition, to validate the methodology, the new technique is compared with two other methods of solution: the Approximating Sequence of Riccati Equations (ASRE) technique and an indirect variational method, which provides the benchmark optimal open-loop solution.
