Direct Methods for Optimal Ascent Guidance

Abstract

An ascent guidance algorithm determines the thrust vector that allows the spacecraft to reach the desired orbit. Generally, optimal ascent guidance algorithms try to reach the orbit while minimizing mission time or fuel. A renewed interest in new-generation space missions necessitates the development of optimal ascent guidance algorithms that are efficient in time and control and can accommodate ever-changing mission constraints. These guidance algorithms will pave the way for future autonomous space exploration. The first part of this thesis develops an ascent guidance algorithm that guides a spacecraft from a known initial position to an orbit of known apogee and perigee in minimum time. The algorithm follows an iterative approach that reduces the terminal error over successive iterations while keeping the control inputs within bounds. Every iteration consists of a model-predicting phase in which the initial conditions and system dynamics are used to calculate the error at the end of guidance. It is followed by an optimization phase that helps us to minimize time and accommodate path constraints. Numerical simulations are carried out using a point mass model of a spacecraft. The initial guess for control that is required for simulations is generated using an existing polynomial guidance method. Next, we study the algorithm's behavior for different guess inputs of the thrust and the final time. Further analysis is carried out by varying the learning parameter and initial position of the spacecraft. Finally, we do a comparative study of the algorithm with commercially available optimal control solvers. Simulation results show faster convergence of the proposed minimum-time algorithm compared to other optimal control software. Another essential and desirable characteristic of a guidance algorithm is lower control effort spent in achieving the mission objective. In the second part of this thesis, we augment the cost function of the algorithm with a weighted running cost on the control effort. The weights of the running cost allow us to tune the algorithm to achieve a balance between the mission time and the control effort invested in guidance. Numerical simulations are carried out to analyze algorithm behavior for different initial conditions and by steadily increasing the weight of the running cost. As the main result, we observe that the control effort can be reduced signi ficantly with a correspondingly small trade-off in mission time.