A low‐thrust guidance law based on Lyapunov feedback control and hybrid genetic algorithm

Abstract

PurposeThis paper seeks to examine the development of the on‐board guidance law for multi‐revolutions orbit transfer spacecraft with low‐thrust propulsion systems.Design/methodology/approachIn the research, first, a set of equinoctial elements is utilized to avoid the singularities in dynamical equation of classical orbit elements. A thruster switch law is derived by analyzing the efficiency of the changing of each orbit elements. Second, by using the theory of Lyapunov feedback control, analytic expressions of thrust angles are derived. Finally, the weights of the Lyapunov function are adjusted by hybrid genetic algorithm to improve the performance of the guidance law.FindingsFirst, the dynamical equations of classical orbit elements are always singularity during the orbit transfer. By using modified equinoctial elements, these singularities could be avoided. Second, the trajectory is sensitive to the weights in Lyapunov function. With reasonable weights, the key parameters under the control of the guidance law presented in this paper are very close to that of optimal trajectory.Research limitations/implicationsIn further research, some dynamical weights methods will be used in the control law to improve the performance index, and approach the optimal solution.Practical implicationsThe guidance law presented in this paper could be easily used as an on‐board algorithm for the multi‐revolutions orbit transfer or stationkeeping. Furthermore, it could also be utilized as an initial design method for low‐thrust orbit transfer.Originality/valueProviding a low‐thrust guidance law by combining the concept of Lyapunov feedback control with hybrid genetic algorithm. This method has a super convergence and a low‐computational cost.