Abstract: This article proposes a non-decoupling three dimensional (3D) robust guidance law by combining the advantages of the differential geometry control and Lie-group control methods. First, a differential geometrical description equation is obtained based on differential geometry theory without the need to estimate the parameter of available time-to-go. Then, the relation between azimuth angle and its change rate is established through spinor description. Finally, corresponding to no ending constraints and ending constraints, guidance laws are designed respectively by using the Lyapunov stability theory, which can satisfy the restriction of ending constraints with no requirement for the estimation of time-to-go. Simulation results demonstrate that the proposed guidance law can be applied to the guidance of high-speed maneuvering bank-to-turn (BTT) missiles.

Key words: missiles, 3D guidance law, differential geometry control, Lie-group control, bank-to-turn