New three-dimensional guidance law for BTT missiles based on differential geometry and Lie-group

A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn (BTT) missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on BTT missiles' motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight (LOS) azimuth when the terminal angular constraints are considered. Under these circumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are respectively designed by using proportional control and generalized proportional-derivative (PD) control in SO(3) group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.