Generalization of Linearly Parametrized Trajectory Shaping Guidance Laws

Abstract A class of trajectory shaping guidance laws is extended, unified, and generalized. Various existing guidance laws based on linear or linearized formulation, in which desired terminal conditions are considered as fixed terminal output constraints, usually have linear-in-parameter structure. From this observation, the supposition made in this study is that a guidance law can be designed by representing the command as a product of a basis function vector and a constant coefficient vector. The design can be diversified by the ways of formulation and the choices of basis function vector. Flexibility of tuning is introduced into the proposed design framework through the tuning of basis function vector. After formulating a linear system equation and selecting an appropriate basis function vector, the constant coefficient vector can be determined to satisfy the terminal constraints by considering them as the boundary conditions. Various existing guidance laws can be unified in the proposed framework, and the design can be extended to a more general form. New guidance laws can be designed using the proposed framework by taking different way of formulation or basis function vector.