Three-Dimensional Nonlinear Path-Following Guidance Law Based on Differential Geometry

Abstract A new three-dimensional nonlinear path-following guidance law is proposed using differential geometry. The guidance law is designed based on the look-ahead angle and the radially shifted distance which gives an additional degree of freedom to generate acceleration command for precise path-following. A modified Frenet-Serret frame is utilized to describe the desired path, and the closest projection point is taken as a reference point on the desired path. To implement the guidance law for the vehicle in a flow-field, a command modifying logic is proposed to generate the sideways command which is orthogonal to the flow-relative velocity. Numerical simulations are performed to verify the performance of the proposed guidance law.