Three-Dimensional Nonlinear Differential Geometric Path-Following Guidance Law

A three-dimensional nonlinear guidance law for path-following is proposed using differential geometry of space curves. The proposed guidance law makes a vehicle converge to and then follow a given desired path of general shape, which does not require strict restrictions on initial position and velocity. To take the advantages of the look-ahead effect for precise and robust path-following, the proposed guidance law takes the form of pure pursuit guidance, which is designed to align the velocity of the vehicle with the look-ahead vector. The look-ahead angle and the radially shifted distance are designed using differential geometry of the desired path. The proposed guidance law generates the normal acceleration command required for exact path-following and finally overcomes the limitations of previously developed look-ahead point-based methods in the case of general three-dimensional path-following. Stability analysis on the guidance law to follow constant-curvature planar paths is performed. The performance of the proposed guidance law is demonstrated by numerical simulations for various types of desired paths.