Three-Dimensional Nonlinear Differential Geometric Path-Following Guidance Law
Namhoon Cho(Agency for Defense Development, Daejeon)

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AIAA Journal


Volume 38, Number 12December 2015



■ Researchers

Namhoon Cho∗

Agency for Defense Development, Daejeon 34186, Republic of Korea

Youdan Kim†

Seoul National University, Seoul 08826, Republic of Korea

Sanghyuk Park

Department of Aerospace and Mechanical Engineering, Korea Aerospace University


■ Abstract

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.



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