Differential geometric guidance law design based on fixed-time convergent error dynamics method

A differential geometric guidance law design method with the characteristic of fixed-time convergence is proposed. Firstly, a new control parameter selection mechanism is presented for the recently proposed Fixed-Time convergence Error Dynamics (FxTED) method. The number of control parameters are reduced from four to three, and a more accurate upper-bound of the error settling time is obtained. Secondly, for the guidance law design problem against stationary targets, the FxTED method is extended to the arc-length domain based on the classical differential geometry curve theory, and the differential geometric guidance law design method with the property of fixed-range convergence is proposed. Then, to address the problems of impact-angle-control guidance and flight-range-control guidance, two fixed-range convergence differential geometric guidance laws are designed. Finally, the effectiveness of the proposed method is verified through numerical simulation examples.