Polynomial Shaping Guidance Law for Impact Time Control

In this paper, the impact time control problem has been investigated by applying the polynomial shaping method. By modifying the kinematics between the maneuvering target and interceptor into relative engagement kinematics, this paper provides a method to deal with the impact time control problem against a maneuvering target. Shaping the relative range with remained intercept time, a guidance law called relative range polynomial impact time control guidance (RPITCG) law is proposed. The coefficients of the polynomial terms are determined by the boundary conditions. Then the relative acceleration is given in form of proportional navigation (PN) with a time varying navigation gain. Another guidance law called remained intercept time polynomial impact time control guidance (TPITCG) law is proposed by shaping the remained intercept time with relative range. The characteristics of the proposed guidance law have been analyzed. Nonlinear simulations are performed to validate the efficiency of the proposed guidance laws in various engagement conditions. Comparison with other studies demonstrates the practicality and flexibility of the proposed guidance laws in the design of desired impact times.