Optimal Guidance Law for Impact Angle and Acceleration Constraints with Time-Varying Gains

In this paper, we establish an optimal guidance law for impact angle and acceleration constraints (OGL-IAAC). The optimal guidance law for impact angle (OGL) is widely used due to its energy optimality and analytic solutions. However, acceleration constraints may degrade the performance of the OGL owing to the significant guidance command at the initial and terminal time and hence saturated acceleration values may generate guidance errors. We introduce a new weighting function based on the guidance command closed-form solution of the OGL to address this problem. Then, we derive a new guidance law by using Schwarz's inequality. The proposed guidance law generates time-varying gains to ensure that the guidance command is within the acceleration constraint. Moreover, the gains converge to the same values as those of the OGL when the time-to-go approaches zero. The proposed guidance law is demonstrated by simulations to investigate the performance and effect of varying coefficients of the weighting function.