Analytical missile guidance laws with a time-varying transformation

Abstract

ConclusionsAn approximate method for computing near-optimal, minimumfuel, planar lunar trajectories for low-thrust spacecraft has been developed. Our method approximates the long-duration powered Earth-escape and moon-capture spirals with curve fits from universal low-thrust trajectory solutions and numerically computes the translunar coasting trajectory between the curve-fit boundaries using the restricted three-body problem dynamics. The approximate method requires only four optimization variables, and solutions are readily obtained by using sequential quadratic programming. Nearoptimal solutions for a wide range of initial thrust-to-weight ratios and initial and terminal circular orbit altitudes are obtained both quickly and with little computational load. The performance and orbit transfer characteristics of the near-optimal solutions exhibit a very close match with published optimal lunar trajectory solutions. This method would be a useful preliminary design tool for spacecraft and mission designers.

Analytical solution of missile terminal guidance

“…For a maneuvering target, when the heading 6 T is an arbitrary function of T, we model it as a polynominal in T, and ultimately through the change of independent variable by Eqs. (16) and (19), we have OT as a polynominal in the independent variable z.…”

“…-0) and (ft -OT) are reasonably small. This leads to the linearized system for terminal guidance : r is decoupled and upon integration, we have the linear relation • = 1 -(nl)r (16). For the integration of the other two equations, we change the independent variable from r to r to have the new system d£ dr r1 " ' (n -de_ _ a(n -1) + br dr (n-l)r(nl)r an + 6r a (n -l)r (n -l)r(17) 0 T .…”

Analytical Solution of Missile Terminal Guidance

“…Yuan et al [14]- [15] also presented closed-from solutions of true proportional navigation for both maneuvering and nonmaneuvering targets and solution of generalized proportional navigation. Balakrishnan [16] introduced a class of proportional navigation laws through an approximation of time-to-go and a transformation of state variables.…”