An Ascending Phase Guidance for Space Launch Vehicles Based on Velocities-to-Be-Gained

In this paper, a modified guidance law is presented based on zero-effort errors or velocities-to-be-gained for explicit or implicit implementation. First, a closedloop guidance scheme is introduced for the ascending phase of flight. Second, a first-order nonlinear differential equation of the sensitivity matrix is obtained in terms of gravity gradient, partial derivatives of sensitivity matrices, and velocity-to-be-gained. This differential equation may be solved simultaneously with the implicit guidance equation onboard obtaining the velocity-to-be-gained. Third, an algorithm to calculate the thrust direction is presented in terms of zero-effort errors or velocities-to-be-gained