Vehicle control for fuel optimization

The problem of predicting the minimum fuel trajectory for a six degree of freedom vehicle which has a motion characterized by the first order differential equations of translational and rotational dynamics is considered. The thrust direction and center of gravity of the vehicle are assumed to be fixed with respect to the vehicle. Thrust magnitude and the control moment are used as control variables and appear linearly in the equation of motion. Pontryagin's Maximum Principle is used to solve the variational problem. With this formulation, the extremal controls are bang-bang with the exception of the singular case.