Optimal rigid body motions, part 1: Approximate formulation

Optimal rigid-body motions

“…(6)(7)(8), while minimizing the control effort given by Eq. (9). The parameters for this problem are the initial and final conditions of the states /?, q, and r and the final time t f .…”

“…Using a version of Pontryagin's minimum principle, which states that an optimal control (M*, N*) is one that minimizes the Hamiltonian tf over all possible controls (M, N) 9 we derive, quite simply, the extremal control (M *, N*) as…”

“…9. The approximate dynamic model consists of two simple integrators representing the pitch and yaw dynamics and a bilinear isoperimetric constraint representing the roll dynamics.…”