## 4.6 Trajectory Equations

There are three trajectory modes currently available on Ranger
NBV. These are selectable using the interface described in Section
3.3.1. The open loop with latch mode simply latches the estimated
quaternion as the desired quaternion when the rotational hand
controller is returned to the neutral position. The last two
trajectory modes (resolved rate and spacecraft dynamics) propagate
the desired attitude forward as a function of rotational hand
controller values and current vehicle state.

The resolved rate trajectory mode uses the rotational hand controller
values to specify the desired angular velocity of the desired
attitude. The first derivative of the desired angular velocity is
calculated and passed to the controller. Additionally, the desired
angular velocity is used to propagate the current desired attitude
forward for the duration of the next time step by using a 4th order
Runge-Kutta integration on (4.9). This is shown in Figure 4-8.

Figure 4-8 Resolved rate trajectory mode

The spacecraft dynamics trajectory mode is shown in block diagram
in Figure 4-9. The rotational hand controller specifies the desired
moment to be applied to a simulated spacecraft. The rotational
dynamics (4.1) and the quaternion kinematics (4.9) equations are
integrated (4th order Runge-Kutta), and the output passed to the
controller as the desired trajectory.

Figure 4-9 Spacecraft dynamics trajectory mode