The controllers in the last section calculate a vector indicating
the desired moment to be applied to the Ranger NBV in order to cause
it to track the specified trajectory. The vehicle must use its
thruster system to apply an approximation of the desired torque to
the vehicle.
The jet select logic algorithm first sums the contribution of the
individual components of the force and moment vectors to each of the
thrusters. Desired forces are x, y, and z, and desired moments in
roll pitch and yaw are _{ },
_{ },
and _{ }.

_{} 
(4.55) 
Moment commands that request a thruster to spin forward are scaled by a thruster scale factor. The forward thrust requests related to roll, pitch or yaw are scaled back so that the thrust on opposing sides of the vehicle are symmetric, producing pure moments without undesired translation.

_{} 
(4.56) 
This is due to the fact that the thrusters generate more thrust in the forward direction than in the reverse direction for a given angular velocity. This is caused by the fact that the propellers are optimized to run in the forward direction (Section 2.3.1.2). For the thrusters currently used by Ranger NBV,_{ } has been empirically determined to be 0.69. Equations (4.55) and (4.56) form the initial thruster velocity vector T'. Unfortunately, the thrusters are limited in overall force capability. If any of the thrusters are being requested to run faster than the speed that has been determined to produce maximum torque (Section 2.3.1.2), then the output of all of the thrusters are scaled back by a factor equal to the fastest desired speed. The thruster speeds used in this algorithm are normalized so that ±1 indicates maximum forward and reverse output.

_{} 
(4.57) 
Although scaling all of the thrusters back so that none are requested
to spin faster than maximum speed reduces the magnitude of the
commanded moment, it preserves the desired axis of the commanded
moment.
Figure 47 shows the location of the thrusters associated with each
of the elements of the thrust vector T.
Figure 47 Location of thrusters with respect to elements of the thrust vector