Hi @krakjack, welcome to the forum 
The force directions in any diagram are somewhat arbitrary, as long as they are appropriately accounted for with negations as relevant when determining the resultant forces. In the case of a vehicle like the BlueROV2 Heavy, which uses T200 Thrusters that have non-symmetric thrust, I would personally be inclined to display and model the force directions based on the front direction of each thruster, and abstract away the propeller and control signal specifics (which is effectively what ArduSub does). That is not what seems to have been done in the figure you’ve referred to, and from a quick skim of the thesis it looks like the thrust asymmetries were ignored (see Section 5.3), in which case the specific directions aren’t really important, just their consistent application through any calculations.
Our thrusters use brushless DC motors that can have their rotation direction swapped by either swapping two of the phase wires controlling a thruster, or just reversing the PWM signal sent to it (which our ArduSub autopilot firmware has a parameter per thruster to do), so the effect of “positive input” to a thruster depends on its wiring and software configuration.
That said, physically speaking the installed propeller orientation/type in a thruster determines which way the water flows through it when the propeller turns in a given direction. The propellers are set to counter rotate (see Figure 3.4), which keeps vehicle torques balanced.
By inspection, it seems like Figure 4.2 in the thesis mostly uses an approach where
- negative signal (1100-1500 PWM) → counter-clockwise propeller rotation, and
- positive signal (1500-1900 PWM) → clockwise propeller rotation
except that thrusters 3 and 4 have their assigned forces the opposite way around to that convention. I’m not sure why that would be the case, and the choice may have been completely arbitrary (i.e. the mostly consistent rotation directions could be a coincidence). Equation (4.61) follows the force arrows shown on their diagram, so it seems that part of the thesis is at least self-consistent.
I haven’t read or analysed the thesis and its results in any particular depth, but there doesn’t seem to be an obvious issue with that part of the model, although it may need to be accounted for later. If it’s not then perhaps you can try negating thrusters 3 and 4 to see if that aids stability, and if it doesn’t you can try instead negating thrusters 1, 2, 3, 4, 5, and 8 such that positive input corresponds to each thruster’s individual forward direction.