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Predicting Operator Capacity for Supervisory Control of Multiple UAVs  25
                           the revised model is both more conservative and closer to the actual num-
                           ber of vehicles under successful control. While under low workload, both the
                           experiment and prediction indication that operators could have controlled
                           more vehicles than four, the only high workload scenario in which operators
                           demonstrated any spare capacity was with the super-active (management-
                           by-exception) decision support. Moreover, wait time caused by the lack of
                           situation awareness dominated overall wait time. In addition, this research
                           demonstrates that both workload and automated decision support can dra-
                           matically affect wait times and thus, operator capacity.
                              While more pessimistic than the original fan-out equation (1), the revised
                           fan-out equation can really only be helpful for broad “ballpark” predictions
                           of operator capacity. This methodology could provide system engineers with
                           a system feasibility metric for early manning estimations, but what primar-
                           ily limits either version of the fan-out equation is the inability to represent
                           any kind of cost trade space. Theoretically fan-out, revised or otherwise, will
                           predict the maximum number of vehicles an operator can effectively control,
                           but what is effective is often a dynamic constraint. Moreover, the current
                           equations for calculating fan-out do not take into account explicit perfor-
                           mance constraints. In light of the need to link fan-out to some measure of
                           performance, as well as the inevitability of wait times introduced by human
                           interaction, we propose that instead of a simple maximum limit prediction,
                           we should instead find the optimal number of UAVs such that the mission
                           performance is maximized.


                           3.4 The Overall Cost Function
                           Maximizing UAV mission performance is achieved when the overall per-
                           formance of all of the vehicles, or the team performance, is maximized.
                           Consider multiple UAVs that need to visit multiple targets, either for destruc-
                           tion (SEAD missions as discussed previously) or imaging (typical of Intelli-
                           gence, Search, and Reconnaissance (ISR) missions). A possible cost function
                           is expressed in (4):

                                      C = Total Fuel Cost + Total Cost of Missed Targets
                                          +Total Operational Cost                           (4)

                              Total Fuel Cost is the amount of fuel spent by all the vehicles for the
                           duration of the mission multiplied by the cost of consuming that fuel. The
                           Total Cost of Missed Targets is the number of targets not eliminated by
                           any of the UAVs multiplied by the cost of missing a single target. The
                           Total Operational Cost is the total operation time for the mission multiplied
                           by some operational cost per time unit, which would include costs such as
                           maintenance and ground station operation costs. This more detailed cost func-
                           tion is given in (5).
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