Defining the Performance Measures and Comparing the Transfer Algorithms

the Transfer Algorithms

It is desired to test the effect of both the switching method and the shooting method when applied to the target tracking example described in 2.5, where a UAV is trans- ferring to an optimal circular tracking path. To do this two performance measures are introduced denoting the probability of the target tracking the UAV, Equation5.14, and the probability of the UAV tracking the target, Equation5.15.

ρtarget_vis = Σ∆t see target T (5.14) ρUAV vis = Σ∆tsee UAV T (5.15)

The target tracking mission in question is already designed to optimise these visibility indices through its placement of the tracking circle and therefore these are not directly controlled by the transferring path planner. These indices however are only at their optimal state when the UAV is actually flying the final circular path. During the transfer there is no direct control of the visibility indexes but depending on where the UAV is located and how it is flying the values of the indices will change. The desired outcome is to maximise Equation5.15while minimising Equation5.14even while transferring so

that the UAV can potentially begin tracking the target before it reaches the tracking path. As the UAV gets closer to the tracking circle these indices will approach their optimal values. It is also at this point where the switching method could have most effect as being able to react to target motion during a path update could provide a beneficial change in these indices over the shooting method.

Using these visibility indexes a simulation was run to analyse the probability differences between the switching and shooting methods to test if providing mission information had an effect. The algorithm is set up so that the UAV calculates a path update every 10 seconds assuming that the target has randomly moved and the target tracking circle has therefore been updated. Each run lasts a total of 100 seconds or 10 path updates with visibility information for each second stored for use in calculating the visibility indices. One thousand runs for each method was completed with each method utilising the same random path information to provide a direct comparison. Figure 5.5 shows the comparison between the switching and shooting methods, it can be seen that there is no significant difference in the visibility indexes.

0 0.2 0.4 0.6 0.8 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

ρ

ρ

Non Switcher Data Switcher Data

Figure 5.5: Comparison of Visibility Index of the Switching and Non Switching Cost

Functions

This result indicates that the switching method is for the majority of the time activating the minimum distance cost which is the same cost utilised by the shooting method. There is some discrepancy between results indicating that the remaining switching states are activated on occasion but not enough to impact the visibility indexes significantly. When investigating the histogram plots. Figure5.6and Figure 5.7, for ρUAV

vis for both methods

it can also be seen that the number of paths that have greater than 60% probability of the UAV viewing the target during the transfer is higher for the non switching method.

This indicates that the non switching method is able to get the UAV closer to the final circular path than the Switching method. Therefore not only is the Shooting method the algorithm that is most used, it is also capable of manoeuvring the UAV closer to its intended destination. 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 120 140 160 180

ρ

Values >60% = 301

Figure 5.6: Histogram plot for the value ofρUAVvis for the non switching method

0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 120 140 160 180

ρ

Values >60% = 278

5.4

Summary

A switching algorithm was developed to provide more flexibility in the transfer paths for a target tracking mission. Using key visibility indexes the transfer paths for the switcher were compared against the singular cost function transfer paths. The results indicated no significant difference in the visibility indexes for either method. Given that one of the switching modes was the singular cost function it is clear that during the transfer operation the UAV spends the majority of its time utilising the singular cost function to produce paths, and that adding flexibility to the path planning effort by providing more cost function choice yields no significant effect on the target tracking mission being carried out. In addition it was also seen that the single cost function path produced a higher number of results with greater than 60% visibility index indicating that this method was also able to move the UAV closer to the desired target tracking path that the switching method. These result further validate the single cost functions developed in Chapter 3and its suitability for the target tracking mission posed.

Conclusions and Further Work