Figures 5-5 and 5-6 plot the eect of varying the relative costs of the two replicated tasks, nd-locations and report-progress, on the average energy required to perform the mission for each of the four experimental setups, using the energy function, mis-sion energy(vermis-sion), dened in equations 5.1 and 5.2. In the case of nd-locations,
1.0 0.8
0.6 0.4
0.2 0.0
2 Robots, no awareness 2 or 3 Robots, full awareness
Relative Cost of find-locations
Percent reduction in avg. energy required per mission
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Figure 5-5: This graph shows the percentage reduction in average energy required as a function of the relativend-locations cost. Here, the worst energy performance is the baseline case with three robots and no awareness. The percent reduction in average energy required to complete the mission from this baseline case for the remaining three experimental versions is shown.
the worst version is the three-robot team with no awareness of the actions of the other robots. The two-robot team with no awareness performs from 1% to 31% bet-ter than the three-robot/no-awareness version (depending upon the relative cost of nd-locations), while both the two-robot team and the three-robot team with full awareness performed from 2% to 62% better than the worst case.
In the case of report-progress, the worst versions were both the two- and three-robot teams with no awareness. Performing from 2% to 29% better was the two-three-robot team with full awareness, while the three-robot team with awareness performed from 3% to 51% better (again, depending upon the relative cost of report-progress).
As expected, the team performance improves with awareness, regardless of the task coverage aorded by the robot team | that is, regardless of the redundancy in robot capabilities for each task | because replication of actions is prevented. We also observe that for any level of team redundancy, the degree of improvement with awareness increases as the relative cost of the redundant action increases. This, too, is expected, since the energy saved with awareness is a direct function of the energy required to perform the redundant action.
Two additional points are interesting to note:
5.2. THE IMPORTANCEOF ROBOTAWARENESS 141
1.0 0.8
0.6 0.4
0.2 00.0
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2 Robots, full awareness 3 Robots, full awareness
Relative Cost of report-progress
Percent reduction in avg. energy required per mission
Figure 5-6: Of the 4 experimental versions for the hazardous waste cleanup mission, the ones requiring the most average energy to complete the mission are the situations involving no awareness of the actions of the other robots; both of these baseline cases require the same average energy to complete the mission. The percentage reduction in average energy required to complete the mission from these baseline cases is shown as a function of the relative energy cost of the report-progresstask.
In the case of the nd-locations task, the energy performance of the two-robot team without awareness (version III) was better than the three-robot team without awareness (version IV), whereas for thereport-progresstask, the energy performances of these two teams were identical. In other words, the energy required to perform thend-locations task without awareness is multiplied by a factor ofn (the number of robots on the team), whereas the energy required to perform the report-progresstask without awareness is proportional only to the number of spill object moves of the mission.
In the case of the report-progress task, the energy performance of the three-robot team with awareness (version II) was better than the two-three-robot team with awareness (version I), whereas in the nd-locations task, the energy per-formances of these two teams were identical. In other words, the energy re-quirement of thend-locations task with awareness is xed, whereas the energy requirement of the report-progress task with awareness is proportional to the number of spill objects moves divided byn (the number of robots on the team).
The rst situation occurs because of dierences in the extent to which the eect of the actions of other robots can be sensed through the world. In this situation, both teams lack awareness of the actions of other robots. The tasks that they might replicate due to this lack of awareness are thend-locations task and several instances of the report-progress task. Although neither of these task eects can be sensed through the world by this team, thereport-progresstask is closely tied to the move-spill task which is detectable through the world. Since the only time a robot tries to initiate the report-progress task is after it has completed the transport of a spill object to the goal, and since there are a xed number of spill objects to be moved, the question of whether to report the progress only arises a xed number of times for the team as a whole. Also, since the time required for one robot to nd and move a spill object (see gure 5-3) is approximately the same as the time allowed between progress reports, robots in both versions III and IV are motivated to report their progress almost every time that they deliver a spill object4. Thus, regardless of whether the team consists of two or of three robots without awareness, the report-progress behavior set is activated a xed number of times, which means that the energy requirements remain the same.
On the other hand, thend-locations task, whose eects cannot be sensed through the world, is replicated by each robot on the team having the ability to perform that task, which means that as redundancy across robots increases, so does the energy usage. The lesson from this rst situation, then, is that in the absence of robot
4For experimental versions III and IV, the actual percentage of progress reports per move of a spill object is about 86% (see gure 5-4).
5.2. THE IMPORTANCEOF ROBOTAWARENESS 143 awareness, redundancy across robots is detrimental for those redundant robot tasks whose eects cannot be sensed through the world.
The second situation observed from gures 5-5 and 5-6 arises due to dierences in the required number of instances of tasks and how well those instances can be distributed across the robot team. In this situation, both robot teams in question (versions I and II) have full awareness of the actions of other robots. The dierences lie in the number of instances required by the hazardous waste cleanup mission of the nd-locationstask versus thereport-progresstask and how well they can be distributed across robots. While only a single instance of thend-locations task is required, up to 8 instances of thereport-progresstask are necessary to completethe mission. Although each instance of these tasks can be distributed to any robot team member with the required capabilities, no single instance can be broken down into parts to be shared by more than one robot. Thus, in the case of the one required instance of the nd-locations task, once one of the robots has selected that action, the other robots have to just wait patiently for the rst robot to nish that action (of course, another robot may take over the task due to failure by the rst robot, but that is another issue). In this case, an increased degree of redundancy across the team for this action does not provide any advantage, and so the performance of the two-robot team is not dierent from that of the three-robot team when both have awareness.
The benet provided by the three-robot team over the two-robot team (both with full awareness) in the case of thereport-progresstask is obtained via a reduction in the required number of instances of the task. Since the three-robot team can complete the xed amount of spill-moving required by the mission faster than the two-robot team, the time required to complete the mission is shortened. This is turn leads to a reduction in the number of progress reports required by the mission, which leads to less work for each robot to obtain the proper number of reports. Thus, the lesson learned here is that increased redundancy of robot capabilities in the presence of full robot awareness helps when the mission requires several instances of tasks that can be distributed across the robot team; it does not help, however, for single instances of tasks that cannot be shared.