«The Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 May 13, 2005 Submitted in partial fulfillment of the requirements for the ...»
The rover start and final goal position is located at the point labeled Return To Start at the southeast (bottom right) of the plot. The plan follows the circuit in a clockwise direction to match the motion of the sun in the sky, for a total planned distance of 5.6 km.
Figure 5-6 plots Experiment 1 results versus Universal Coordinated Time (UTC). Given the longitude of the test site, the local time is computed by subtracting 6 hours from the UTC time. Figure 5-6a) is a plot of progress distance, mimicking the sequential planning diagrams in Figure 4-8. The dashed line to the left of the figure is the line of fastest approach, whose slope is v max = D map ⁄ ∆T min (see Section 4.5 for definitions). It emerges from the opening of the start time interval, and denotes the earliest reachable portion of the state space. Meanwhile, the dashed line to the right of the figure is the line of minimum allowable rover speed. Since the goals for these experiments were Via Point
The labeled points indicate the planned arrival time at each goal Via Point, and their cumulative radial distance ρ from the start position, through all earlier goals. The solid trace through the goals is the progress distance of the plan versus time. One immediately sees that the average speed of the plan, as denoted by the average slope, is slower than both the fastest possible approach line and the slowest allowable approach line. By multiplying the duration factors listed in Table 5-2, one computes the overall duration factor to be 1.337, larger than the factor imposed on the slowest allowable approach line. One also observes that the major component of this increase is the loiter factor. The Experiment 1 plan included 13 Charge actions. At 20 minutes each, stationary activities account for over 4 hours of the plan.
Figure 5-6b) displays the Experiment 1 minimum required battery energy predicted by TEMPEST, on the same time scale. The target end-of-traverse battery charge was set at 194 W-hr (700 kJ). Observe that, with exception to the final ascent to the goal battery state-of-charge, the plan maintains the required battery energy well below the maximum battery capacity of 250 W-hr, shown by the upper limit of the error bars. The peaks in the energy curve correspond to conditions following Charge actions, and anticipate the times of greater energy demand in the plan. The final ascent of the curve at the end of the plan meets the demand placed at the final Via Point goal - to achieve an energy of 194 W-hr. The prominence of the final goal energy requirement relative to the rest of the plan indicates that it was set too conservatively to enable the route to be repeated on successive days. In theory, the final goal energy could have been set to the required energy at the start of the plan.
What explains the peaks and troughs of energy demand earlier in the plan? To answer this question, we examine the time-varying lighting and the solar array sun angles imposed by the plan. The five frames of Figure 5-7 depict snapshots of the planned route, the projected lighting on the terrain, and the sun and solar array orientations at various times for Experiment 1. The varying shading of the background reflects the changing average sun angle of incidence on the terrain, from just before local noon in Figure 5-7a to roughly one hour before local midnight in Figure 5-7d.
Predicted shadows appear as black regions in Figure 5-7d. Vectors representing the sun direction and solar array normal emanate from the rover position in each frame. Note that the solar array normal points 90 degrees to the left of the driving direction, as it does for Hyperion (see Figure 5-1).
SUN-SYNCHRONOUS NAVIGATIONtively. The histogram indicates that over 32% of the route was spent within 10 degrees of optimal solar array pointing. We attribute the bias in sun angles toward the aft of the rover to the Get Earliest Start Time Path heuristic (see Section 5.4). Following the application of energy-based heuristics, TEMPEST selects the earliest path opportunity.
For clockwise paths in the northern hemisphere, earlier opportunities will bias sun angles aft, as the Earth has not progressed as far in its daily rotation.
The second histogram, in Figure 5-8b, depicts the same quantities for the executed Experiment 1. Qualitatively, one can immediately see the similarities between the profiles, indicating integrity of the execution to the mission plan.
Given how closely the plan was followed during execution, differences in these profiles are likely due to off-pointing that occurred during actions taken by the Local Navigator to avoid obstacles .
5.5.2 Execution The Experiment 1 mission execution proceeded smoothly over entire the 24 hour test. Because the nominal rover speed given to TEMPEST for planning was so conservative (8 cm/s as compared to 30 cm/s), Hyperion typically completed each Drive action well in advance anticipated by the plan. However, to keep on schedule, human controllers refrained from sending the next Drive action target until the start time specified in the plan. Therefore, the motion of the rover was uniform, but rather alternated between its top speed of 30 cm/s and rest at each of the Drive action goals. Figure 5-9 shows the Experiment 1 executed progress distance as a function of time, compared to the plan. With exception for a few delays, the executed rate of progress matched the plan very closely.
Figure 5-9: Experiment 1 Executed Progress Distance: Execution followed the plan very closely Perhaps the best measure of success is in how successfully the plan enabled battery charge management. Due to high noise levels in current measurements recorded on Hyperion during the experiments, the battery charge could not be estimated. However, battery voltage provides an indirect measure of whether the battery is charged or is approaching discharge. Battery voltage should remain roughly constant over a wide range of charge states, but will begin to drop
SUN-SYNCHRONOUS NAVIGATIONas the battery becomes low on charge. The battery voltages plotted in Figure 5-10 show that the plan maintained the battery potential near the nominal 24 Volts for the entire 24-hour mission.
Though Experiment 1 proved the feasibility of the sun-synchronous navigation strategy, it did not prove whether the strategy provided any substantial benefit above more standard navigation approaches. Unintentionally, Experiment 2 provided strong evidence that sun-synchronous navigation, and TEMPEST, were essential in sustaining the rover over an extended traverse.
5.6 Experiment 2 Results Table 5-3 summarizes the results for Experiment 2, whose planned route is superimposed on a terrain contour map in Figure 5-11. In contrast to Experiment 1, the execution of Experiment 2 was fraught with operational difficulties which caused the rover to fall far behind the schedule specified by the plan. The sharp decline in rover performance that occurred as a result of the deviation from the plan schedule clearly showed the sustaining effect of sun-synchro
nous navigation, and of TEMPEST planning. The next subsection analyzes the Experiment 2 plan in detail. The discussion of the Experiment 2 execution follows in a second subsection.
5.6.1 Planning A majority of the southeast portion of the circuit for Experiment 2 followed the route of Experiment 1. However, new Via Point goals directed the route significantly farther west and north, circumnavigating a rocky outcrop informally named “Marine Peak” (see the topographic feature to the East of Via Points 9, 10 and 11 in Figure 5-11). The Via Points were placed at an average distance of 249 meters. This route, at 8.4 km, was substantially more ambitious given the success of the first experiment. To enable a plan this long, the average drive speed used in planning Experiment 2 was 11 cm/s, or 400 m/hr, only 37% of the maximum speed, but 39% faster than for Experiment 1.
Figure 5-12 plots Experiment 2 results versus Universal Coordinated Time (UTC). Recall that the local time is computed by subtracting 6 hours from the UTC time. Figure 5-12a) is a plot of progress distance. As in Figure 5-6a, it shows the dashed lines representing the earliest possible approach and latest allowable approach. The lines originate at the open and close of the 24-hour start time interval, respectively. Also as in Experiment 1, the worst-case time increase factor ( ˜ R ˜ A ˜ L ) was set to 1.265. The actual duration increase factor, computed as the multiplication of f R, fff f A, and f L as listed in Table 5-3, was 1.342, very similar to the factor from Experiment 1. However, the avoidance factor from Experiment 2 was noticeably higher, and the loiter factor, noticeably less. Though the specific reason for greater avoidance is not obvious, the reduction in loiter factor is the result of a lower number of Charge actions in Experiment 2. Four of twelve Charge actions were designated between Via Points 9 and 13, and account for the reduction in slope in the curve before the plan halfway point.
SUN-SYNCHRONOUS NAVIGATIONFigure 5-11: Experiment 2 Route and Elevation Map: The route starts and ends at the point marked ‘Return To Start’, and traversed a nominal distance of 8.4 km, including a circumnavigation around the terrain feature known informally as Marine Peak at the West end of the route.
Figure 5-12b) displays the corresponding Experiment 2 minimum required battery energy profile. The Mission Specification end-of-traverse battery charge was reduced to 139 W-hr (500 kJ). As before, the plan maintains the minimum energy well below the capacity of the battery, with the exception to the rise to the final goal target. Again, the target energy could have been set far lower (to empty in this case) and still would have allowed sufficient energy in the battery to repeat the route on following days.
Figure 5-12: Experiment 2 Results vs. Time: a) Progress Distance; b) Minimum Required Battery Energy
SUN-SYNCHRONOUS NAVIGATIONCuriously, the greatest demand on battery energy, according to the Experiment 2 plan, occurs on the northwest leg of the plan (between Via Points 7 and 8, or 23:58 to 01:39 UTC) in the position where the energy profile was least demanding for Experiment 1. The least demand on battery energy appears to come between Via Points 15 and 18 (06:27 and 09:25 UTC), also curiously at the place in the route for Experiment 1 that demanded the greatest energy.
5.6.2 Execution The execution of Experiment 2 was repeatedly interrupted near the beginning by communications loss between the operations tent sheltering the human controllers and Hyperion. Since each Drive action target was sent manually over wireless ethernet, communications outages forced the rover to stop moving. Figure 5-13 shows the executed progress distance for Experiment 2. Note that the execution started roughly an hour late. Despite the conservatism in the rover speed assumed in the TEMPEST model (11 cm/s for planning as compared to 30 cm/s maximum speed), the delays eventually caused the robot to fall way behind schedule.
Figure 5-13: Experiment 2 Executed Progress Distance: the most substantial delay put Hyperion behind the plan by several hours, causing significant battery discharge
As time passed, the sun became more and more biased towards the front of the vehicle. During periods of good communications, Hyperion’s stereo cameras became blinded by sunlight, disabling autonomous local navigation. In an effort to keep up with the plan at any cost, human operators decided to teleoperate the vehicle using panoramic imagery produced by Hyperion. Unfortunately, the panoramic imagery was also negatively affected by the sunlight, worsening the already low-resolution images. Finally, teleoperated driving caused the robot to drive into a rock that it was unable to cross. During the struggle to surmount the obstacle, Hyperion’s front axle rotated beyond an angle limit imposed by software. The recovery from this final fault entailed physically moving Hyperion away from the rock and re-starting rover software. At 13 hours into the mission, Hyperion was over 3 hours behind schedule.
Figure 5-14: Experiment 2 Battery Voltages: evidence strongly suggests that falling behind the TEMPEST schedule, which resulted in poor sun angles, caused the substantial battery discharge during the mission.
These successive delays strongly negatively impacted rover power. Each delay caused the sun to be biased to the rover’s front, or even towards the vehicle’s right side (opposite the active side of the solar array). Though operating energy costs (i.e. driving, electronics, etc.) were fairly uniform over the route, the poor sun angles drastically reduced incoming energy to offset those costs. The battery state-of-charge could not be estimated due to high current measurement noise. However, the battery voltages plotted in Figure 5-14 provide a clear measure of Hyperion’s declinSUN-SYNCHRONOUS NAVIGATION ing battery charge. Unlike in Experiment 1, Experiment 2 voltages dip to below the designed bus voltage of 24 Volts, indicating a substantial battery discharge. This dip corresponds in time to the period of greatest delay.
Interestingly, once Hyperion was rescued through a manual intervention, human operators teleoperated the rover at full speed to catch up with the original plan. Human operators were repeatedly forced to command Charge actions to maintain minimum battery charge. Observe in Figure 5-13 how the progress distance trace re-acquires the plan line following the most substantial delay. Meanwhile, the battery voltage in Figure 5-14 climbs back to pre-delay levels in the latter part of the mission.