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Figure 4-15 shows the required battery energy profile over the same time span, also with a blue dashed line. Note that the re-plan still enables the robot to start from an empty battery. However, well in advance of nightfall, the plan requires a steady increase in battery charge to generate reserves for the night. The battery energy requirement falls overnight - the morning sun is sufficient to charge the battery to the required Goal 2 level.
Standard path planners like A* or D* do not adequately address the problem presented in this example. While A* can efficiently find a path to avoid terrain obstacles, and D* is able to re-plan efficiently to avoid unexpectedly difficult terrain, neither is able to anticipate the need to charge in advance of nightfall. Depending on the actual initial battery state-of-charge of the rover, following a plan that ignores energy could have disastrous consequences. The example can be extrapolated to the consideration of other resources, which might also be critical to data quality, time efficiency or rover survival.
MISSION-DIRECTED PATH PLANNING.
Figure 4-15: Battery Energy Requirement vs. Time: The initial plan enables the rover to start from total battery discharge to reach to the goal charge level. The detour from the re-plan requires the rover to perform stationary charging to nearly full capacity in anticipation of the nighttime hibernation. Note the similarity between the re-plan profile in the morning after hibernation and the original plan profile.
4.7 Discussion This chapter presents an approach to mission-directed path planning that displays elements of the five attributes listed in Chapter 1. It displays over-the-horizon foresight by considering large-scale terrain beyond the view of the robot in planning. It exhibits temporal and resource cognizance through a consideration of time and energy variables in the state space, and in the enforcement of resource capacity constraints through ISE global constraint planning. It demonstrates an ability to handle some degree of uncertainty by enabling efficient re-planning in response to state and model updates. And the approach directs its focus to the mission objectives in terms of achieving goals, accommodating goal action requirements and respecting constraints on activities.
The example in simulation highlights how TEMPEST coordinates route, timing and battery energy to achieve multiple goals. Unlike many approaches to temporal planning, TEMPEST approaches the problem as a whole rather than by a simpler, but sub-optimal, hierarchical breakdown. Incorporating this strategic planning capability into a rover could provide a significant boost to rover safety, mission time efficiency and reliability. Specifically, TEMPEST
MISSION-DIRECTED PATH PLANNING FOR PLANETARY ROVER EXPLORATION
enabled a contingency plan that became necessary once the robot detected that its original route was not feasible.
Where a rover employing traditional techniques would have had to suspend its operations to wait for further instructions from human operators, the simulated robot was able to re-specify its route and schedule to achieve the originally-stated objectives.
The examples in this thesis all deal with problems combining space, time and energy. Other factors are important to planetary surface exploration and might be considered under the TEMPEST approach. Rover health, limited by rough driving, extended exposure to dust, or thermal cycling, could be treated as a resource. One or more rover auxiliary health variables could be added to a model. The state transition function, as derived from the World Model and Rover Model, could describe the effect of activities on vehicle health. Greater mechanical damage might be sustained in areas of rough terrain or on steep slopes. Dust might accumulate on solar arrays as a function of time1, and, if represented as a DPARMS state variable, could adversely affect the collection of solar energy. The transition function could model the change in temperature of certain components as a function of activity level, sun exposure and material properties. Thermal cycles of sufficient size might accumulate in another counter variable. TEMPEST could plan paths that prevent vehicle health variables from dropping below minimum tolerable lower bounds. Alternatively, one type of vehicle damage cost could be minimized over a path, while meeting constraints on other variables and mission goals.
Data from science and exploration activities might also be considered a resource. Data transmitted to Earth might be a resource to maximize. Completion of goal activities could add data to vehicle memory. Limitations in the size of memory could limit the data stored aboard the rover. Communications activities could downlink data to Earth, at a maximum data rate, to achieve greater overall reward. Downlink could only happen when in view of Earth or an orbiting relay spacecraft.
1. However, a monotonic increase in dust is probably inappropriate for Mars. Both Spirit and Opportunity experienced several events that removed a substantial layer of dust from their arrays, presumably from Martian “dust devils.”
MISSION-DIRECTED PATH PLANNING
5. Sun-Synchronous Navigation Sun-synchronous navigation is a promising strategy for rover-based planetary exploration in polar environments. It entails synchronizing a robot’s route and timing with the motion of the sun to provide continual solar energy while maintaining a benign thermal environment. In 2001, the Sun-Synchronous Navigation project built a solar-powered rover, Hyperion, and software to achieve semi-autonomous sun-synchronous navigation, and tested the combined system in planetary-relevant polar terrain on Devon Island in the Canadian Arctic. A significant outcome of that research effort was the first version of TEMPEST, tailored specifically for sun-synchronous route planning. As a background to the development and testing of TEMPEST, this chapter begins by describing the sun-synchronous navigation strategy and provides an overview of the field experiment, the rover Hyperion, and its software architecture.
Several following sections then describe the planning approach used, and provide experimental results from the Arctic field experiment.
Figure 5-1: Hyperion Rover: Sun-synchronous navigation enabled solar powered travel over kilometers without the added complication and mass of a gimbal mechanism.
5.1 The Polar Navigation Problem The idea for sun-synchronous navigation emerged from mission design studies in the context of lunar polar exploration. The Moon’s axis of rotation is oriented just 1.53 ° from perpendicular to the ecliptic plane, the plane of the Earth’s orbit about the Sun . Therefore, directly at either of the lunar poles, the maximum sun elevation angle ever achieved is 1.53 °. In the summer months, as on Earth’s poles, the sun remains above the horizon continually, albeit only above the lunar “arctic circles” at 88.47 ° latitude, within just 46 km from the poles. But with such lowskimming sun angles, terrain features cause extensive shadows, decreasing the effectiveness of solar-powered operations. Furthermore, without an atmosphere, the thermal contrast between sunlit and shadowed conditions is drastic.
Figure 5-2: Lunar Sun Elevation Angle Variations for Polar and Sub-Polar Positions. At mid-summer at a pole (a), the sun remains above the horizon at a roughly constant angle. Below the arctic circle, the sun elevation oscillates between a maximum elevation (b) above the horizon and a minimum elevation (c) below the horizon.
One might suspect that moving slightly away from the poles would improve sunlight exposure. Figure 5-2 is a diagram showing sun elevation angles for polar and sub-polar positions. It depicts the Moon’s axis of rotation ω and observing positions with surface normals n, which coincide with the zenith vectors. Directly at a lunar pole in summer, the sun elevation is roughly constant, inscribing a “halo” in the lunar sky, just above the horizon, whose center is at zenith (Figure 5-2a). Moving away from the poles to lower latitudes, the zenith vector oscillates around the pole, nodding towards and away from the sun. The center of the “halo” inscribed by the sun in the lunar sky tilts a corresponding angle from the zenith, causing the sun elevation to oscillate between a minimum value at local midnight and a maximum value at local noon. At the arctic circle, the sun meets the horizon at its lowest point in the sky, and past the arctic circle towards the equator, the sun dips below the horizon for some portion of each lunar rotation (Figure 5c). Meanwhile, with increasing distance from the pole, the peak elevation continues to increase (Figure 5-2b). So, by moving from the pole, sun angles get better and worse from a solar power standpoint - higher mid-day sun angles mean terrain will cause fewer shadows, but nightfall becomes inevitable. At first glance, it might seem that the only feasible surface exploration strategy would employ a rover with the means of surviving the extreme thermal range of lunar day and night. Closer analysis shows this is not the case.
MISSION-DIRECTED PATH PLANNING FOR PLANETARY ROVER EXPLORATION
5.2 Navigation Strategy An alternate strategy avoids nightfall by circumnavigating the pole. By travelling in a direction opposite lunar rotation, synchronized with the sun, a vehicle could maintain day conditions as in Figure 5-2b for months at a time. The selected latitude of travel must balance at least three competing pressures: to maintain higher solar elevation angles to minimize shadowing for solar energy and to keep the rover warm; to prevent the rover from overheating; and to reduce the circumpolar distance to enable the traverse at reasonable speeds. Surprisingly, the length of the lunar day and small diameter the Moon result in a required average speed of 0.37 m/s at a constant latitude of 5 ° 1. The high available solar energy, unattenuated by an atmosphere, provides ample power for locomotion and other activities.
The combination of long day, low radius and high solar energy is even better on Mercury .
The advantages sun-synchronous navigation are significant. Staying in sunlight means a rover can rely entirely on solar energy - the technical, economic and political challenges of using radioisotope power sources can be prohibitive. Maintaining a consistent solar geometry also simplifies the vehicle design. Solar arrays can be pointed in a fixed direction on the rover, removing the need for complex and heavy gimbal mechanisms. A vehicle can be designed for a narrower range of operating temperatures, and thermal radiators can be pointed in a direction opposite the sun to improve radiation efficiency. Consistent light simplifies navigation using optical cameras. Of course, circumnavigating a polar region of a planet or moon presents other enormous challenges - among them, vehicle endurance to enable hundreds or thousands of kilometers of travel, and reliable rover autonomy software to sustain travel during periods out of view of Earth (for the Moon), or too distant to enable real-time control from Earth (Mercury).
However, a scaled-down version of sun-synchronous navigation improves solar-powered polar exploration over a regional, rather than global scale. Poleward of the arctic circles of Earth and Mars, a rover could follow path circuits in an area of scientific interest, and synchronize its travel with the sun. During summer months, falling prey to nightfall is no longer a danger, but the problems of power management and thermal regulation remain. Without the requirement to circumnavigate the pole, the vehicle endurance issues diminish substantially. Sun-synchronous navigation over a region simplifies solar geometry, enabling a simpler rover design, and provides access to areas that can be circumnavigated with cyclic paths.
A key challenge in enabling access to regions of terrain is to ensure that paths are repeatable. Under solar power with re-chargeable batteries, a sun-synchronous route must charge the batteries to at least the minimum required level to execute the next day’s route. Ideally, a rover would follow a circular route, and point its solar array continually toward the sun (see Figure 5-3). In the diagram, the array points radially outward to avoid shadows cast by centrallylocated features. As the Earth rotates, the vehicle orientation rotates a corresponding amount by following the path
1. Of course this speed ignores the increase in path length required to avoid the massive terrain obstacles known to be prevalent near the lunar poles.
SUN-SYNCHRONOUS NAVIGATIONarc. As long as the charge rate from solar power equals or exceeds the power consumed through driving and other operations, the batteries will remain sufficiently charged.
This idealized model is flawed in several ways. First, it is undesirable to force the vehicle to remain in motion - scientific measurements often entail extended contact with rocks or soil, or require a very stable platform. Second, vehicle power loads may outweigh available solar power, forcing periodic periods of stationary battery charging, with corresponding reduction in circuit path length. Third, medium and large-scale terrain will significantly divert a rover from a circular path.
These added complications make planning sun-synchronous routes a difficult task for humans. The objective of an automated sun-synchronous navigation planner is to take these complications into account, and still produce plans that can be repeated over much of a summer season.
5.3 Field Experiment The Sun-Synchronous Navigation project explored a range of issues surrounding the regional variant of the sun-synchronous strategy described above, from robot mechanical and power system design to automated planning and execution software. Of greatest importance, the project sought to perform tests with a real robot executing sunsynchronous paths in a planetary-relevant polar environment on Earth.
MISSION-DIRECTED PATH PLANNING FOR PLANETARY ROVER EXPLORATION