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«The Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 May 13, 2005 Submitted in partial fulfillment of the requirements for the ...»

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Planetary motion defines the gross schedule for daylight, solar flux and opportunities for communications downlinks to Earth. Exposure to the Earth or the sun is governed by whether line-of-sight visibility exists between the surface position and the source object. Lighting and communications shadows cast by large terrain features (mentioned in Section 4.1.1) vary with time. At a fixed position, shadow and sunlight schedules vary little day to day, and can be


captured in a simple model that repeats. Since shadowing is a localized phenomenon, the schedule of lighting and shadow will not be repeatable for a rover that moves sufficiently far. Line-of-sight visibility to an orbiting communications relay is further complicated by the spacecraft’s own motion. Consequently, the ephemerides for orbiting communications spacecraft may change dramatically opportunity to opportunity, even for a stationary vehicle. Therefore, planning for communications visibility must capture position and time dependencies. Predicting the ephemerides of the sun, Earth and orbiting relay spacecraft, and to determine whether they are shadowed or visible at specific times is critical in selecting routes that provide sufficient energy or enable communications at particular points in the path.

A mission-directed path planner must also ensure that paths obey navigational and other operational constraints.

Many of these are time-dependent. A mission might dictate geometric constraints on activities, where the geometry is time-varying. As an example, consider stereo vision for autonomous navigation. Stereo vision is strongly affected by lighting levels. Glinting sunlight on camera lenses and entry of the solar disk into the camera field of view causes “phantom obstacles” to be generated in depth maps, or causes the rover to be blinded. To prevent glinting and blinding, locomotion actions might be disallowed when the sun is within a specified angle from the camera boresight.

Assuming the cameras point at or below horizontal, driving would be prevented in certain directions in the morning and evening, but would be unconstrained during midday. Restricting photographic measurements to times when the sun is shining on the desired target is a second example of a constraint on time-varying geometry. Operational constraints may also be purely temporal. A communications downlink to Earth might be geometrically feasible over a range of times, but operationally feasible only over a shorter time window allocated to the mission. Low power, low activity phases like hibernation might only be allowed during nighttime.

A central theme of this work is the modeling and long-distance path planning in the presence of time-dependent effects, time-varying geometry, and variability of traverse speed as a function of terrain or other effects.

4.1.3 Resource Planning A central problem of mission planning is ensuring the availability of resources for activities. A resource is a quantity that must be expended to achieve goals, but that is in limited supply. There are different types of resources. Metric resources are storable quantities, for example time, energy or fuel, that are expended through activities that require the resource. From a planning perspective, metric resources can also be more abstract - the finite lifetime of a motor, or the temperature margin on a thermally-sensitive instrument. Metric resources further subdivide into monotonic resources and non-monotonic resources. Monotonic resources can only be expended; non-monotonic resources can also be replenished through collection activities. Metric resources are described by continuous, real-valued variables.

Unit resources describe components that are fully committed during an activity and become uncommitted at the termination of the activity. These are described by Boolean variables describing either commitment or availability, as in a camera or a motor. This research addresses metric resources and not unit resources.


Metric resources are a critical factor in planning paths in the mission context. Without the required energy, a vehicle cannot perform its primary activities. The route a vehicle follows from place to place has a substantial effect on both the expense and collection of resources. Contrary to the assumption of many simple path planners, the shortest route is not necessarily the least costly. Steep, soft, slippery or rocky terrain requires more power than level, firm and flat terrain. For vehicles that collect resources like solar energy from the environment, the choice of path can dramatically influence the available resource levels. All other parameters being equal, a path in shadow cannot yield the same energy as a path that is fully exposed to the sun.

A mission-directed planner must, at minimum, guarantee satisfactory resources for desired mission activities, and may also provide a plan that is optimal in terms of resources. It must consider the balance between resource consumption and collection, and, based upon specified activity models and stated requirements, provide the necessary resources at all phases of the plan. Another focus of this work is to enable metric resource planning to achieve satisfactory or optimal energy profiles in the context of planetary mission exploration.

–  –  –

4.1.4 Coupling of Variables The effects of terrain, time, resources and mission return are highly interwoven. None can be considered in isolation from the others. The diagram in Figure 4-1 illustrates some of the common interrelationships in surface mission operations. Terrain affects the speed of travel and causes vehicle wear. It also causes shadowing of sunlight and communications. Sunlight provides solar energy for battery charging, and enables imagery for navigation and science, but also causes thermal cycling and resulting wear on the vehicle. The mission objectives, science and exploration activities, are supported by battery charge and constrained by vehicle wear. Once data has been collected, communications with Earth enables its transfer to an operations team. Therefore, to achieve the ultimate objective of


retrieving data from the robot, mission planning must consider a variety of factors in concert. The challenge for automated planning research is to provide a method for solving this problem in a computationally practical way.

4.2 TEMPEST TEMPEST (TEmporal Mission Planner for the Exploration of Shadowed Terrain) is a path planner designed for mission-directed reasoning. It combines five models that define the relevant features of the mission-directed planning domain, and uses the Incremental Search Engine (ISE) to search for plans that achieve mission objectives while satisfying operational constraints (see Figure 4-2). The following sections describe the TEMPEST models, and explain how they collectively contribute to the more formally-defined functions required by ISE.

–  –  –

Mission-directed path planning must consider the interactions between several elements:

• Planetary environment through which a path must be planned

• Robotic vehicle that is operating

–  –  –

• Actions the vehicle can take that are relevant to the problem

• Physical and operational constraints on the available actions

• Mission objectives TEMPEST composes five models corresponding the above elements. A World Model captures relevant environmental phenomena for the planetary surface; a Rover Model describes relevant components of the vehicle operating in the planetary environment; an Action Set comprises the activities the vehicle can execute to traverse across terrain, maintain resources, and achieve mission objectives, and the effect they have on vehicle state; a Constraint Set imposes restrictions on the available actions, in terms of the state of the World Model and Rover Model; and finally, a Mission Specification describes the initial state of the vehicle, the immediate goals of the mission, and the specific actions and conditions under which the goals can be satisfied.

The models must be tailored to the planning problem to encompass all of the desired rover-environment-mission interactions. However, as stated earlier, it is not computationally practical to represent the domain at high resolution when plans are intended to span kilometers and tens of hours. Hence, the models are purposely coarse. They provide reasonable projections of action outcomes under various environmental conditions, but at a resolution that permits sufficiently high performance on a rover processor. Each of these models is described in greater detail in Sections 4.2.1 through 4.2.5.

The models are the foundation for defining the ISE state space, the start and goals, transition arcs between states, and the constraints on them. Section 4.2.6 briefly describes how model information is used to define these ISE domain components.

4.2.1 World Model A model of the planetary environment is fundamental in producing plans that avoid hazardous terrain, consider sunlight exposure and follow the most time and energy efficient routes. The World Model captures the relevant features of the planet environment in which a vehicle operates. It is one of two basis models for defining the state space, for computing arc transition costs and for determining the conditions under which constraints are satisfied or violated.

To reflect local conditions defined by the underlying models, the World Model is set to a particular state, defined by a position on a planetary surface, time and surface orientation. With each update to the state, the World Model calls on its underlying components to compute the local conditions. It currently includes, but is not limited to, the following



Geodetic Reference - All maps in the World Model are referenced to a geodetic reference, a reference biaxial ellipsoid (ellipsoid of rotation) that approximates the shape of the planetary body, from which transformations between

coordinate frames can be defined [7]. The coordinate frames that apply to all maps are:

• Planet Cartesian: a frame whose origin is at the center of the reference ellipsoid, and whose axes are defined by

the following:

- X : in the plane of the equator of the reference ellipsoid, and in the plane of the prime meridian of the system.

- Z : the axis of symmetry of the ellipsoid, and parallel to the axis of rotation of the planetary body.

- Y = Z × X to make a right-handed frame.

• Geodetic: a system comprising latitude, longitude and altitude. The geodetic system has two variants, based loosely on the NASA Planetary Data System convention [27], planetocentric and planetographic. In the World

Model, they are defined as follows:


- Latitude:

- Longitude:

- Altitude:


- Latitude:

- Longitude:

- Altitude:

• Topocentric: a Cartesian frame whose origin is a point on the planetary surface. Its axes are defined as follows:

- X : in the plane tangent to the surface of the reference ellipsoid, in the direction of constant latitude East.

- Z : the reference ellipsoid surface normal.

- Y = Z × X such that Y points North along a meridian.

Elevation Map - A map of the operations area encodes elevations, above the reference ellipsoid, in a two-dimensional grid of positions. Spatial resolutions for this data are typically 10-30 meters per pixel, far larger than the vehicle footprint. Though the model allows smaller ratios of map pixel to vehicle size, a high ratio preserves the assumption that vehicle turning radius is insignificant with respect to cell size. The elevation map also computes vectors between points on the map.

Slope Map - The World Model derives slope and slope aspect from the elevation map, and encodes each quantity at the same spatial resolution as in the elevation map. In addition, the slope map computes the transformations between

the topocentric frame and two other frames:

• Gradient: a frame whose origin coincides with the origin of the topocentric frame, and whose axes are defined


- X : in the plane of the local terrain surface, in the direction of steepest ascent (gradient).

- Z : the terrain surface normal.

- Y = Z × X to make a right-handed frame.

–  –  –

• Pointing: a frame that describes the orientation of an object on the terrain surface. Its origin coincides with that of

the gradient and topocentric frames, but its axes are defined by:

- X : in the plane of the local terrain surface, at an arbitrary angle from the direction of steepest ascent.

- Z : the terrain surface normal.

- Y = Z × X to make a right-handed frame.

Ephemeris - The ephemeris model predicts the vector of source bodies in the planet Cartesian frame of an observing body at a particular time. The ephemeris model uses CSPICE, ephemeris generation software that provides relative position and orientation for all major bodies in the Solar System [1]. In counterpoint to the guiding principle of coarse modeling, CSPICE is a very accurate tool, accounting for speed-of-light delays and stellar aberration in determining a body’s apparent location. The ephemeris time standard - barycentric dynamical time - is the basis time reference in the World Model.

Figure 4-3: Example LOS map for sunlight on natural terrain, in this case a system of canyons exposed to the sun from the direction of the top of the image.

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